Fabrice Ardhuin | Ifremer - Academia.edu (original) (raw)
Papers by Fabrice Ardhuin
Journal of Geophysical Research, 2006
1] Waves have many effects on near-surface dynamics: Breaking waves enhance mixing, waves are ass... more 1] Waves have many effects on near-surface dynamics: Breaking waves enhance mixing, waves are associated with a Lagrangian mean drift (the Stokes drift), waves act on the mean flow by creating Langmuir circulations and a return flow opposite to the Stokes drift, and, last but not least, waves modify the atmospheric surface roughness. A realistic ocean model is proposed to embrace all these aspects, focusing on near-surface mixing and surface drift associated with the wind and generated waves. The model is based on the generalized Lagrangian mean that separates the momentum into a wave pseudomomentum and a quasi-Eulerian momentum. A wave spectrum with a reasonably high frequency range is used to compute the Stokes drift. A turbulent closure scheme based on a single evolution equation for the turbulent kinetic energy includes the mixing due to breaking wave effects and wave-turbulence interactions. The roughness length of the closure scheme is adjusted using observations of turbulent kinetic energy near the surface. The model is applied to unstratified and horizontally uniform conditions, showing good agreement with observations of strongly mixed quasi-Eulerian currents near the surface when waves are developed. Model results suggest that a strong surface shear persists in the drift current because of the Stokes drift contribution. In the present model the surface drift only reaches 1.5% of the wind speed. It is argued that stratification and the properties of drifting objects may lead to a supplementary drift as large as 1% of the wind speed. Citation: Rascle, N., F. Ardhuin, and E. A. Terray (2006), Drift and mixing under the ocean surface: A coherent one-dimensional description with application to unstratified conditions,
Ocean Modelling, 2008
Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and curre... more Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and currents below the mixed layer. Drift and mixing are also functions of the surface Stokes drift U ss , volume Stokes transport T S , a wave breaking height scale H swg , and the flux of energy from waves to ocean turbulence Φ oc . Here we describe a global database of these parameters, estimated from a wellvalidated numerical wave model, that uses traditional forms of the wave generation and dissipation parameterizations, and covers the years 2003-2007. Compared to previous studies, the present work has the advantage of being consistent with the known physical processes that regulate the wave field and the air-sea fluxes, and also consistent with a very large number of in situ and satellite observations of wave parameters. Consequently, some of our estimates differ significantly from previous estimates. In particular, we find that the mean global integral of Φ oc is 68 TW, and the yearly mean value of T S is typically 10-30% of the Ekman transport, except in well-defined regions where it can reach 60%. We also have refined our previous estimates of U ss by using a better treatment of the high frequency part of the wave spectrum. In the open ocean, U ss 0.013U 10 , where U 10 is the wind speed at 10 m height.
Geophysical Research Letters, 2009
Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to est... more Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to estimate the dissipation of swell energy for a number of storms. Swells can be very persistent with energy efolding scales exceeding 20,000 km. For increasing swell steepness this scale shrinks systematically, down to 2800 km for the steepest observed swells, revealing a significant loss of swell energy. This value corresponds to a normalized energy decay in time β = 4.2 × 10 −6 s −1 . Many processes may be responsible for this dissipation. The increase of dissipation rate in dissipation with swell steepness is interpreted as a laminar to turbulent transition of the boundary layer, with a threshold Reynolds number of the order of 100,000. These observations of swell evolution open the way for more accurate wave forecasting models, and provide a constraint on swell-induced air-sea fluxes of momentum and energy.
