J. Argain - Profile on Academia.edu (original) (raw)

Papers by J. Argain

The momentum flux profiles produced by trapped lee waves

<p>Orographic gravity waves (also known as mountain waves) cause the atmosp... more <p>Orographic gravity waves (also known as mountain waves) cause the atmosphere to exert a drag force on mountains. By Newton’s 3<sup>rd</sup> law, the mountains exert an equal and opposite force on the atmosphere. It is clear from linear wave theory how to develop a framework for representing this reaction force in parametrizations for vertically propagating waves in climate and weather prediction models: the waves break and dissipate either due to critical levels (where the wind speed is perpendicular to the horizontal wavenumber vector, or zero), or due to the progressive decrease of density with height. But the situation is more complicated for trapped lee waves, which propagate horizontally near the surface, and where the wave energy is alternately reflected at the ground and at an elevated layer where the waves become evanescent. It is clear that boundary layer friction should be responsible for most of the dissipation of trapped lee waves, but it is not clear, even in the inviscid approximation, what form the wave momentum flux profiles that force the large-scale mean flow will take. This is due to the complications associated with the fact that trapped lee waves have both horizontal and vertical momentum (and pseudo-momentum) fluxes, which oscillate indefinitely with the wave phase downstream of the orography. No mechanism equivalent to critical levels, or density decay with height, acting on vertically propagating mountain waves, is available for trapped lee waves. In this study, this limitation is overcome by accounting for the effects of weak friction. While for an inviscid trapped lee wave train, the horizontally integrated momentum flux is ill-defined (except at the surface), in a dissipative problem where friction exists, no matter how small, the wave train necessarily decays downstream, and so is spatially bounded. This allows the areally integrated effect of the trapped lee wave to be expressed in terms of the divergence of the vertical flux of horizontal wave momentum (as for vertically-propagating waves). On the other hand, the form of the momentum flux profile (which defines this divergence) is different from any form that could be inferred from inviscid theory, although it is independent of the magnitude of friction, as long as this is small. These results from linear theory are compared with high-resolution numerical simulations of trapped lee waves for the two-layer atmosphere of Scorer, which confirm the form of the momentum flux profiles, and suggest that these may be independent of the adopted form of friction, at least to some extent. The results therefore facilitate the formulation of parametrizations for trapped lee waves with a much more solid physical  basis, and are likely to be generalizable to other atmospheric profiles.</p>

Atmosphere

Earth system modelling is currently playing an increasing role in weather forecasting and underst... more Earth system modelling is currently playing an increasing role in weather forecasting and understanding climate change, however, the operation, deployment and development of numerical Earth system models are extremely demanding in terms of computational resources and human effort. Merging synergies has become a natural process by which national meteorological services assess and contribute to the development of such systems. With the advent of joining synergies at the national level, the second edition of the workshop on Numerical Weather Prediction in Portugal was promoted by the Portuguese Institute for the Sea and Atmosphere, I.P. (IPMA), in cooperation with several Portuguese Universities. The event was hosted by the University of Évora, during the period of 11–12 of November 2021. It was dedicated to surface–atmosphere interactions and allowed the exchange of experiences between experts, students and newcomers. The workshop provided a refreshed overview of ongoing research and ...

Trapped lee waves in layered atmospheres: an important source of low-level drag?

