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.

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 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.

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.

A Numerical Computation of a Confined Rotating Flow

1970 ◽  
Vol 37 (2) ◽  
pp. 480-487 ◽  
Author(s):  
Hsien-Ping Pao
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Bottom Boundary Layer ◽  
Navier Stokes ◽  
Bottom Boundary ◽  
Small Reynolds Numbers ◽  
Viscous Core ◽  
High Reynolds

A numerical investigation of a viscous incompressible fluid confined in a closed circular cylindrical container is made. The top and side wall are in rotation with a constant angular velocity, and the bottom is held fixed. A numerical scheme using the full Navier-Stokes equations is developed. For small or moderate Reynolds numbers (Re = ΩL2/ν), the convergence of iteration is quite rapid. When the Reynolds number increases, the flow in the bottom boundary layer and the viscous core is intensified. An initial value problem is also investigated for Re = 1000 and 5000. The flow development of the bottom boundary layer and the viscous core is clearly exhibited. Some experimental investigation is also made. The numerical solution agrees very well with the analytic solution for small Reynolds numbers and with the experimental observation for moderate and high Reynolds numbers.

scholarly journals TURBULENCE APPEARANCE AT THE BOTTOM OF A SOLITARY WAVE

2012 ◽  
Vol 1 (33) ◽  
pp. 17
Author(s):  
Paolo Blondeaux ◽  
Jan Pralits ◽  
Giovanna Vittori
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Solitary Wave ◽  
Threshold Value ◽  
Bottom Boundary Layer ◽  
Laminar Regime ◽  
Bottom Boundary ◽  
Local Water ◽  
The Stability ◽  
Theoretical Results

The conditions leading to transition and turbulence appearance at the bottom of a solitary wave are determined by means of a linear stability analysis of the laminar flow in the bottom boundary layer. The ratio between the wave amplitude and the thickness of the viscous bottom boundary layer is assumed to be large and a 'momentary' criterion of instability is used. The results obtained show that the laminar regime becomes unstable, during the decelerating phase, if the height of the wave is larger than a threshold value which depends on the ratio between the boundary layer thickness and the local water depth. A comparison of the theoretical results with the experimental measurements of Sumer et al. (2010) seems to support the stability analysis.

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.

Dynamic Response of Pipes Transporting Fluids

1974 ◽  
Vol 96 (2) ◽  
pp. 591-596 ◽  
Author(s):  
Hong-Sun Liu ◽  
C. D. Mote
Keyword(s):  
Mass Transport ◽  
Large Error ◽  
Clear Understanding ◽  
Reference Frequency ◽  
Axial Tension ◽  
Velocity Relationship ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Theoretical Results ◽  
Theoretical Developments

The natural frequency-mass transport velocity relationship was experimentally determined on aluminum tubes throughout a broad mass transport velocity range. Simply-supported, clamped-clamped, and clamped-free conditions were examined. The results are compared with available theoretical developments in each case. Results indicate the theories examined have a range of application limited to the lower transport velocities and even there their application requires knowledge of the no transport reference frequency and the transport dependent axial tension. Process modelling in the higher transport regime is unsatisfactory, and use of the examined theoretical results there should be carefully considered. Since most conditions of instability are associated with high flow velocity, the application of the examined theories to the prediction of response near instability should be done with the clear understanding that large error is possible.

Mass transport under sea waves propagating over a rippled bed

1996 ◽  
Vol 314 ◽  
pp. 247-265 ◽  
Author(s):  
G. Vittori ◽  
P. Blondeaux
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Outer Edge ◽  
Bottom Boundary Layer ◽  
Sea Waves ◽  
Bottom Boundary ◽  
Order Of Magnitude ◽  
Wave Slope ◽  
Rippled Bed ◽  
Sea Wave

Mass transport under a progressive sea wave propagating over a rippled bed is investigated. Wave amplitudes a* of the same order of magnitude as that of the boundary layer thickness δ* and of the ripple wavelength l* are considered. All the above quantities are assumed to be much smaller than the wavelength L* of the sea wave and much larger than the amplitude 2ε* of the ripples. The analysis is carried out up to the second order in the wave slope a*/L* and in the parameter ε*/δ* which is a measure of ripple steepness. Because of these assumptions, the slow damping of wave amplitude in the direction of wave propagation is taken into account. Attention is focused on the bottom boundary layer where an order (ε*/δ*)2 correction of the steady velocity components described by Longuet-Higgins (1953) is found. This correction persists at the outer edge of the bottom boundary layer and affects the solution in the entire water column.

Sign in / Sign up

Export Citation Format

Share Document