Eos, Transactions American Geophysical Union, 2005
The availability of new operational services for ocean circulation modelling presents a unique op... more The availability of new operational services for ocean circulation modelling presents a unique opportunity to rethink the operational forecasting of ocean waves and how circulation and waves may be combined to provide a better understanding of the upper ocean and enhanced services to society. The large-scale oil spill caused by the wreck of the tanker Prestige off the Spanish coast in November 2002, and uncertainties on the fate of that pollution, illustrated the gaps in means of observations and knowledge of relevant processes. The idea of a coupled atmosphere-waves-ocean model was proposed by Klaus Hasselmann , in the context of climate modelling. As waves are the "gearbox" between the atmosphere and the ocean, a detailed understanding of
Journal of Physical Oceanography, 2006
The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence ... more The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.
Journal of Fluid Mechanics, 2007
A theory is presented that describes the scattering of random surface gravity waves by small-ampl... more A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η 2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.
Journal of Physical Oceanography, 2003
State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated... more State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated using extensive field observations of swell evolution across the North Carolina continental shelf and hindcasts performed with the spectral wave prediction model CREST. The spectral energy balance equation, including bottom friction and wave-bottom scattering source terms, was integrated numerically for selected time periods with swelldominated conditions. Incident wave spectra at the model boundary were estimated from buoy measurements near the shelf break, assuming weak spatial variations in the offshore wave field. The observed strong and variable decay of the significant wave height across the shelf is predicted accurately with an overall scatter index of 0.15. Predicted wave directional properties at the peak frequency also agree well with observations, with a 5Њ root-mean-square error on the mean direction at the peak frequency and a 0.22 scatter index for the directional spread. Slight modifications are proposed for the laboratory-based empirical constants in the movable bed bottom friction source term, reducing the wave height scatter index to 0.13. A significant negative bias in the predicted directional spread (about Ϫ20%) suggests that other wave scattering processes not included in the energy balance equation broaden the wave field near the shore. Other residual errors may be largely the result of neglected spatial variations in the offshore wave conditions and, to a lesser extent, insufficient knowledge of the sediment properties.
Journal of Physical Oceanography, 2007
Wind-sea generation was observed during two experiments off the coast of North Carolina. One even... more Wind-sea generation was observed during two experiments off the coast of North Carolina. One event with offshore winds of 9-11 m s Ϫ1 directed 20°from shore normal was observed with eight directional stations recording simultaneously and spanning a fetch from 4 to 83 km. An opposing swell of 1-m height and 10-s period was also present. The wind-sea part of the wave spectrum conforms to established growth curves for significant wave height and peak period, except at inner-shelf stations where a large alongshore wind-sea component was observed. At these short fetches, the mean wave direction m was observed to change abruptly across the wind-sea spectral peak, from alongshore at lower frequencies to downwind at higher frequencies. Waves from another event with offshore winds of 6-14 m s Ϫ1 directed 20°-30°from shore normal were observed with two instrument arrays. A significant amount of low-frequency wave energy was observed to propagate alongshore from the region where the wind was strongest. These measurements are used to assess the performance of some widely used parameterizations in wave models. The modeled transition of m across the wind-sea spectrum is smoother than that in the observations and is reproduced very differently by different parameterizations, giving insights into the appropriate level of dissipation. Calculations with the full Boltzmann integral of quartet wave-wave interactions reveal that the discrete interaction approximation parameterization for these interactions is reasonably accurate at the peak of the wind sea but overpredicts the directional spread at high frequencies. This error is well compensated by parameterizations of the wind input source term that have a narrow directional distribution. Observations also highlight deficiencies in some parameterizations of wave dissipation processes in mixed swell-wind-sea conditions.
