scholarly journals NEAR BOTTOM VELOCITIES IN WAVES WITH A CURRENT; ANALYTICAL AND NUMERICAL COMPUTATIONS

1984 ◽  
Vol 1 (19) ◽  
pp. 79 ◽  
Author(s):  
W.G.M. Van Kesteren ◽  
W.T. Bakker
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Bottom Friction ◽  
Bottom Boundary Layer ◽  
Two Dimensional ◽  
Layer Model ◽  
Bottom Boundary ◽  
Waves And Currents ◽  
A Current ◽  
Bottom Velocities

In this paper, starting from the Prandtl hypothesis a three-dimensional numerical bottom boundary layer model has been developed, which allows to calculate bottom friction by a combination of waves and currents. The model has been compared with two-dimensional analytical computations which gave similar results. The bottom friction values found are comparable to the ones, found by Lundgren (1972), however in the most relevant cases somewhat less. Furthermore in the two-dimensional case the model has been compared with measurements of Bakker and Van Doom (1978). With respect to the oscillatory motion, still some minor deviations occur between theory and measurements, due to deficiencies of the Prandtl theory.

A logarithmic bottom boundary layer model for the unsteady and non-uniform swash flow

2021 ◽  
pp. 104048
Author(s):  
Fangfang Zhu ◽  
Nicholas Dodd ◽  
Riccardo Briganti ◽  
Magnus Larson ◽  
Jie Zhang
Keyword(s):  
Boundary Layer ◽  
Bottom Boundary Layer ◽  
Layer Model ◽  
Bottom Boundary ◽  
Boundary Layer Model

scholarly journals Cylinder wakes in shallow oscillatory flow: the coastal island wake problem

2019 ◽  
Vol 874 ◽  
pp. 158-184 ◽  
Author(s):  
Paul M. Branson ◽  
Marco Ghisalberti ◽  
Gregory N. Ivey ◽  
Emil J. Hopfinger
Keyword(s):  
Boundary Layer ◽  
Oscillatory Flow ◽  
Bottom Friction ◽  
Stability Parameter ◽  
Bottom Boundary Layer ◽  
Ekman Pumping ◽  
Bottom Boundary ◽  
Island Wakes ◽  
Island Wake ◽  
The Stability

Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the understanding of this complex flow phenomenon. Here, three-dimensional velocity field measurements of cylinder wakes in shallow-water oscillatory flow are conducted across a parameter space that is typical of tidal flow around shallow islands. The wake form in steady flows is typically described in terms of the stability parameter $S=c_{f}D/h$ (where $D$ is the island diameter, $h$ is the water depth and $c_{f}$ is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan–Carpenter number $KC=U_{0}T/D$ (where $U_{0}$ is the tidal velocity amplitude and $T$ is the tidal period). In this study we demonstrate that when the influence of bottom friction is confined to a Stokes boundary layer the stability parameter is given by $S=\unicode[STIX]{x1D6FF}^{+}/KC$ where $\unicode[STIX]{x1D6FF}^{+}$ is the ratio of the wavelength of the Stokes bottom boundary layer to the depth. Three classes of wake form are observed with decreasing wake stability: (i) steady bubble for $S\gtrsim 0.1$; (ii) unsteady bubble for $0.06\lesssim S\lesssim 0.1$; and (iii) vortex shedding for $S\lesssim 0.06$. Transitions in wake form and wake stability are shown to depend on the magnitude and temporal evolution of the wake return flow. Scaling laws are developed to allow upscaling of the laboratory results to island wakes. Vertical and lateral transport depend on three parameters: (i) the flow aspect ratio $h/D$; (ii) the amplitude of tidal motion relative to the island size, given by $KC$; and (iii) the relative influence of bottom friction to the flow depth, given by $\unicode[STIX]{x1D6FF}^{+}$. A model of wake upwelling based on Ekman pumping from the bottom boundary layer demonstrates that upwelling in the near-wake region of an island scales with $U_{0}(h/D)KC^{1/6}$ and is independent of the wake form. Finally, we demonstrate an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability.

scholarly journals The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Downslope Regime

