Instability of gravity-driven free-surface flow past a deformable elastic solid

2006 ◽  
Vol 18 (4) ◽  
pp. 044103 ◽  
Author(s):  
Vasileios Gkanis ◽  
Satish Kumar
Keyword(s):  
Free Surface ◽  
Elastic Solid ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Past ◽  
Gravity Driven

Minimising wave drag for free surface flow past a two-dimensional stern

2011 ◽  
Vol 23 (7) ◽  
pp. 072101 ◽  
Author(s):  
Osama Ogilat ◽  
Scott W. McCue ◽  
Ian W. Turner ◽  
John A. Belward ◽  
Benjamin J. Binder
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Wave Drag ◽  
Surface Flow ◽  
Two Dimensional ◽  
Flow Past

Free-surface flow past oscillating singularities at resonant frequency

1982 ◽  
Vol 120 ◽  
pp. 139-154 ◽  
Author(s):  
G. Dagan ◽  
T. Miloh
Keyword(s):  
Free Surface ◽  
Resonant Frequency ◽  
Free Surface Flow ◽  
Generalized Solution ◽  
Surface Flow ◽  
Third Order ◽  
Large Wave ◽  
Drag Forces ◽  
Flow Past ◽  
Lift And Drag

This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(ε½) and O(εlogε) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.

scholarly journals Free surface flow past topography: A beyond-all-orders approach

2012 ◽  
Vol 23 (4) ◽  
pp. 441-467 ◽  
Author(s):  
CHRISTOPHER J. LUSTRI ◽  
SCOTT W. MCCUE ◽  
BENJAMIN J. BINDER
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Numerical Solutions ◽  
Power Series Expansion ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Asymptotic Results ◽  
Stagnation Points ◽  
Flow Past ◽  
Stokes Lines

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck, (2006) Exponential asymptotics and gravity waves. J. Fluid Mech.567, 299–326, the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of inclination. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

Effect of buoyancy on the free surface flow past a permeable bed

1978 ◽  
Vol 11 (4) ◽  
pp. 265-275 ◽  
Author(s):  
N. Rudraiah ◽  
R. Veerabhadraiah
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Past

Steep waves in free-surface flow past narrow topography

2017 ◽  
Vol 29 (6) ◽  
pp. 062107 ◽  
Author(s):  
Stephen L. Wade ◽  
Benjamin J. Binder ◽  
Trent W. Mattner ◽  
James P. Denier
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Past ◽  
Steep Waves
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