Journal of Physical Oceanography, 2009
The surface current response to winds is analyzed in a two-year time series of a 12 MHz (HF) Well... more The surface current response to winds is analyzed in a two-year time series of a 12 MHz (HF) Wellen Radar (WERA) off the West coast of France. Consistent with previous observations, the measured currents, after filtering tides, are of the order of 1.0 to 1.8% of the wind speed, in a direction 10 to 40 degrees to the right of the wind, with systematic trends as a function of wind speed. This Lagrangian current can be decomposed as the vector sum of a quasi-Eulerian current U E , representative of the top 1 m of the water column, and part of the wave-induced Stokes drift U ss at the sea surface. Here U ss is estimated with an accurate numerical wave model, thanks to a novel parameterization of wave dissipation processes. Using both observed and modelled wave spectra, Uss is found to be very well approximated by a simple function of the wind speed and significant wave height, generally increasing quadratically with the wind speed. Focusing on a site located 100 km from the mainland, the wave induced contribution of Uss to the radar measurement has an estimated magnitude of 0.6 to 1.3% of the wind speed, in the wind direction, a fraction that increases with wind speed. The difference U E of Lagrangian and Stokes contributions is found to be of the order of 0.4 to 0.8% of the wind speed, and 45 to 70 degrees to the right of the wind. This relatively weak quasi-Eulerian current with a large deflection angle is interpreted as evidence of strong near-surface mixing, likely related to breaking waves and/or Langmuir circulations. Summer stratification tends to increase the UE response by up to a factor 2, and further increases the deflection angle of U E by 5 to 10 degrees. At locations closer to coast, Uss is smaller, and UE is larger with a smaller deflection angle. These results would be transposable to the world ocean if the relative part of geostrophic currents in U E were weak, which is expected. This decomposition into Stokes drift and quasi-Eulerian current is most important for the estimation of energy fluxes to the Ekman layer.
Ocean Modelling, 2008
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean... more The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms.
Journal of Geophysical Research, 2002
1] Sand ripples with wavelengths between 0.5 and 3 m were observed on the bottom across the U.S. ... more 1] Sand ripples with wavelengths between 0.5 and 3 m were observed on the bottom across the U.S. east coast continental shelf off North Carolina during three side-scan sonar surveys in September and December 1999. Ripples were present in about 75% of the survey images, in particular, in regions with coarser sediments. Analysis of surficial sediment samples shows that median grain diameters range from 0.1 to 4.7 mm with large variations on the inner shelf over distances <1 km. The observed ripple properties are consistent with wave-generated vortex ripples. Analysis of concurrent wave observations indicates that the ripple crests were aligned perpendicular to the average direction of nearbottom wave-induced motions during preceding events that were sufficiently energetic to mobilize surficial sediments. Furthermore, the ripple wavelengths proportionality to nearbottom wave orbital excursions is consistent with wave-formed vortex ripples. These findings support the hypothesis that the observed strong attenuation of waves across the shelf resulted from form drag over large vortex ripples.
Journal of Physical Oceanography, 2008
The lowest order sigma-transformed momentum equation given by Mellor takes into account a phaseav... more The lowest order sigma-transformed momentum equation given by Mellor takes into account a phaseaveraged wave forcing based on Airy wave theory. This equation is shown to be generally inconsistent because of inadequate approximations of the wave motion. Indeed the evaluation of the vertical flux of momentum requires an estimation of the pressure p and coordinate transformation function s to first order in parameters that define the large-scale evolution of the wave field, such as the bottom slope. Unfortunately, there is no analytical expression for p and s at that order. A numerical correction method is thus proposed and verified. Alternative coordinate transforms that allow a separation of wave and mean flow momenta do not suffer from this inconsistency nor do they require a numerical estimation of the wave forcing. Indeed, the problematic vertical flux is part of the wave momentum flux, thus distinct from the mean flow momentum flux, and not directly relevant to the mean flow evolution.
J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S002211... more J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S0022112001006218 Printed in the United Kingdom ... Bragg scattering of random surface gravity waves ... By FABRICE ARDHUIN1,2 AND THC HERBERS2 1Centre Militaire d'Océanographie, Service ...
Journal of Geophysical Research, 2006
The effects of a submarine canyon on the propagation of ocean surface waves are examined with a t... more The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three-dimensional coupled-mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. Yet, a spectral refraction model predicts an even larger reduction by about a factor 10, because low frequency components cannot cross the canyon in the geometrical optics approximation. The coupled-mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy 'tunnels' across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, indicating that evanescent modes and high order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles.