Quarterly Journal of the Royal Meteorological Society

While it is known that trapped lee waves propagating at low levels in a stratified atmosphere exe... more While it is known that trapped lee waves propagating at low levels in a stratified atmosphere exert a drag on the mountains that generate them, the distribution of the corresponding reaction force exerted on the atmospheric mean circulation, defined by the wave momentum flux profiles, has not been established, because for inviscid trapped lee waves these profiles oscillate indefinitely downstream. A framework is developed here for the unambiguous calculation of momentum flux profiles produced by trapped lee waves, which circumvents the difficulties plaguing the inviscid trapped lee wave theory. Using linear theory, and taking Scorer's two-layer atmosphere as an example, the waves are assumed to be subject to a small dissipation, expressed as a Rayleigh damping. The resulting wave pattern decays downstream, so the momentum flux profile integrated over the area occupied by the waves converges to a well-defined form. Remarkably, for weak dissipation, this form is independent of the value of Rayleigh damping coefficient, and the inviscid drag, determined in previous studies, is recovered as the momentum flux at the surface. The divergence of this momentum flux profile accounts for the areally-integrated drag exerted by the waves on the atmosphere. The application of this framework to this and other types of trapped lee waves potentially enables the development of physically-based parametrizations of the effects of trapped lee waves on the atmosphere.

Quarterly Journal of the Royal Meteorological Society, 2020

Boundary-Layer Meteorology, 2017

A method is proposed for estimating the surface-layer depth () and the friction velocity (*) as a... more A method is proposed for estimating the surface-layer depth () and the friction velocity (*) as a function of stability (here quantified by the Obukhov length,) over the complete range of unstable flow regimes. This method extends the one developed previously by the authors for stable conditions in Argaín et al. (Boundary-Layer Meteorol, 2009, Vol.130, 15-28), but uses a qualitatively different approach. The method is specifically used to calculate the fractional speed-up () in flow over a ridge, although it is suitable for more general boundary-layer applications. The behaviour of () and * () as a function of is indirectly assessed via calculation of  () using the linear model of Hunt et al.

Quarterly Journal of the Royal Meteorological Society, 2012

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrosta... more The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l 2 /l 1 and of the corresponding dimensionless interface height l 1 H, for selected values of the dimensionless ridge width l 1 a and ratio of wind speeds in the two layers. When l 2 /l 1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l 2 /l 1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l 1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l 2 /l 1 and slightly higher values of l 1 H than the propagating wave drag maxima. As l 1 a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l 2 /l 1. These results are confirmed by numerical simulations for l 2 /l 1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models. Copyright

Quarterly Journal of the Royal Meteorological Society, 2012

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonan... more A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l 0 = 2, where l 0 is the unperturbed value of the Scorer parameter and n is the wavenumber of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l 0 = 2. Both nonhydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

Journal of the Atmospheric Sciences, 2008

Internal gravity waves generated in two-layer stratified shear flows over mountains are investiga... more Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too dif...

Journal of the Atmospheric Sciences, 2013

The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves pro... more The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped-lee-wave drag, which is given by a closed analytical expression, is comparable to propagating-wave drag, especially in moderately to strongly nonhydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parameterization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating-wave drag is maximized for approximately hydrostatic flow, trapped-lee-wave drag is maximized for l2a = O(1) (where l2 is the Scorer parameter in the stable layer and a is the mountain width). ...

Boundary-Layer Meteorology, 2008

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-... more A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

A linear model of gravity waves generated by stratified airflow over mountains is developed. The ... more A linear model of gravity waves generated by stratified airflow over mountains is developed. The model provides simple, closed-form formulas for the surface drag in a situation where conditions for wave resonance exist. The wind is constant near the surface and decreases linearly above. The drag normalized by its value in the absence of shear is found to depend on two parameters: the height of the interface where the shear is discontinuous and the Richardson number, Ri, in the region above. This drag attains maxima when the height of the interface induces constructive interference between the upward and downward propagating reflected waves, and minima when there is destructive interference. The amplitude of the drag modulation becomes larger for lower Ri. It is also shown that, for Ri<2.25, the locations where wave breaking is first predicted to occur in flow over a 2D ridge become displaced horizontally and vertically by an amount depending on Ri.

