On the mass transport induced by oscillatory flow in a turbulent boundary layer

1970 ◽  
Vol 43 (1) ◽  
pp. 177-185 ◽  
Author(s):  
B. Johns
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Mass Transport ◽  
Eddy Viscosity ◽  
Oscillatory Flow ◽  
Standing Waves ◽  
Turbulent Layer ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Limiting Value

Oscillatory flow in a turbulent boundary layer is modelled by using a coefficient of eddy viscosity whose value depends upon distance from a fixed boundary. A general oscillatory flow is prescribed beyond the layer, and the model is used to calculate the mass transport velocity induced by this within the layer. The result is investigated numerically for a representative distribution of eddy viscosity and the conclusions interpreted in terms of the mass transport induced by progressive and standing waves. For progressive waves, the limiting value of the mass transport velocity at the outer edge of the layer is the same as for laminar flow. For standing waves, the limiting value is reduced relative to its laminar value but, within the lowermost 25% of the layer, there is a drift which is reversed relative to the limiting value. This is considerably stronger than its counterpart in the laminar case and, in view of the greater thickness of the turbulent layer, it may make a dominant contribution to the net movement of loose bed material by a standing wave system.

Double boundary layers in standing interfacial waves

1976 ◽  
Vol 76 (4) ◽  
pp. 819-828 ◽  
Author(s):  
B. D. Dore
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Layer Structure ◽  
Standing Waves ◽  
Boundary Layer Theory ◽  
Two Dimensional ◽  
Transport Velocity ◽  
Oscillatory Velocity ◽  
Mass Transport Velocity ◽  
The Mean

The double-boundary-layer theory of Stuart (1963, 1966) and Riley (1965, 1967) is employed to investigate the mass transport velocity due to two-dimensional standing waves in a system comprising two homogeneous fluids of different densities and viscosities. The most important double-boundary-layer structure occurs in the neighbourhood of the oscillating interface, and the possible existence of jet-like motions is envisaged at nodal positions, owing to the nature of the mean flows in the layers. In practice, the magnitude of the mass transport velocity can be a significant fraction of that of the primary, oscillatory velocity.

Mass transport in water waves over an elastic bed

1995 ◽  
Vol 450 (1939) ◽  
pp. 371-390 ◽  
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Mass Transport ◽  
Water Waves ◽  
Viscous Boundary Layer ◽  
Curvilinear Coordinate ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Orthogonal Curvilinear Coordinate System ◽  
Viscous Boundary

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

Mass transport in a turbulent boundary layer under a progressive water wave

1984 ◽  
Vol 146 ◽  
pp. 303-312 ◽  
Author(s):  
S. J. Jacobs
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Water Wave ◽  
Approximate Solutions ◽  
Reynolds Numbers ◽  
Bottom Boundary Layer ◽  
Bottom Boundary ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Theoretical Results

The bottom boundary layer under a progressive water wave is studied using Saffman's turbulence model. Saffman's equations are analysed asymptotically for the case Re [Gt ] 1, where Re is a Reynolds number based on a characteristic magnitude of the orbital velocity and a characteristic orbital displacement. Approximate solutions for the mass-transport velocity at the edge of the boundary layer and for the bottom stress are obtained, and Taylor's formula for the rate of energy dissipation is verified. The theoretical results are found to agree well with observations for sufficiently large Reynolds numbers.

Mass transport in the bottom boundary layer of cnoidal waves

1976 ◽  
Vol 74 (3) ◽  
pp. 401-413 ◽  
Author(s):  
M. De St Q. Isaacson
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Wave Theory ◽  
Bottom Boundary Layer ◽  
Inviscid Fluid ◽  
Viscous Boundary Layer ◽  
Cnoidal Waves ◽  
Bottom Boundary ◽  
Transport Velocity ◽  
Mass Transport Velocity

This study deals with the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport velocity distributions through the boundary layer are derived and compared with that predicted by Longuet-Higgins (1953) for sinusoidal waves. The mass transport at the outer edge of the boundary layer is compared with various theoretical results for an inviscid fluid based on cnoidal wave theory and also with previous experimental results. The effect of the viscous boundary layer is to establish uniquely the bottom mass transport and this is appreciably greater than the somewhat arbitrary prediction for an inviscid fluid.