Journal of Fluid Mechanics, 2002
J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S002211... more J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S0022112001006218 Printed in the United Kingdom ... Bragg scattering of random surface gravity waves ... By FABRICE ARDHUIN1,2 AND THC HERBERS2 1Centre Militaire d'Océanographie, Service ...
Journal of Physical Oceanography, 2003
State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated... more State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated using extensive field observations of swell evolution across the North Carolina continental shelf and hindcasts performed with the spectral wave prediction model CREST. The spectral energy balance equation, including bottom friction and wave-bottom scattering source terms, was integrated numerically for selected time periods with swelldominated conditions. Incident wave spectra at the model boundary were estimated from buoy measurements near the shelf break, assuming weak spatial variations in the offshore wave field. The observed strong and variable decay of the significant wave height across the shelf is predicted accurately with an overall scatter index of 0.15. Predicted wave directional properties at the peak frequency also agree well with observations, with a 5Њ root-mean-square error on the mean direction at the peak frequency and a 0.22 scatter index for the directional spread. Slight modifications are proposed for the laboratory-based empirical constants in the movable bed bottom friction source term, reducing the wave height scatter index to 0.13. A significant negative bias in the predicted directional spread (about Ϫ20%) suggests that other wave scattering processes not included in the energy balance equation broaden the wave field near the shore. Other residual errors may be largely the result of neglected spatial variations in the offshore wave conditions and, to a lesser extent, insufficient knowledge of the sediment properties.
Journal of Geophysical Research, 2007
1] The effects of a submarine canyon on the propagation of ocean surface waves are examined with ... more 1] The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three-dimensional coupled-mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/ transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. However, a spectral refraction model predicts an even larger reduction by about a factor 10, because low-frequency components cannot cross the canyon in the geometrical optics approximation. The coupled-mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy 'tunnels' across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, confirming that evanescent modes and high-order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles.
Journal of Physical Oceanography, 2001
A hybrid Eulerian-Lagrangian wave model is presented that solves the spectral energy balance equa... more A hybrid Eulerian-Lagrangian wave model is presented that solves the spectral energy balance equation for surface gravity waves in varying depth. The energy of each spectral component is advected along (Lagrangian) ray trajectories. The source terms in the energy balance equation (e.g., interactions between wave components and nonconservative processes) are computed on a fixed Eulerian grid and interpolated onto the ray trajectories. The source terms are integrated in time along the rays. This integration is performed in parallel over the entire model domain. The main advantage of this new model, named CREST (Coupled Rays with Eulerian Source Terms), is that refraction of waves by subgrid-scale depth variations is evaluated accurately using precomputed rays, and thus the model can be applied with relatively coarse source term grids to large coastal areas. Hindcasts of swell evolution across the North Carolina continental shelf are presented for a source term restricted to energy dissipation in the bottom boundary layer over a movable sandy seabed. The results show that the hybrid Eulerian-Lagrangian method is a viable approach for accurate wave predictions in large coastal regions with nonstationary boundary conditions. Good agreement between model predictions and field observations of swell decay supports the hypothesis that, in the absence of strong local wind forcing, the evolution of waves across a wide, sandy continental shelf is dominated by refraction and bottom friction, which is well represented by a moveable bed parameterization. * Additional affiliation: Service Hydrographique et Océanographique de la Marine,
Ocean Engineering, 2007
We have hindcast the wind and wave conditions in the Mediterranean Sea for two 1-month periods. F... more We have hindcast the wind and wave conditions in the Mediterranean Sea for two 1-month periods. Four different meteorological models and three different wave models have been used. The results have been compared with satellite and buoy wind and wave observations. Several conclusions concerning both the instruments and the models have been derived. The quality of both wind and wave results has been assessed. Close to the coasts high resolution, nested wave models are required for sufficient reliability.
