An analytical model of capped turbulent oscillatory bottom boundary layers (original) (raw)
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Bottom friction and its effects on periodic long wave propagation
Coastal Engineering, 2007
A new Boussinesq-type model describing periodic wave propagation over a constant depth has been developed for the cases where the effects of a turbulent boundary layer are significant. In this paper, the eddy viscosity model is employed in the turbulent boundary layer and is further approximated as a linear function of the distance measured from the seafloor. The boundary-layer velocities are coupled with the irrotational velocity in the core region through the boundary conditions. The leading order effects of the boundary layer on wave propagation appear in the depthintegrated continuity equation to account for the velocity deficit inside the boundary layer. The bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity are part of the solutions. An iterative scheme is introduced to find them. A numerical example for the evolution of periodic waves propagating in a one-dimensional channel is discussed to illustrate the numerical procedure and the physics involved.
Chapter 6 Dynamics of the Bottom Boundary Layer
2008
The bottom boundary layer (BBL) conveys the transfer and exchange of physical, chemical, and biological properties between the sea floor and the sea, and has strong implications in the dissipation of the energy produced by large-scale ocean currents. This chapter describes the dynamics of theBBL. . It can be sub-divided into three principal sub-layers namely: (1) a bottom Ekman layer influenced by an equilibrium among the Coriolis force, the pressure gradient, and the turbulent friction, (2) a viscous layer mainly dominated by the viscous stresses, and (3) a transitional or logarithmic layer where turbulent stresses play a dominant role. The characteristics of each sub-layer can help increase the insight into the main processes involved in the BBL. The characteristics can be determined by––influence of wind stress and interactions with the sea floor and suspended particles. An analysis of the dynamics of the BBL is also important for obtaining useful estimates of basic quantities such as friction velocity or the bed-shear stress. The friction velocity characterizes the dynamics of the BBL.
Journal of Geophysical Research, 2003
1] On the basis of the transitional k-w turbulence model, we propose a new k-w turbulence model for one-dimension vertical (1DV) oscillating bottom boundary layer in which a separation condition under a strong, adverse pressure gradient has been introduced and the diffusion and transition constants have been modified. This new turbulence model agrees better than the Wilcox original model with both a direct numerical simulation (DNS) of a pure oscillatory flow over a smooth bottom in the intermittently turbulent regime and with experimental data from Jensen et al. [1989], who attained the fully turbulent regime for pure oscillatory flows. The new turbulence model is also found to agree better than the original one with experimental data of an oscillatory flow with current over a rough bottom by Dohmen-Janssen [1999]. In particular, the proposed model reproduces the secondary humps in the Reynolds stresses during the decelerating part of the wave cycle and the vertical phase lagging of the Reynolds stresses, two shortcomings of all previous modeling attempts. In addition, the model predicts suspension ejection events in the decelerating part of the wave cycle when it is coupled with a sediment concentration equation. Concentration measurements in the sheet flow layer give indication that these suspension ejection events do occur in practice.
Numerical Modeling of Turbulent Bottom Boundary Layer over Rough Bed under Irregular Waves
IPTEK The Journal for Technology and Science, 2011
AbstractA numerical model of turbulent bottom boundary layer over rough bed under irregular waves is reviewed. The turbulence model is based upon Shear Stress Transport (SST) k- model. The non-linear governing equations of the boundary layer for each turbulence models were solved by using a Crank-Nicolson type implicit finite-difference scheme. Typical the main velocity distribution, turbulence kinetic energy and time series of the bottom shear stress are presented. These results are shown to be in generally good agreement with experimental result. The roughness effects in the properties of turbulent bottom boundary layer for irregular waves are also presented with several values of the roughness parameter (a m /k s ) from a m /k s =5 to a m /k s =3122. The roughness effect tends to decrease the main velocity distribution and to increase the turbulent kinetic energy in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the mean velocity distribution and the kinetic energy turbulent is relatively unaffected. The effect of bed roughness on the bottom shear stress under irregular waves is found that the higher roughness elements increase the magnitude of bottom shear stress along wave cycle. And further, the bottom shear stress under irregular waves is examined with the existing calculation method and the newly proposed method.