2019 ◽  
Vol 49 (2) ◽  
pp. 469-487 ◽  
Author(s):  
Xiaozhou Ruan ◽  
Andrew F. Thompson ◽  
John R. Taylor
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Three Dimensional ◽  
Wall Stress ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Momentum Balance ◽  
Bottom Boundary ◽  
Obukhov Length ◽  
Turbulent Characteristics

AbstractThe dynamics of a stratified oceanic bottom boundary layer (BBL) over an insulating, sloping surface depend critically on the intersection of density surfaces with the bottom. For an imposed along-slope flow, the cross-slope Ekman transport advects density surfaces and generates a near-bottom geostrophic thermal wind shear that opposes the background flow. A limiting case occurs when a momentum balance is achieved between the Coriolis force and a restoring buoyancy force in response to the displacement of stratified fluid over the slope: this is known as Ekman arrest. However, the turbulent characteristics that accompany this adjustment have received less attention. We present two estimates to characterize the state of the BBL based on the mixed layer thickness: Ha and HL. The former characterizes the steady Ekman arrested state, and the latter characterizes a relaminarized state. The derivation of HL makes use of a newly defined slope Obukhov length Ls that characterizes the relative importance of shear production and cross-slope buoyancy advection. The value of Ha can be combined with the temporally evolving depth of the mixed layer H to form a nondimensional variable H/Ha that provides a similarity prediction of the BBL evolution across different turbulent regimes. The length scale Ls can also be used to obtain an expression for the wall stress when the BBL relaminarizes. We validate these relationships using output from a suite of three-dimensional large-eddy simulations. We conclude that the BBL reaches the relaminarized state before the steady Ekman arrested state. Calculating H/Ha and H/HL from measurements will provide information on the stage of oceanic BBL development being observed. These diagnostics may also help to improve numerical parameterizations of stratified BBL dynamics over sloping topography.

Two-dimensional vortex structures in the bottom boundary layer of progressive and solitary waves

2013 ◽  
Vol 728 ◽  
pp. 340-361 ◽  
Author(s):  
Pietro Scandura
Keyword(s):  
Boundary Layer ◽  
Solitary Waves ◽  
Small Amplitude ◽  
Flow Instability ◽  
Vortex Structures ◽  
Bottom Boundary Layer ◽  
Two Dimensional ◽  
Bottom Boundary ◽  
Vortex Layer ◽  
Vortex Tubes

AbstractThe two-dimensional vortices characterizing the bottom boundary layer of both progressive and solitary waves, recently discovered by experimental flow visualizations and referred to as vortex tubes, are studied by numerical solution of the governing equations. In the case of progressive waves, the Reynolds numbers investigated belong to the subcritical range, according to Floquet linear stability theory. In such a range the periodic generation of strictly two-dimensional vortex structures is not a self-sustaining phenomenon, being the presence of appropriate ambient disturbances necessary to excite certain modes through a receptivity mechanism. In a physical experiment such disturbances may arise from several coexisting sources, among which the most likely is roughness. Therefore, in the present numerical simulations, wall imperfections of small amplitude are introduced as a source of disturbances for both types of wave, but from a macroscopic point of view the wall can be regarded as flat. The simulations show that even wall imperfections of small amplitude may cause flow instability and lead to the appearance of vortex tubes. These vortices, in turn, interact with a vortex layer adjacent to the wall and characterized by vorticity opposite to that of the vortex tubes. In a first stage such interaction gives rise to corrugation of the vortex layer and this affects the spatial distribution of the wall shear stress. In a second stage the vortex layer rolls up and pairs of counter-rotating vortices are generated, which leave the bottom because of the self-induced velocity.

Two-dimensional instability of the bottom boundary layer under a solitary wave

2015 ◽  
Vol 27 (4) ◽  
pp. 044101 ◽  
Author(s):  
Mahmoud M. Sadek ◽  
Luis Parras ◽  
Peter J. Diamessis ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Solitary Wave ◽  
Bottom Boundary Layer ◽  
Two Dimensional ◽  
Bottom Boundary ◽  
Dimensional Instability
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