scholarly journals IMPROVEMENT OF BOTTOM BOUNDARY LAYERS MODELING UNDER INTERACTIONS OF WAVE AND WAVE-INDUCED CURRENT

2011 ◽  
Vol 1 (32) ◽  
pp. 46
Author(s):  
Jinhai Zheng ◽  
Chi Zhang ◽  
Yigang Wang ◽  
Zeki Demirbilek
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Bottom Boundary Layer ◽  
Induced Current ◽  
Horizontal Pressure Gradient ◽  
Bottom Boundary ◽  
Bottom Boundary Layers ◽  
Horizontal Pressure ◽  
The Mean ◽  
Wave Induced

The bottom boundary layer characteristics beneath waves transforming on a natural beach are specifically affected both by wave and wave-induced current. This study presents an improved approach for coastal bottom boundary layers modeling under interactions of wave and wave-induced current. The improvement is achieved by formulating the mean horizontal pressure gradient term in the boundary layer equation with wave parameters and mean water level. This formulation represents the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient in a spatially transforming wave field, accounting for the effect of the wave-induced cross-shore current. Model is validated with experimental data for normally incident shoaling wave over a sloping bed. Calculated results agree well with data for instantaneous velocity profiles, wave oscillating amplitudes and mean velocity profiles. In particular, model reasonably reproduces the observed local onshore mean flow near the bottom beneath shoaling wave. It is revealed that the proposed formulation of the mean horizontal pressure gradient plays an important role in bottom boundary layer modeling under wave transforming over an variable near-shore bathymetry, and that the present model can be conveniently and reliably coupled with a sediment transport model to study coastal processes in engineering applications.

scholarly journals NUMERICAL MODELING OF A TURBULENT BOTTOM BOUNDARY LAYER UNDER SOLITARY WAVES ON A SMOOTH SURFACE

2018 ◽  
pp. 26
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Solitary Waves ◽  
Bottom Boundary Layer ◽  
Stream Velocity ◽  
Bottom Boundary ◽  
Sediment Movement ◽  
Bottom Boundary Layers ◽  
Turbulent Models

A number of studies on bottom boundary layers under sinusoidal and cnoidal waves were carried out in the past owing to the role of bottom shear stress on coastal sediment movement. In recent years, the bottom boundary layers under long waves have attracted considerable attention due to the occurrence of huge tsunamis and corresponding sediment movement. In the present study two-equation turbulent models proposed by Menter(1994) have been applied to a bottom boundary layer under solitary waves. A comparison has been made for cross-stream velocity profile and other turbulence properties in x-direction.

The Relationships among Wind, Horizontal Pressure Gradient, and Turbulent Momentum Transport during CASES-99

2013 ◽  
Vol 70 (11) ◽  
pp. 3397-3414 ◽  
Author(s):  
Jielun Sun ◽  
Donald H. Lenschow ◽  
Larry Mahrt ◽  
Carmen Nappo
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Pressure Gradient ◽  
Coriolis Force ◽  
Wind Direction ◽  
Momentum Flux ◽  
Momentum Transport ◽  
Horizontal Pressure Gradient ◽  
Horizontal Pressure ◽  
Turbulent Momentum

Abstract Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground occurred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s−1, WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP. In the along-wind direction, the horizontal pressure gradient is observed to be well correlated with the quadratic wind speed, which is demonstrated to be an approximate balance between the horizontal pressure gradient and the vertical convergence of the turbulent momentum flux. That is, antitriptic balance occurs in the along-wind direction when the wind is toward higher pressure. In the crosswind direction, the pressure gradient varies approximately linearly with wind speed and opposes the Coriolis force, suggesting the importance of the Coriolis force and approximate geotriptic balance of the airflow. A simple one-dimensional planetary boundary layer eddy diffusivity model demonstrates the possibility of wind directed toward higher pressure for a baroclinic boundary layer and the contribution of the vertical turbulent momentum flux to this phenomenon.

Large eddy simulation of a stratified boundary layer under an oscillatory current

2009 ◽  
Vol 643 ◽  
pp. 233-266 ◽  
Author(s):  
BISHAKHDATTA GAYEN ◽  
SUTANU SARKAR ◽  
JOHN R. TAYLOR
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Mixed Layer ◽  
Numerical Study ◽  
Bottom Boundary Layer ◽  
Mean Velocity ◽  
Bottom Boundary ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Mean