TURBULENCE MODELING OF A WAVE BOUNDARY LAYER ON A ROUGH BOTTOM
Coastal Engineering 2008 - Proceedings of the 31st International Conference, 2009
The original k-co model by Wilcox (WL) and two versions of blended k-w/k-S model, namely; Baseline (BSL) model and Shear Stress Transport (SST) model were applied to the wave boundary layers on a rough bottom. The model results were compared with the available experimental data. The three models show good agreement with the experimental data for velocity, turbulent kinetic energy and Reynolds stress. The SST model is superior in predicting shear velocity in one of the experimental cases. However, a detailed comparison revealed that SST model underestimates the friction factor for lower values of particle excursion length to roughness ratio, whereas, WL and BSL models showed good agreement with the experimental data. The results of this study would be useful for practicing engineers and researchers in choosing an appropriate model for calculating bottom shear stress.
Turbulent properties in a homogeneous tidal bottom boundary layer
Journal of Geophysical Research, 1999
Profiles of mean and turbulent velocity and vorticity in a tidal bottom boundary layer are reported. Friction velocities estimated (1) by the profile method using the time mean streamwise velocity, (2) by the eddy-correlation method using the turbulent Reynolds stress, and (3) by the dissipation method using the turbulent kinetic energy dissipation rate e are in good agreement. The mean streamwise velocity component exhibits two distinct log layers. In both layers, e is inversely proportional to the distance from the bottom Z. The lower log layer occupies the bottom 3 m. In this layer, the turbulent Reynolds stress is nearly constant. The dynamics in the lower log layer are directly related to the stress induced by the seabed. The upper log layer spans 5 to 12 m above the bottom. In this layer, the turbulent Reynolds stress decreases toward the surface. The friction velocity estimated by the profile method in the upper log layer is about 1.8 times of that estimated in the lower log layer. Form drag might be important in the upper log layer. A detailed study of upstream topography is required for the bed stress estimate. The mean profile of vertical flux of spanwise vorticity is nearly uniform with Z and is at least a factor of 5 larger than the vertical divergence of turbulent Reynolds stress to which it may be compared. A new method of estimating the friction velocity is proposed that uses the vertical flux of turbulent spanwise vorticity. This is supported by the fact that the vertical eddy diffusivity for the turbulent vorticity is about equal in magnitude and vertical structure to the eddy viscosity for the turbulent momentum. The friction velocity calculated from the vorticity flux is equal to that estimated by the other three methods. Turbulent enstrophy, corrected for the sensor response function, is proportional to Z -1 for the entire water column. The relation between e and enstrophy for high-Reynolds-number flows is confirmed by our observations.
Bottom friction effects on linear wave propagation
Wave Motion, 2009
Bottom boundary layer effects on the linear wave propagation over mild slope bottoms are analyzed. A modified WKB approximation is presented including boundary layer effects. Within the boundary layer, two cases are considered: laminar (constant viscosity) and turbulent. Boundary layer effects are introduced by coupling the velocity inside the boundary layer to the irrotational velocity in the core region through the bottom boundary condition. This formulation properly accounts for the phase between near bed velocity and bed shear stress. The resulting differential equation for the energy conservation introduces a new term accounting for the energy losses due to the boundary layer effects.
Energy balance of wind waves as a function of the bottom friction formulation
Coastal Engineering, 2001
Four different expressions for wave energy dissipation by bottom friction are intercompared. For this purpose, the SWAN Ž . wave model and the wave data set of Lake George Australia are used. Three formulations are already present in SWAN Ž . ver. 40.01 : the JONSWAP expression, the drag law friction model of Collins and the eddy-viscosity model of Madsen. The eddy-viscosity model of Weber was incorporated into the SWAN code. Using Collins' and Weber's expressions, the depth-and fetch-limited wave growth laws obtained in the nearly idealized situation of Lake George can be reproduced. The wave model has shown the best performance using the formulation of Weber. This formula has some advantages over the other formulations. The expression is based on theoretical and physical principles. The wave height and the peak frequency obtained from the SWAN runs using Weber's bottom friction expression are more consistent with the measurements. The formula of Weber should therefore be preferred when modelling waves in very shallow water. q Ž . R. Padilla-Hernandez .