Orographic gravity wave drag amplification by parametric resonance

ABSTRACT One of the mechanisms identified by Wells and Vosper (2010) for the amplification of gra... more ABSTRACT One of the mechanisms identified by Wells and Vosper (2010) for the amplification of gravity wave drag produced in flow over mountains, which makes this force substantially exceed its linear estimate even for very low mountain heights, requires a Scorer parameter profile that oscillates with height with a wavelength half that of the primary waves generated by the vertically-averaged Scorer parameter. This mechanism, first mentioned by Phillips (1968) in an oceanic context, relies on a resonance process, and Wells and Vosper claim that this resonance is intrinsically nonlinear. In the present study (see Teixeira et al. 2012), we examine this mechanism in more detail, considering flow over an isolated mountain with a Scorer parameter that is constant in the vertical apart from a superposed small-amplitude sinusoidal oscillation. This problem is treated both using an analytical perturbation method and numerical simulations with a mesoscale model. It is shown that the processes leading to drag enhancement (or reduction) are linear, since they result from the interaction between the primary wave and the Scorer parameter oscillation. These processes may therefore be captured in a linear framework, by expanding the solution to the Taylor-Goldstein equation in powers of a small parameter proportional to the amplitude of the Scorer parameter oscillation. A semi-analytical model based on this approach produces results that are qualitatively similar to those obtained in the numerical simulations. The drag normalized by its value for a constant Scorer parameter is studied as a function of the wavelength and phase of the Scorer parameter oscillation. Only higher-order effects may be attributed to nonlinearity. However, it is shown that the results are quite sensitive to friction, in particular no drag enhancement is produced for some values of the phase of the Scorer parameter oscillation unless friction is included in some form. This implies that, in numerical simulations, the drag behaviour should be sensitive to the numerical diffusion inherent to the discretization schemes and to the type of turbulence closure employed in the numerical model. In our study, the semi-analytical model uses a simple Rayleigh damping coefficient to represent friction, and the value of this parameter is estimated from the numerical simulations. While most of the numerical simulations are nominally inviscid, a first assessment of the effect of physical friction, using simulations with turbulence closures, is also carried out. Additionally, non-hydrostatic effects are assessed, and found to have an important impact on the drag amplification, weakening the resonance process due to wave dispersion.

Quarterly Journal of the Royal Meteorological Society, 2005

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are inv... more High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z 1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z 1 , and the Richardson number, Ri, in the shear layer. The drag oscillates as z 1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z 1. Drag maxima correspond to constructive interference of the upward-and downward-propagating waves in the region z < z 1 , while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z 1 increases as Ri decreases. The critical level, z c , plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

Neutral and stably-stratified turbulent boundary layer flows past topography

In this work, we study neutral and stably-stratified turbulent boundary layer flows over orograph... more In this work, we study neutral and stably-stratified turbulent boundary layer flows over orography using a non-hydrostatic microscale-mesoscale numerical model, which has been validated previously with observations. To allow for a simulation of flows over complex topography, the ...

Estimating the friction velocity in stable boundary layers

... JL Argain, University of Algarve, Faro, Portugal; and PMA Miranda and MAC Teixeira. A new met... more ... JL Argain, University of Algarve, Faro, Portugal; and PMA Miranda and MAC Teixeira. A new method is proposed for the calculation of friction velocity in stable turbulent boundary layer flows, where gravity waves propagation is possible. ...

The dependence of mountain wave reflection on the abruptness of atmospheric profile variations

Quarterly Journal of the Royal Meteorological Society, 2020

It is known from geometric optics that a change in refractive index is potentially reflective if ... more It is known from geometric optics that a change in refractive index is potentially reflective if it occurs over scales much smaller than the wavelength of the incident waves. The limitations of this assumption for hydrostatic orographic gravity waves are tested here using linear theory and a method recently developed by the authors to evaluate the reflection coefficient, based on the wave drag. Two atmospheric profiles optimally suited to this method are adopted, the first with piecewise constant static stability (representative of a tropopause), and the second with constant wind speed near the surface, and a linearly decreasing wind aloft below a critical level (relevant to downslope windstorms). Both profiles consist of two atmospheric layers separated by a transition layer with controllable thickness, where the parameters vary continuously. The variation of the reflection coefficient between its maximum (for a zero‐thickness transition layer) and zero, as the ratio of the thickne...