A numerical study based on large eddy simulation is performed to investigate a bottom boundary layer under an oscillating tidal current. The focus is on the boundary layer response to an external stratification. The thermal field shows a mixed layer that is separated from the external stratified fluid by a thermocline. The mixed layer grows slowly in time with an oscillatory modulation by the tidal flow. Stratification strongly affects the mean velocity profiles, boundary layer thickness and turbulence levels in the outer region although the effect on the near-bottom unstratified fluid is relatively mild. The turbulence is asymmetric between the accelerating and decelerating stages. The asymmetry is more pronounced with increasing stratification. There is an overshoot of the mean velocity in the outer layer; this jet is linked to the phase asymmetry of the Reynolds shear stress gradient by using the simulation data to examine the mean momentum equation. Depending on the height above the bottom, there is a lag of the maximum turbulent kinetic energy, dissipation and production with respect to the peak external velocity and the value of the lag is found to be influenced by the stratification. Flow instabilities and turbulence in the bottom boundary layer excite internal gravity waves that propagate away into the ambient. Unlike the steady case, the phase lines of the internal waves change direction during the tidal cycle and also from near to far field. The frequency spectrum of the propagating wave field is analysed and found to span a narrow band of frequencies clustered around 45°.

scholarly journals Acceleration of a Stratified Current over a Sloping Bottom, Driven by an Alongshelf Pressure Gradient*

2005 ◽  
Vol 35 (8) ◽  
pp. 1305-1317 ◽  
Author(s):  
David C. Chapman ◽  
Steven J. Lentz
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Vertical Shear ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Model Calculations ◽  
Bottom Boundary ◽  
Bottom Stress ◽  
Sloping Bottom

Abstract An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S > 0.2) has a major impact. These results are supported by numerical model calculations.

scholarly journals BED SHEAR STRESS IN UNSTEADY FLOW

2011 ◽  
Vol 1 (32) ◽  
pp. 8 ◽  
Author(s):  
Paul Andrew Guard ◽  
Peter Nielsen ◽  
Tom E Baldock
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Water Surface ◽  
Free Stream ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Horizontal Pressure Gradient ◽  
Friction Factors ◽  
Horizontal Pressure

Standard engineering methods of estimating bed shear stress using friction factors can fail spectacularly in unsteady hydrodynamic conditions. This paper demonstrates this fact using direct measurements of bed shear stresses under irregular waves using a shear plate apparatus. The measurements are explained in terms of the influence of the horizontal pressure gradient and the shear stresses acting on the surface of the plate. The horizontal fluid velocity at the edge of the boundary layer and the water surface elevation and slope were also measured. The paper demonstrates that the water surface measurements can be used to obtain accurate estimates of the forces on the bed, by employing Fourier analysis techniques or an innovative convolution integral method. The experimental results indicate that an offshore bed shear stress may be recorded while the free stream velocity remains onshore at all times. This demonstrates the failure of the standard engineering friction factor method in this scenario, since negative friction factors would be required. Important questions are raised regarding the appropriate definition for the bed shear stress when the vertical gradient of the shear stress is large. It is shown that it is problematic to define a single value for a “bed” shear stress in the presence of a strong horizontal pressure gradient. It is also argued that the natural driver for any model used to predict bed shear stress is the pressure gradient (or its proxy the free stream acceleration), rather than the velocity. This allows for accurate calculation of both acceleration effects (more rapid acceleration leads to a thinner boundary layer and higher shear stress) and also the direct action of the horizontal pressure gradient.

scholarly journals Dissipative Losses in Nonlinear Internal Waves Propagating across the Continental Shelf

2007 ◽  
Vol 37 (7) ◽  
pp. 1989-1995 ◽  
Author(s):  
J. N. Moum ◽  
D. M. Farmer ◽  
E. L. Shroyer ◽  
W. D. Smyth ◽  
L. Armi
Keyword(s):  
Boundary Layer ◽  
Potential Energy ◽  
Continental Shelf ◽  
Water Depth ◽  
Wave Speed ◽  
Bottom Boundary Layer ◽  
Propagation Path ◽  
Nonlinear Internal Wave ◽  
Bottom Boundary ◽  
Wave Induced

Abstract A single nonlinear internal wave tracked more than 100 wavelengths across Oregon’s continental shelf over a 12-h period exhibited nearly constant wave speed, c = 0.75 m s−1, and amplitude, a = 15 m. The wavelength L gradually decreased from 220 m in 170-m water depth to 60 m in 70-m water depth. As the water shallowed beyond 50 m, the wave became unrecognizable as such. The total energy decreased from 1.1 to 0.5 MJ m−1. The rate at which wave energy was lost, −dE/dt = 14 [7, 22] W m−1, was approximately equal to the energy lost to turbulence dissipation, ρɛ = 10 [7, 14] W m−1, as inferred from turbulence measurements in the wave cores plus estimates in the wave-induced bottom boundary layer. The approximate balance, dE/dt = −ρɛ, differs from the solibore model of Henyey and Hoering in which the potential energy across the wave balances ρɛ. However, other evidence suggests that the wave evolved from a solibore-like state to a dissipative solitary wavelike state over the observed propagation path.

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