Journal of Geophysical Research, 2006
1] Waves have many effects on near-surface dynamics: Breaking waves enhance mixing, waves are ass... more 1] Waves have many effects on near-surface dynamics: Breaking waves enhance mixing, waves are associated with a Lagrangian mean drift (the Stokes drift), waves act on the mean flow by creating Langmuir circulations and a return flow opposite to the Stokes drift, and, last but not least, waves modify the atmospheric surface roughness. A realistic ocean model is proposed to embrace all these aspects, focusing on near-surface mixing and surface drift associated with the wind and generated waves. The model is based on the generalized Lagrangian mean that separates the momentum into a wave pseudomomentum and a quasi-Eulerian momentum. A wave spectrum with a reasonably high frequency range is used to compute the Stokes drift. A turbulent closure scheme based on a single evolution equation for the turbulent kinetic energy includes the mixing due to breaking wave effects and wave-turbulence interactions. The roughness length of the closure scheme is adjusted using observations of turbulent kinetic energy near the surface. The model is applied to unstratified and horizontally uniform conditions, showing good agreement with observations of strongly mixed quasi-Eulerian currents near the surface when waves are developed. Model results suggest that a strong surface shear persists in the drift current because of the Stokes drift contribution. In the present model the surface drift only reaches 1.5% of the wind speed. It is argued that stratification and the properties of drifting objects may lead to a supplementary drift as large as 1% of the wind speed. Citation: Rascle, N., F. Ardhuin, and E. A. Terray (2006), Drift and mixing under the ocean surface: A coherent one-dimensional description with application to unstratified conditions,
Ocean Modelling, 2008
Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and curre... more Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and currents below the mixed layer. Drift and mixing are also functions of the surface Stokes drift U ss , volume Stokes transport T S , a wave breaking height scale H swg , and the flux of energy from waves to ocean turbulence Φ oc . Here we describe a global database of these parameters, estimated from a wellvalidated numerical wave model, that uses traditional forms of the wave generation and dissipation parameterizations, and covers the years 2003-2007. Compared to previous studies, the present work has the advantage of being consistent with the known physical processes that regulate the wave field and the air-sea fluxes, and also consistent with a very large number of in situ and satellite observations of wave parameters. Consequently, some of our estimates differ significantly from previous estimates. In particular, we find that the mean global integral of Φ oc is 68 TW, and the yearly mean value of T S is typically 10-30% of the Ekman transport, except in well-defined regions where it can reach 60%. We also have refined our previous estimates of U ss by using a better treatment of the high frequency part of the wave spectrum. In the open ocean, U ss 0.013U 10 , where U 10 is the wind speed at 10 m height.
Geophysical Research Letters, 2009
Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to est... more Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to estimate the dissipation of swell energy for a number of storms. Swells can be very persistent with energy efolding scales exceeding 20,000 km. For increasing swell steepness this scale shrinks systematically, down to 2800 km for the steepest observed swells, revealing a significant loss of swell energy. This value corresponds to a normalized energy decay in time β = 4.2 × 10 −6 s −1 . Many processes may be responsible for this dissipation. The increase of dissipation rate in dissipation with swell steepness is interpreted as a laminar to turbulent transition of the boundary layer, with a threshold Reynolds number of the order of 100,000. These observations of swell evolution open the way for more accurate wave forecasting models, and provide a constraint on swell-induced air-sea fluxes of momentum and energy.
Eos, Transactions American Geophysical Union, 2005
The availability of new operational services for ocean circulation modelling presents a unique op... more The availability of new operational services for ocean circulation modelling presents a unique opportunity to rethink the operational forecasting of ocean waves and how circulation and waves may be combined to provide a better understanding of the upper ocean and enhanced services to society. The large-scale oil spill caused by the wreck of the tanker Prestige off the Spanish coast in November 2002, and uncertainties on the fate of that pollution, illustrated the gaps in means of observations and knowledge of relevant processes. The idea of a coupled atmosphere-waves-ocean model was proposed by Klaus Hasselmann , in the context of climate modelling. As waves are the "gearbox" between the atmosphere and the ocean, a detailed understanding of
Journal of Physical Oceanography, 2006
The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence ... more The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.
