Wave-induced vorticity in free-surface boundary layers: application to mass transport in edge waves

1975 ◽  
Vol 70 (2) ◽  
pp. 257-266 ◽  
Author(s):  
B. D. Dore
Keyword(s):  
Free Surface ◽  
Mass Transport ◽  
Gravity Waves ◽  
Surface Boundary ◽  
Edge Waves ◽  
Vorticity Field ◽  
Surface Boundary Layer ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Wave Induced

The time-averaged vorticity field within the free-surface boundary layer associated with a general class of propagating gravity waves is considered. The principal results are applied in a calculation of the mass transport velocity field for edge waves.

Interaction of finite-amplitude waves with vertically sheared current fields

2009 ◽  
Vol 627 ◽  
pp. 179-213 ◽  
Author(s):  
OKEY G. NWOGU
Keyword(s):  
Free Surface ◽  
Transport Equation ◽  
Gravity Waves ◽  
Modulational Instability ◽  
Surface Boundary ◽  
Mean Flow ◽  
Vorticity Field ◽  
Time Step ◽  
Vorticity Transport ◽  
Wave Induced

A computationally efficient numerical method is developed to investigate nonlinear interactions between steep surface gravity waves and depth-varying ocean currents. The free-surface boundary conditions are used to derive a coupled set of equations that are integrated in time for the evolution of the free-surface elevation and tangential component of the fluid velocity at the free surface. The vector form of Green's second identity is used to close the system of equations. The closure relationship is consistent with Helmholtz's decomposition of the velocity field into rotational and irrotational components. The rotational component of the flow field is given by the Biot–Savart integral, while the irrotational component is obtained from an integral of a mixed distribution of sources and vortices over the free surface. Wave-induced changes to the vorticity field are modelled using the vorticity transport equation. For weak currents, an explicit expression is derived for the wave-induced vorticity field in Fourier space that negates the need to numerically solve the vorticity transport equation. The computational efficiency of the numerical scheme is further improved by expanding the kernels of the boundary and volume integrals in the closure relationship as a power series in a wave steepness parameter and using the fast Fourier transform method to evaluate the leading-order contribution to the convolution integrals. This reduces the number of operations at each time step from O(N2) to O(NlogN) for the boundary integrals and O[(NM)2] to O(NlogN) for the volume integrals, where N is the number of horizontal grid points and M is the number of vertical layers, making the model an order of magnitude faster than traditional boundary/volume integral methods. The numerical model is used to investigate nonlinear wave–current interaction in depth-uniform current fields and the modulational instability of gravity waves in an exponentially sheared current in deep water. The numerical results demonstrate that the mean flow vorticity can significantly affect the growth rate of extreme waves in narrowband sea states.

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.

scholarly journals THE EFFECT OF ROUGHNESS ON THE MASS-TRANSPORT OF PROGRESSIVE GRAVITY WAVES

1966 ◽  
Vol 1 (10) ◽  
pp. 11 ◽  
Author(s):  
Arthur Brebner ◽  
J.A. Askew ◽  
S.W. Law
Keyword(s):  
Mass Transport ◽  
Gravity Waves ◽  
Orbital Motion ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Maximum Value ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
The Mean

On the basis of non-viscous small amplitude firstorder theory the maximum value of the horizontal orbital motion at the bed in water of constant depth his given by /U/n yy* »* " r •»** */i where k = /L, H is the wave height crest to trough, T is the period, and L the wave length (L = Sry2jr Arf 2*%/L ). On the basis of finite amplitude wave theory where the particle orbits are not closed ana by the insertion of the viscous laminar boundary layer (the conducti6n solution) the mean drift velocity or mass transport velocity on a perfectly smooth bed is given by Longuet- Higgins (1952) as 7, K H* kcr where

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.

Sediment transport by waves and currents

1983 ◽  
Vol 10 (1) ◽  
pp. 142-149 ◽  
Author(s):  
Michael C. Quick
Keyword(s):  
Sediment Transport ◽  
Mass Transport ◽  
Power Relationship ◽  
Zero Current ◽  
Transport Direction ◽  
Transport Velocity ◽  
Waves And Currents ◽  
Mass Transport Velocity ◽  
Combined Action ◽  
The Waves

Sediment transport is measured under the combined action of waves and currents. Measurements are made with currents in the direction of wave advance and with currents opposing the wave motion. Theoretical relationships are considered that predict the wave velocity field and the mass transport velocity for zero current and for steady currents.Following Bagnold's approach, a transport power relationship is developed to predict the sediment transport rate. Making assumptions for the mass transport velocity, the transport power is shown to agree with the measured sediment transport rates. It is particularly noted that the sediment transport direction is mainly determined by the direction of wave movement, even for adverse currents, until the waves start to break. Keywords: sediment transport, waves and currents, coastal engineering.

The effect of a semi-contaminated free surface on mass transport

1974 ◽  
Vol 75 (2) ◽  
pp. 283-294 ◽  
Author(s):  
D. Porter ◽  
B. D. Dore
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Mass Transport ◽  
Mixed Boundary ◽  
Surface Film ◽  
Vertical Displacement ◽  
Mass Transport Velocity ◽  
Harmonic Equation ◽  
The Waves

AbstractThe mass transport velocity field is determined for surface waves which propagate from a region with a clean free surface into a region beneath an inextensible surface film. The waves are assumed to be incident normally on the edge of the film. Determination of this velocity field requires the investigation of a mixed boundary value problem for the bi-harmonic equation, the solution of which is obtained using the Wiener–Hopf technique. Streamlines for the mean motion of the fluid particles are thus obtained. It is found that considerable vertical displacement of fluid is possible due to the presence of the surface film.

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