Drift velocity of spatially decaying waves in a two-layer viscous system

1995 ◽  
Vol 299 ◽  
pp. 217-239 ◽  
Author(s):  
Ismael Piedra-Cueva
Keyword(s):  
Mass Transport ◽  
Lower Layer ◽  
Mass Conservation ◽  
Layer System ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Lagrangian Coordinate ◽  
Progressive Waves ◽  
Lagrangian Coordinate System ◽  
Good Agreement

This paper analyses the mass transport velocity in a two-layer system induced by the action of progressive waves. First the movement inside the two layers is obtained. Next the mass transport of spatially decaying waves is calculated by solving the momentum and mass conservation equations in the Lagrangian coordinate system. Two different physical situations are analysed: the first is waves in a closed channel and the second is waves in an unbounded domain, where the steady-state mass flux may be non-zero. The influence of the viscous properties of the lower layer on the mass transport in both layers is studied. Comparison with the experiments of Sakakiyama & Bijker (1989) in a water-mud system shows good agreement. The results show that the mass transport velocity can be quite different from the velocity given by the rigid bed theory, depending on the physical properties of the lower layer.

scholarly journals MASS TRANSPORT IN PROGRESSIVE WAVES OF PERMANENT TYPE

1980 ◽  
Vol 1 (17) ◽  
pp. 3 ◽  
Author(s):  
Toshito Tsuchiya ◽  
Takashi Yasuda ◽  
Takao Yamashita
Keyword(s):  
Mass Transport ◽  
Finite Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Stokes Drift ◽  
Amplitude Wave ◽  
Wave Tank ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Progressive Waves

Mass transport phenomenon was first recognized by Stokes in 1847 using a Lagrangian description. Later, a basic theory for the mass transport in water waves in viscous fluid and of finite depth was derived by Longuet-Higgins in 1953. Theoretical solutions of mass transport in progressive waves of permanent type are subjected to the definitions of wave celerity in deriving the various finite amplitude wave theories. As it has been generally acknowledged that the Stokes wave theory can not yield a correct prediction of mass transport in the shallow depths, some new theories have been developed. Recently the authors(1974 § 1977) have derived a new finite amplitude wave theory in shallow water for quasi- Stokes and cnoidal waves by the so-called reductive perturbation method, in which the mass transport is formulated both in Lagrangian and Eulerian descriptions. On the experimental verification, Russell and 0sorio(1957) investigated and compared Longuet-Higgins' solution with experimental data of Lagrangian mass transport velocity obtained in a normal closed wave tank of finite length. Since then, many investigations, and nearly all of them, have employed the finite length of wave tank in carrying out their experiments. However, no experiment has yet been attempted at verifying the Stokes drift in progressive waves of permanent type in a wave tank of infinite length. It is not realistic nor economical in constructing such an infinitely long flume to investigate experimentally the mass transport velocity in progressive waves. Instead of using such an ideal wave tank, a new one incorporated with natural water re-circulation was equipped to carry out experiments by the authors(1978). It was confirmed from these experiments that mass transport in progressive waves of permanent type exists in the Same direction of wave propagation throughout the depth, and agrees with both the Stokes drift and the authors' new formulations, within the test range of experiments.

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.

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.

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.

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

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