Reflection of nonlinear mountain waves by critical levels: behaviour of the reflection coefficient

Quarterly Journal of the Royal Meteorological Society

Critical levels, where the wind vanishes in the atmosphere, are of key importance for gravity wav... more Critical levels, where the wind vanishes in the atmosphere, are of key importance for gravity wave drag parametrization. The reflectivity of these levels to mountain waves is investigated here using a combination of high-resolution numerical simulations and insights from linear theory. A methodology is developed for relating the reflection coefficient R of 2D hydrostatic orographic gravity waves to the extrema of the associated drag as a function of an independent flow parameter. This method is then used to infer the variation of the reflection coefficient with flow nonlinearity. To isolate the effect of critical levels, a wind profile with negative shear is adopted, which is characterized by its Richardson number Ri and the dimensionless mountain height Nh0/U0, based on the mountain height h0, Brunt-Vaisala frequency N and surface incoming wind speed U0. Subject to the assumptions of linear theory, the drag is shown to be modified by wave refraction and reflection. The modulation of the drag by wave reflection is used to derive the reflection coefficient from the drag diagnosed from the numerical simulations. Despite considerable uncertainty, the critical level is found to have an R that first increases with Nh0/U0 for low values of this parameter, and for stronger nonlinearity saturates to a value of about 0.6. The flow configuration in this saturated regime is characterized in the case of high-drag states by constructive wave interference, resembling downslope windstorms. Wave reflection by critical levels enhances the flow nonlinearity and the associated drag amplification, more than doubling it for values of Nh0/U0 as low as 0.12. These results emphasize the need to represent this process in orographic gravity wave drag parametrizations, and suggest a possible way of doing it using a prescribed critical level reflection coefficient, derived using the present methodology.

The momentum flux profiles produced by trapped lee waves

&amp;lt;p&amp;gt;Orographic gravity waves (also known as mountain waves) cause the atmosp... more &amp;lt;p&amp;gt;Orographic gravity waves (also known as mountain waves) cause the atmosphere to exert a drag force on mountains. By Newton&amp;amp;#8217;s 3&amp;lt;sup&amp;gt;rd&amp;lt;/sup&amp;gt; law, the mountains exert an equal and opposite force on the atmosphere. It is clear from linear wave theory how to develop a framework for representing this reaction force in parametrizations for vertically propagating waves in climate and weather prediction models: the waves break and dissipate either due to critical levels (where the wind speed is perpendicular to the horizontal wavenumber vector, or zero), or due to the progressive decrease of density with height. But the situation is more complicated for trapped lee waves, which propagate horizontally near the surface, and where the wave energy is alternately reflected at the ground and at an elevated layer where the waves become evanescent. It is clear that boundary layer friction should be responsible for most of the dissipation of trapped lee waves, but it is not clear, even in the inviscid approximation, what form the wave momentum flux profiles that force the large-scale mean flow will take. This is due to the complications associated with the fact that trapped lee waves have both horizontal and vertical momentum (and pseudo-momentum) fluxes, which oscillate indefinitely with the wave phase downstream of the orography. No mechanism equivalent to critical levels, or density decay with height, acting on vertically propagating mountain waves, is available for trapped lee waves. In this study, this limitation is overcome by accounting for the effects of weak friction. While for an inviscid trapped lee wave train, the horizontally integrated momentum flux is ill-defined (except at the surface), in a dissipative problem where friction exists, no matter how small, the wave train necessarily decays downstream, and so is spatially bounded. This allows the areally integrated effect of the trapped lee wave to be expressed in terms of the divergence of the vertical flux of horizontal wave momentum (as for vertically-propagating waves). On the other hand, the form of the momentum flux profile (which defines this divergence) is different from any form that could be inferred from inviscid theory, although it is independent of the magnitude of friction, as long as this is small. These results from linear theory are compared with high-resolution numerical simulations of trapped lee waves for the two-layer atmosphere of Scorer, which confirm the form of the momentum flux profiles, and suggest that these may be independent of the adopted form of friction, at least to some extent. The results therefore facilitate the formulation of parametrizations for trapped lee waves with a much more solid physical&amp;amp;#160; basis, and are likely to be generalizable to other atmospheric profiles.&amp;lt;/p&amp;gt;