Journal of Fluid Mechanics, 2007
A theory is presented that describes the scattering of random surface gravity waves by small-ampl... more A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η 2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.
Journal of Physical Oceanography, 2003
State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated... more State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated using extensive field observations of swell evolution across the North Carolina continental shelf and hindcasts performed with the spectral wave prediction model CREST. The spectral energy balance equation, including bottom friction and wave-bottom scattering source terms, was integrated numerically for selected time periods with swelldominated conditions. Incident wave spectra at the model boundary were estimated from buoy measurements near the shelf break, assuming weak spatial variations in the offshore wave field. The observed strong and variable decay of the significant wave height across the shelf is predicted accurately with an overall scatter index of 0.15. Predicted wave directional properties at the peak frequency also agree well with observations, with a 5Њ root-mean-square error on the mean direction at the peak frequency and a 0.22 scatter index for the directional spread. Slight modifications are proposed for the laboratory-based empirical constants in the movable bed bottom friction source term, reducing the wave height scatter index to 0.13. A significant negative bias in the predicted directional spread (about Ϫ20%) suggests that other wave scattering processes not included in the energy balance equation broaden the wave field near the shore. Other residual errors may be largely the result of neglected spatial variations in the offshore wave conditions and, to a lesser extent, insufficient knowledge of the sediment properties.
Journal of Physical Oceanography, 2007
Wind-sea generation was observed during two experiments off the coast of North Carolina. One even... more Wind-sea generation was observed during two experiments off the coast of North Carolina. One event with offshore winds of 9-11 m s Ϫ1 directed 20°from shore normal was observed with eight directional stations recording simultaneously and spanning a fetch from 4 to 83 km. An opposing swell of 1-m height and 10-s period was also present. The wind-sea part of the wave spectrum conforms to established growth curves for significant wave height and peak period, except at inner-shelf stations where a large alongshore wind-sea component was observed. At these short fetches, the mean wave direction m was observed to change abruptly across the wind-sea spectral peak, from alongshore at lower frequencies to downwind at higher frequencies. Waves from another event with offshore winds of 6-14 m s Ϫ1 directed 20°-30°from shore normal were observed with two instrument arrays. A significant amount of low-frequency wave energy was observed to propagate alongshore from the region where the wind was strongest. These measurements are used to assess the performance of some widely used parameterizations in wave models. The modeled transition of m across the wind-sea spectrum is smoother than that in the observations and is reproduced very differently by different parameterizations, giving insights into the appropriate level of dissipation. Calculations with the full Boltzmann integral of quartet wave-wave interactions reveal that the discrete interaction approximation parameterization for these interactions is reasonably accurate at the peak of the wind sea but overpredicts the directional spread at high frequencies. This error is well compensated by parameterizations of the wind input source term that have a narrow directional distribution. Observations also highlight deficiencies in some parameterizations of wave dissipation processes in mixed swell-wind-sea conditions.