The second approximation to mass transport in cnoidal waves

1976 ◽  
Vol 78 (3) ◽  
pp. 445-457 ◽  
Author(s):  
Michael De St Q. Isaacson
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Perturbation Parameter ◽  
Depth Range ◽  
Third Order ◽  
Cnoidal Waves ◽  
The Third ◽  
First Approximation ◽  
Transport Velocity ◽  
Mass Transport Velocity

A second approximation is developed for the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport profiles through the boundary layer are obtained by considering terms of up to third order in the perturbation parameter. A comparison with results based on a first approximation indicates that the effect of the third-order terms is to predict a smaller mass-transport velocity and that this difference is generally significant, particularly for waves extending to the intermediate depth range. The predicted correction to the first approximation is qualitatively supported by experimental evidence.

scholarly journals A STUDY ON MASS TRANSPORT IN BOUNDARY LAYERS IN STANDING WAVES

1968 ◽  
Vol 1 (11) ◽  
pp. 15 ◽  
Author(s):  
Hideaki Noda
Keyword(s):  
Mass Transport ◽  
Boundary Layers ◽  
Standing Waves ◽  
Bottom Boundary Layer ◽  
Particle Methods ◽  
Bottom Boundary ◽  
Laminar Boundary Layers ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Basic Equations

This paper deals with the mass transport in the boundary layers developed on smooth and horizontal bottoms by standing waves in shallow water. In a theoretical approach, the basic equations of laminar boundary layers are applied to solving the oscillatory motion in the boundary layers caused by the standing waves. The mass transport velocities are derived on the basis of solutions of the second approximation which describe the flow velocity near the bottom, and the effects of convective terms involved in the basic equations are investigated. Experimental measurements in standing waves of mass transport velocity in the bottom boundary layer were carried out using dye-streak and solid-particle methods. The experimental data are compared with the theoretical prediction.

Mass transport under partially reflected waves in a rectangular channel

1994 ◽  
Vol 266 ◽  
pp. 121-145 ◽  
Author(s):  
Jiangang Wen ◽  
Philip L.-F. Liu
Keyword(s):  
Mass Transport ◽  
Vector Potential ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Scalar Potential ◽  
Second Order ◽  
Nonlinear Transport ◽  
Reflected Waves ◽  
Transport Velocity ◽  
Mass Transport Velocity

Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.

scholarly journals Wind-Driven Ageostrophic Transport in the North Equatorial Countercurrent of the Eastern Pacific at 95°W

2009 ◽  
Vol 39 (11) ◽  
pp. 2985-2998 ◽  
Author(s):  
Janet Sprintall ◽  
Sean Kennan ◽  
Yoo Yin Kim ◽  
Peter Niiler
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Ekman Transport ◽  
Momentum Balance ◽  
Altimeter Data ◽  
Turbulent Stress ◽  
Wind Stress Curl ◽  
Turbulent Layer ◽  
Near Surface ◽  
The North

Abstract Observations of horizontal velocity from two shipboard acoustic Doppler current profilers (ADCPs), as well as wind, temperature, and salinity observations from a cruise during June–July 2001, are used to compute a simplified mean meridional momentum balance of the North Equatorial Countercurrent (NECC) at 95°W. The terms that are retained in the momentum balance and derived using the measurements are the Coriolis and pressure gradient forces, and the vertical divergence of the turbulent stress. All terms were vertically integrated over the surface turbulent layer. The K-profile parameterization (KPP) prescribed Richardson number (Ri) is used to determine the depth of the turbulent boundary layer h at which the turbulent stress and its gradient vanish. At the time of the cruise, surface drifters and altimeter data show the flow structure of the NECC was complicated by the presence of tropical instability waves to the south and a strong Costa Rica Dome to the north. Nonetheless, a consistent, simplified momentum balance for the surface layer was achieved from the time mean of 19 days of repeat transects along 95°W with a 0.5° latitude resolution. The best agreement between the ageostrophic transport determined from the near-surface cruise measurements and the wind-derived Ekman transport was obtained for an Ri of 0.23 ± 0.05. The corresponding h ranges from ∼55 m at 4°N to ∼30 m within the NECC core (4.5°–6°N) and shoaling to just 15 m at 7°N. In general, the mean ageostrophic and Ekman transports decreased from south to north along the 95°W transect, although within the core of the NECC both transports were relatively strong and steady. This study underscores the importance of the southerly wind-driven eastward Ekman transport in the turbulent boundary layer before the NECC becomes fully developed later in the year through indirect forcing from the wind stress curl.

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