Atmosphere

Earth system modelling is currently playing an increasing role in weather forecasting and underst... more Earth system modelling is currently playing an increasing role in weather forecasting and understanding climate change, however, the operation, deployment and development of numerical Earth system models are extremely demanding in terms of computational resources and human effort. Merging synergies has become a natural process by which national meteorological services assess and contribute to the development of such systems. With the advent of joining synergies at the national level, the second edition of the workshop on Numerical Weather Prediction in Portugal was promoted by the Portuguese Institute for the Sea and Atmosphere, I.P. (IPMA), in cooperation with several Portuguese Universities. The event was hosted by the University of Évora, during the period of 11–12 of November 2021. It was dedicated to surface–atmosphere interactions and allowed the exchange of experiences between experts, students and newcomers. The workshop provided a refreshed overview of ongoing research and ...

Trapped lee waves in layered atmospheres: an important source of low-level drag?

Quarterly Journal of the Royal Meteorological Society

While it is known that trapped lee waves propagating at low levels in a stratified atmosphere exe... more While it is known that trapped lee waves propagating at low levels in a stratified atmosphere exert a drag on the mountains that generate them, the distribution of the corresponding reaction force exerted on the atmospheric mean circulation, defined by the wave momentum flux profiles, has not been established, because for inviscid trapped lee waves these profiles oscillate indefinitely downstream. A framework is developed here for the unambiguous calculation of momentum flux profiles produced by trapped lee waves, which circumvents the difficulties plaguing the inviscid trapped lee wave theory. Using linear theory, and taking Scorer's two-layer atmosphere as an example, the waves are assumed to be subject to a small dissipation, expressed as a Rayleigh damping. The resulting wave pattern decays downstream, so the momentum flux profile integrated over the area occupied by the waves converges to a well-defined form. Remarkably, for weak dissipation, this form is independent of the value of Rayleigh damping coefficient, and the inviscid drag, determined in previous studies, is recovered as the momentum flux at the surface. The divergence of this momentum flux profile accounts for the areally-integrated drag exerted by the waves on the atmosphere. The application of this framework to this and other types of trapped lee waves potentially enables the development of physically-based parametrizations of the effects of trapped lee waves on the atmosphere.

Quarterly Journal of the Royal Meteorological Society, 2020

Boundary-Layer Meteorology, 2017

A method is proposed for estimating the surface-layer depth () and the friction velocity (*) as a... more A method is proposed for estimating the surface-layer depth () and the friction velocity (*) as a function of stability (here quantified by the Obukhov length,) over the complete range of unstable flow regimes. This method extends the one developed previously by the authors for stable conditions in Argaín et al. (Boundary-Layer Meteorol, 2009, Vol.130, 15-28), but uses a qualitatively different approach. The method is specifically used to calculate the fractional speed-up () in flow over a ridge, although it is suitable for more general boundary-layer applications. The behaviour of () and * () as a function of is indirectly assessed via calculation of  () using the linear model of Hunt et al.

Quarterly Journal of the Royal Meteorological Society, 2012

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrosta... more The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l 2 /l 1 and of the corresponding dimensionless interface height l 1 H, for selected values of the dimensionless ridge width l 1 a and ratio of wind speeds in the two layers. When l 2 /l 1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l 2 /l 1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l 1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l 2 /l 1 and slightly higher values of l 1 H than the propagating wave drag maxima. As l 1 a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l 2 /l 1. These results are confirmed by numerical simulations for l 2 /l 1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models. Copyright

Quarterly Journal of the Royal Meteorological Society, 2012

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonan... more A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l 0 = 2, where l 0 is the unperturbed value of the Scorer parameter and n is the wavenumber of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l 0 = 2. Both nonhydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

Journal of the Atmospheric Sciences, 2008

Internal gravity waves generated in two-layer stratified shear flows over mountains are investiga... more Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too dif...