Journal of Physical Oceanography, 2009
The surface current response to winds is analyzed in a two-year time series of a 12 MHz (HF) Well... more The surface current response to winds is analyzed in a two-year time series of a 12 MHz (HF) Wellen Radar (WERA) off the West coast of France. Consistent with previous observations, the measured currents, after filtering tides, are of the order of 1.0 to 1.8% of the wind speed, in a direction 10 to 40 degrees to the right of the wind, with systematic trends as a function of wind speed. This Lagrangian current can be decomposed as the vector sum of a quasi-Eulerian current U E , representative of the top 1 m of the water column, and part of the wave-induced Stokes drift U ss at the sea surface. Here U ss is estimated with an accurate numerical wave model, thanks to a novel parameterization of wave dissipation processes. Using both observed and modelled wave spectra, Uss is found to be very well approximated by a simple function of the wind speed and significant wave height, generally increasing quadratically with the wind speed. Focusing on a site located 100 km from the mainland, the wave induced contribution of Uss to the radar measurement has an estimated magnitude of 0.6 to 1.3% of the wind speed, in the wind direction, a fraction that increases with wind speed. The difference U E of Lagrangian and Stokes contributions is found to be of the order of 0.4 to 0.8% of the wind speed, and 45 to 70 degrees to the right of the wind. This relatively weak quasi-Eulerian current with a large deflection angle is interpreted as evidence of strong near-surface mixing, likely related to breaking waves and/or Langmuir circulations. Summer stratification tends to increase the UE response by up to a factor 2, and further increases the deflection angle of U E by 5 to 10 degrees. At locations closer to coast, Uss is smaller, and UE is larger with a smaller deflection angle. These results would be transposable to the world ocean if the relative part of geostrophic currents in U E were weak, which is expected. This decomposition into Stokes drift and quasi-Eulerian current is most important for the estimation of energy fluxes to the Ekman layer.
Ocean Modelling, 2008
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean... more The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms.
Journal of Geophysical Research, 2002
1] Sand ripples with wavelengths between 0.5 and 3 m were observed on the bottom across the U.S. ... more 1] Sand ripples with wavelengths between 0.5 and 3 m were observed on the bottom across the U.S. east coast continental shelf off North Carolina during three side-scan sonar surveys in September and December 1999. Ripples were present in about 75% of the survey images, in particular, in regions with coarser sediments. Analysis of surficial sediment samples shows that median grain diameters range from 0.1 to 4.7 mm with large variations on the inner shelf over distances <1 km. The observed ripple properties are consistent with wave-generated vortex ripples. Analysis of concurrent wave observations indicates that the ripple crests were aligned perpendicular to the average direction of nearbottom wave-induced motions during preceding events that were sufficiently energetic to mobilize surficial sediments. Furthermore, the ripple wavelengths proportionality to nearbottom wave orbital excursions is consistent with wave-formed vortex ripples. These findings support the hypothesis that the observed strong attenuation of waves across the shelf resulted from form drag over large vortex ripples.
Journal of Physical Oceanography, 2008
The lowest order sigma-transformed momentum equation given by Mellor takes into account a phaseav... more The lowest order sigma-transformed momentum equation given by Mellor takes into account a phaseaveraged wave forcing based on Airy wave theory. This equation is shown to be generally inconsistent because of inadequate approximations of the wave motion. Indeed the evaluation of the vertical flux of momentum requires an estimation of the pressure p and coordinate transformation function s to first order in parameters that define the large-scale evolution of the wave field, such as the bottom slope. Unfortunately, there is no analytical expression for p and s at that order. A numerical correction method is thus proposed and verified. Alternative coordinate transforms that allow a separation of wave and mean flow momenta do not suffer from this inconsistency nor do they require a numerical estimation of the wave forcing. Indeed, the problematic vertical flux is part of the wave momentum flux, thus distinct from the mean flow momentum flux, and not directly relevant to the mean flow evolution.
J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S002211... more J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S0022112001006218 Printed in the United Kingdom ... Bragg scattering of random surface gravity waves ... By FABRICE ARDHUIN1,2 AND THC HERBERS2 1Centre Militaire d'Océanographie, Service ...
Journal of Geophysical Research, 2006
The effects of a submarine canyon on the propagation of ocean surface waves are examined with a t... more The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three-dimensional coupled-mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. Yet, a spectral refraction model predicts an even larger reduction by about a factor 10, because low frequency components cannot cross the canyon in the geometrical optics approximation. The coupled-mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy 'tunnels' across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, indicating that evanescent modes and high order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles.
