scholarly journals Wave blocking phenomenon of surface waves on a shear flow with a constant vorticity

2016 ◽  
Vol 28 (3) ◽  
pp. 032102 ◽  
Author(s):  
Philippe Maïssa ◽  
Germain Rousseaux ◽  
Yury Stepanyants
Keyword(s):  
Shear Flow ◽  
Surface Waves ◽  
Constant Vorticity ◽  
Wave Blocking

Shear Flow Driven Compressional Magnetohydrodynamic Surface Waves in Plasmas

2001 ◽  
Vol 63 (2) ◽  
pp. 150-153
Author(s):  
D Jovanović ◽  
J Vranjes ◽  
P K Shukla
Keyword(s):  
Shear Flow ◽  
Surface Waves

scholarly journals Ship waves in the presence of uniform vorticity

2014 ◽  
Vol 742 ◽  
Author(s):  
Simen Å. Ellingsen
Keyword(s):  
Shear Flow ◽  
Finite Depth ◽  
Critical Value ◽  
Wave Problem ◽  
Transverse Waves ◽  
Ship Waves ◽  
Striking Result ◽  
Constant Vorticity ◽  
Shear Current ◽  
Half Angle

AbstractLord Kelvin’s result that waves behind a ship lie within a half-angle $\phi _{\mathit{K}}\approx 19^{\circ }28'$ is perhaps the most famous and striking result in the field of surface waves. We solve the linear ship wave problem in the presence of a shear current of constant vorticity $S$, and show that the Kelvin angles (one each side of wake) as well as other aspects of the wake depend closely on the ‘shear Froude number’ $\mathit{Fr}_{\mathit{s}}=VS/g$ (based on length $g/S^2$ and the ship’s speed $V$), and on the angle between current and the ship’s line of motion. In all directions except exactly along the shear flow there exists a critical value of $\mathit{Fr}_{\mathit{s}}$ beyond which no transverse waves are produced, and where the full wake angle reaches $180^\circ $. Such critical behaviour is previously known from waves at finite depth. For side-on shear, one Kelvin angle can exceed $90^\circ $. On the other hand, the angle of maximum wave amplitude scales as $\mathit{Fr}^{-1}$ ($\mathit{Fr}$ based on size of ship) when $\mathit{Fr}\gg 1$, a scaling virtually unaffected by the shear flow.

Wind-Generated Surface Waves on a Viscous Fluid

1985 ◽  
Vol 52 (1) ◽  
pp. 208-212 ◽  
Author(s):  
C. Katsis ◽  
T. R. Akylas
Keyword(s):  
Shear Flow ◽  
Viscous Fluid ◽  
Surface Waves ◽  
High Viscosity ◽  
Wave Generation ◽  
Generation Mechanism ◽  
Flow Profile ◽  
Wind Speeds ◽  
Dominant Wave ◽  
Tollmien Schlichting

The excitation of surface waves on a viscous fluid by shear flows is studied. Turbulent and laminar air flows over oil of low and high viscosity are considered. It is found that the dominant wave-generation mechanism depends crucially on the shear-flow profile: for a turbulent flow, long surface waves are generated at low wind speeds due to the work done by the stress components in phase with the surface slope, while Kelvin-Helmholtz instability is responsible for the excitation of short waves at higher wind speeds. On the other hand, for a laminar shear flow, direct resonance between surface waves and Tollmien-Schlichting waves in the shear flow is the dominant wave-generation mechanism.

Vorticity effects on nonlinear wave–current interactions in deep water

2015 ◽  
Vol 778 ◽  
pp. 314-334 ◽  
Author(s):  
R. M. Moreira ◽  
J. T. A. Chacaltana
Keyword(s):  
Shear Flow ◽  
Nonlinear Wave ◽  
Deep Water ◽  
Water Waves ◽  
Wave Breaking ◽  
Surface Profile ◽  
Boundary Integral ◽  
Progressive Waves ◽  
Wave Blocking ◽  
Deep Water Waves

The effects of uniform vorticity on a train of ‘gentle’ and ‘steep’ deep-water waves interacting with underlying flows are investigated through a fully nonlinear boundary integral method. It is shown that wave blocking and breaking can be more prominent depending on the magnitude and direction of the shear flow. Reflection continues to occur when sufficiently strong adverse currents are imposed on ‘gentle’ deep-water waves, though now affected by vorticity. For increasingly positive values of vorticity, the induced shear flow reduces the speed of right-going progressive waves, introducing significant changes to the free-surface profile until waves are completely blocked by the underlying current. A plunging breaker is formed at the blocking point when ‘steep’ deep-water waves interact with strong adverse currents. Conversely negative vorticities augment the speed of right-going progressive waves, with wave breaking being detected for strong opposing currents. The time of breaking is sensitive to the vorticity’s sign and magnitude, with wave breaking occurring later for negative values of vorticity. Stopping velocities according to nonlinear wave theory proved to be sufficient to cause wave blocking and breaking.

Surface waves on an inviscid shear flow in a channel

Wave Motion ◽  
1994 ◽  
Vol 19 (2) ◽  
pp. 135-144 ◽  
Author(s):  
John P. McHugh
Keyword(s):  
Shear Flow ◽  
Surface Waves

scholarly journals Diffusion-affected passive scalar transport in an ellipsoidal vortex in a shear flow

2013 ◽  
Vol 20 (4) ◽  
pp. 437-444 ◽  
Author(s):  
K. V. Koshel ◽  
E. A. Ryzhov ◽  
V. V. Zhmur
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Passive Scalar ◽  
Scalar Transport ◽  
Buoyancy Frequency ◽  
Diffusion Term ◽  
Constant Vorticity ◽  
Perturbed State ◽  
Passive Scalar Transport ◽  
Oceanic Eddy

Abstract. By employing an analytical model for a constant-vorticity distributed vortex, namely, the ellipsoidal vortex embedded in a constant buoyancy frequency shear flow, the problem of the passive scalar transport through the vortex's boundary is addressed. Since the model's governing equations do not allow such transition to occur, we implement a low-scale diffusion process into the vortex model. Taking into consideration the diffusion term, we study the passive scalar transport in a steady state (the boundary of the ellipsoidal vortex does not change in time) and in a perturbed state (the boundary of the ellipsoidal vortex changes in time periodically) within the time scope corresponding to the characteristic life cycle of a mesoscale oceanic eddy. An increase of the passive scalar transport through the boundary in the perturbed state in comparison with the steady state due to the irregular dynamics of the surrounding flow is shown. The applicability scopes of the investigation for studying oceanic eddies in nature are discussed.

scholarly journals Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity

2002 ◽  
Vol 461 ◽  
pp. 387-407 ◽  
Author(s):  
SCOTT W. McCUE ◽  
LAWRENCE K. FORBES
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Infinite Plate ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Constant Vorticity ◽  
Uniform Shear ◽  
Uniform Shear Flow

The free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.

Steep, steady surface waves on water of finite depth with constant vorticity

1988 ◽  
Vol 195 (-1) ◽  
pp. 281 ◽  
Author(s):  
A. F. Teles Da Silva ◽  
D. H. Peregrine
Keyword(s):  
Surface Waves ◽  
Finite Depth ◽  
Constant Vorticity
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