Journal of the Atmospheric Sciences, 2013

The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves pro... more The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped-lee-wave drag, which is given by a closed analytical expression, is comparable to propagating-wave drag, especially in moderately to strongly nonhydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parameterization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating-wave drag is maximized for approximately hydrostatic flow, trapped-lee-wave drag is maximized for l2a = O(1) (where l2 is the Scorer parameter in the stable layer and a is the mountain width). ...

Boundary-Layer Meteorology, 2008

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-... more A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

A linear model of gravity waves generated by stratified airflow over mountains is developed. The ... more A linear model of gravity waves generated by stratified airflow over mountains is developed. The model provides simple, closed-form formulas for the surface drag in a situation where conditions for wave resonance exist. The wind is constant near the surface and decreases linearly above. The drag normalized by its value in the absence of shear is found to depend on two parameters: the height of the interface where the shear is discontinuous and the Richardson number, Ri, in the region above. This drag attains maxima when the height of the interface induces constructive interference between the upward and downward propagating reflected waves, and minima when there is destructive interference. The amplitude of the drag modulation becomes larger for lower Ri. It is also shown that, for Ri<2.25, the locations where wave breaking is first predicted to occur in flow over a 2D ridge become displaced horizontally and vertically by an amount depending on Ri.

Orographic gravity wave drag amplification by parametric resonance

ABSTRACT One of the mechanisms identified by Wells and Vosper (2010) for the amplification of gra... more ABSTRACT One of the mechanisms identified by Wells and Vosper (2010) for the amplification of gravity wave drag produced in flow over mountains, which makes this force substantially exceed its linear estimate even for very low mountain heights, requires a Scorer parameter profile that oscillates with height with a wavelength half that of the primary waves generated by the vertically-averaged Scorer parameter. This mechanism, first mentioned by Phillips (1968) in an oceanic context, relies on a resonance process, and Wells and Vosper claim that this resonance is intrinsically nonlinear. In the present study (see Teixeira et al. 2012), we examine this mechanism in more detail, considering flow over an isolated mountain with a Scorer parameter that is constant in the vertical apart from a superposed small-amplitude sinusoidal oscillation. This problem is treated both using an analytical perturbation method and numerical simulations with a mesoscale model. It is shown that the processes leading to drag enhancement (or reduction) are linear, since they result from the interaction between the primary wave and the Scorer parameter oscillation. These processes may therefore be captured in a linear framework, by expanding the solution to the Taylor-Goldstein equation in powers of a small parameter proportional to the amplitude of the Scorer parameter oscillation. A semi-analytical model based on this approach produces results that are qualitatively similar to those obtained in the numerical simulations. The drag normalized by its value for a constant Scorer parameter is studied as a function of the wavelength and phase of the Scorer parameter oscillation. Only higher-order effects may be attributed to nonlinearity. However, it is shown that the results are quite sensitive to friction, in particular no drag enhancement is produced for some values of the phase of the Scorer parameter oscillation unless friction is included in some form. This implies that, in numerical simulations, the drag behaviour should be sensitive to the numerical diffusion inherent to the discretization schemes and to the type of turbulence closure employed in the numerical model. In our study, the semi-analytical model uses a simple Rayleigh damping coefficient to represent friction, and the value of this parameter is estimated from the numerical simulations. While most of the numerical simulations are nominally inviscid, a first assessment of the effect of physical friction, using simulations with turbulence closures, is also carried out. Additionally, non-hydrostatic effects are assessed, and found to have an important impact on the drag amplification, weakening the resonance process due to wave dispersion.

