scholarly journals MASS TRANSPORT OF WAVES ON THE SURFACE OF THE FLUID

2021 ◽  
pp. 148-151
Author(s):  
V.M. Shakhin
Keyword(s):  
Mass Transport ◽  
Cnoidal Waves ◽  
Progressive Waves

This paper is devoted to problem of mass transport of fluid for the surface progressive waves. New solutions for transitional current are obtained. Both Stokes and cnoidal waves are considered.

scholarly journals COMPENSATORY REVERSE FLOW OF PROGRESSIVE WAVES WITH FINITE AMPLITUDE

2017 ◽  
pp. 9
Author(s):  
Victor M. Shakhin ◽  
Tatiana V. Shakhina
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Mass Transport ◽  
Reverse Flow ◽  
Finite Amplitude ◽  
Cnoidal Waves ◽  
Progressive Waves ◽  
Theoretical Results

This paper is devoted to problem of mass transport of fluid for the surface progressive waves. Both Stokes and cnoidal waves are considered. New solutions for the transitional current are obtained. It is discovered that the mass transport of fluid in the direction of wave propagation exists only in the top layer. In the underlying layers a compensatory reverse flow is formed. The existence of a compensatory flow was verified experimentally. It is revealed that theoretical results duly conform to experimental data.

scholarly journals AN EXPERIMENTAL INVESTIGATION OF DRIFT PROFILES IN A CLOSED CHANNEL

2011 ◽  
Vol 1 (6) ◽  
pp. 10 ◽  
Author(s):  
R. C. H. Russell ◽  
J. D. C. Osorio
Keyword(s):  
Mass Transport ◽  
Water Waves ◽  
Order Theory ◽  
Beach Erosion ◽  
Research Station ◽  
Inviscid Fluid ◽  
First Order Theory ◽  
Closed Orbits ◽  
Slow Drift ◽  
Progressive Waves

The first order theory of water waves states that water particles move in closed orbits; that this was not exactly so, and that there was a slow drift of the water in the direction of wave propagation, was first realised by Stokes(1) who proposed a solution of the horizontal drift or mass transport for waves in an inviscid fluid. Recently the effect of the viscosity has been investigated by .Longuet-Higgins (2) Experimental measurements have been made by Caligny (3), the U.S. Beach Erosion Board (4), Bagnold (5), and previously by the Hydraulics Research Station. The evidence from these sources is incomplete. In the experiments described in this paper measurements of the mass transport at all levels were made with progressive waves, varying in length from about 1 1/2 to 50 ft and in water between 6 and 20 in. deep.

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.

Mass Transport in Progressive Waves of Permanent Type

1980 ◽  
Author(s):  
Yoshito Tsuchiya ◽  
Takashi Yasuda ◽  
Takao Yamashita
Keyword(s):  
Mass Transport ◽  
Progressive Waves

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.

Mass transport in Cnoidal waves

1968 ◽  
Vol 73 (18) ◽  
pp. 5973-5979 ◽  
Author(s):  
B. Le Méhauté
Keyword(s):  
Mass Transport ◽  
Cnoidal Waves

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.

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.

Sign in / Sign up

Export Citation Format

Share Document