Journal of Fluid Mechanics, 2002
J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S002211... more J. Fluid Mech. (2002), vol. 451, pp. 133. c 2002 Cambridge University Press DOI: 10.1017/S0022112001006218 Printed in the United Kingdom ... Bragg scattering of random surface gravity waves ... By FABRICE ARDHUIN1,2 AND THC HERBERS2 1Centre Militaire d'Océanographie, Service ...
Journal of Physical Oceanography, 2003
State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated... more State-of-the-art parameterizations of the interactions of waves with a sandy bottom are evaluated using extensive field observations of swell evolution across the North Carolina continental shelf and hindcasts performed with the spectral wave prediction model CREST. The spectral energy balance equation, including bottom friction and wave-bottom scattering source terms, was integrated numerically for selected time periods with swelldominated conditions. Incident wave spectra at the model boundary were estimated from buoy measurements near the shelf break, assuming weak spatial variations in the offshore wave field. The observed strong and variable decay of the significant wave height across the shelf is predicted accurately with an overall scatter index of 0.15. Predicted wave directional properties at the peak frequency also agree well with observations, with a 5Њ root-mean-square error on the mean direction at the peak frequency and a 0.22 scatter index for the directional spread. Slight modifications are proposed for the laboratory-based empirical constants in the movable bed bottom friction source term, reducing the wave height scatter index to 0.13. A significant negative bias in the predicted directional spread (about Ϫ20%) suggests that other wave scattering processes not included in the energy balance equation broaden the wave field near the shore. Other residual errors may be largely the result of neglected spatial variations in the offshore wave conditions and, to a lesser extent, insufficient knowledge of the sediment properties.
Journal of Geophysical Research, 2007
1] The effects of a submarine canyon on the propagation of ocean surface waves are examined with ... more 1] The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three-dimensional coupled-mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/ transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. However, a spectral refraction model predicts an even larger reduction by about a factor 10, because low-frequency components cannot cross the canyon in the geometrical optics approximation. The coupled-mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy 'tunnels' across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, confirming that evanescent modes and high-order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles.
Journal of Physical Oceanography, 2001
A hybrid Eulerian-Lagrangian wave model is presented that solves the spectral energy balance equa... more A hybrid Eulerian-Lagrangian wave model is presented that solves the spectral energy balance equation for surface gravity waves in varying depth. The energy of each spectral component is advected along (Lagrangian) ray trajectories. The source terms in the energy balance equation (e.g., interactions between wave components and nonconservative processes) are computed on a fixed Eulerian grid and interpolated onto the ray trajectories. The source terms are integrated in time along the rays. This integration is performed in parallel over the entire model domain. The main advantage of this new model, named CREST (Coupled Rays with Eulerian Source Terms), is that refraction of waves by subgrid-scale depth variations is evaluated accurately using precomputed rays, and thus the model can be applied with relatively coarse source term grids to large coastal areas. Hindcasts of swell evolution across the North Carolina continental shelf are presented for a source term restricted to energy dissipation in the bottom boundary layer over a movable sandy seabed. The results show that the hybrid Eulerian-Lagrangian method is a viable approach for accurate wave predictions in large coastal regions with nonstationary boundary conditions. Good agreement between model predictions and field observations of swell decay supports the hypothesis that, in the absence of strong local wind forcing, the evolution of waves across a wide, sandy continental shelf is dominated by refraction and bottom friction, which is well represented by a moveable bed parameterization. * Additional affiliation: Service Hydrographique et Océanographique de la Marine,
Ocean Engineering, 2007
We have hindcast the wind and wave conditions in the Mediterranean Sea for two 1-month periods. F... more We have hindcast the wind and wave conditions in the Mediterranean Sea for two 1-month periods. Four different meteorological models and three different wave models have been used. The results have been compared with satellite and buoy wind and wave observations. Several conclusions concerning both the instruments and the models have been derived. The quality of both wind and wave results has been assessed. Close to the coasts high resolution, nested wave models are required for sufficient reliability.