Quarterly Journal of the Royal Meteorological Society, 2005

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are inv... more High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z 1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z 1 , and the Richardson number, Ri, in the shear layer. The drag oscillates as z 1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z 1. Drag maxima correspond to constructive interference of the upward-and downward-propagating waves in the region z < z 1 , while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z 1 increases as Ri decreases. The critical level, z c , plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

Neutral and stably-stratified turbulent boundary layer flows past topography

In this work, we study neutral and stably-stratified turbulent boundary layer flows over orograph... more In this work, we study neutral and stably-stratified turbulent boundary layer flows over orography using a non-hydrostatic microscale-mesoscale numerical model, which has been validated previously with observations. To allow for a simulation of flows over complex topography, the ...

Estimating the friction velocity in stable boundary layers

... JL Argain, University of Algarve, Faro, Portugal; and PMA Miranda and MAC Teixeira. A new met... more ... JL Argain, University of Algarve, Faro, Portugal; and PMA Miranda and MAC Teixeira. A new method is proposed for the calculation of friction velocity in stable turbulent boundary layer flows, where gravity waves propagation is possible. ...

The dependence of mountain wave reflection on the abruptness of atmospheric profile variations

Quarterly Journal of the Royal Meteorological Society, 2020

It is known from geometric optics that a change in refractive index is potentially reflective if ... more It is known from geometric optics that a change in refractive index is potentially reflective if it occurs over scales much smaller than the wavelength of the incident waves. The limitations of this assumption for hydrostatic orographic gravity waves are tested here using linear theory and a method recently developed by the authors to evaluate the reflection coefficient, based on the wave drag. Two atmospheric profiles optimally suited to this method are adopted, the first with piecewise constant static stability (representative of a tropopause), and the second with constant wind speed near the surface, and a linearly decreasing wind aloft below a critical level (relevant to downslope windstorms). Both profiles consist of two atmospheric layers separated by a transition layer with controllable thickness, where the parameters vary continuously. The variation of the reflection coefficient between its maximum (for a zero‐thickness transition layer) and zero, as the ratio of the thickne...

Reflection of nonlinear mountain waves by critical levels: behaviour of the reflection coefficient

Quarterly Journal of the Royal Meteorological Society

Critical levels, where the wind vanishes in the atmosphere, are of key importance for gravity wav... more Critical levels, where the wind vanishes in the atmosphere, are of key importance for gravity wave drag parametrization. The reflectivity of these levels to mountain waves is investigated here using a combination of high-resolution numerical simulations and insights from linear theory. A methodology is developed for relating the reflection coefficient R of 2D hydrostatic orographic gravity waves to the extrema of the associated drag as a function of an independent flow parameter. This method is then used to infer the variation of the reflection coefficient with flow nonlinearity. To isolate the effect of critical levels, a wind profile with negative shear is adopted, which is characterized by its Richardson number Ri and the dimensionless mountain height Nh0/U0, based on the mountain height h0, Brunt-Vaisala frequency N and surface incoming wind speed U0. Subject to the assumptions of linear theory, the drag is shown to be modified by wave refraction and reflection. The modulation of the drag by wave reflection is used to derive the reflection coefficient from the drag diagnosed from the numerical simulations. Despite considerable uncertainty, the critical level is found to have an R that first increases with Nh0/U0 for low values of this parameter, and for stronger nonlinearity saturates to a value of about 0.6. The flow configuration in this saturated regime is characterized in the case of high-drag states by constructive wave interference, resembling downslope windstorms. Wave reflection by critical levels enhances the flow nonlinearity and the associated drag amplification, more than doubling it for values of Nh0/U0 as low as 0.12. These results emphasize the need to represent this process in orographic gravity wave drag parametrizations, and suggest a possible way of doing it using a prescribed critical level reflection coefficient, derived using the present methodology.