scholarly journals BOUSSINESQ MODELLING OF SOLITARY WAVE PROPAGATION, BREAKING, RUNUP AND OVERTOPPING

2011 ◽  
Vol 1 (32) ◽  
pp. 15
Author(s):  
Jana Orszaghova ◽  
Alistair G. L. Borthwick ◽  
Paul H. Taylor
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Wave Breaking ◽  
Laboratory Experiments ◽  
Boussinesq Equations ◽  
Breaking Waves ◽  
One Dimensional ◽  
Nonlinear Shallow Water Equations ◽  
Breaking Parameter ◽  
Surface Profiles

A one-dimensional hybrid numerical model is presented of a shallow-water flume with an incorporated piston paddle. The hybrid model is based on the improved Boussinesq equations by Madsen and Sorensen (1992) and the nonlinear shallow water equations. It is suitable for breaking and non-breaking waves and requires only two adjustable parameters: a friction coefficient and a wave breaking parameter. The applicability of the model is demonstrated by simulating laboratory experiments of solitary waves involving runup at a plane beach and overtopping of a laboratory seawall. The predicted free surface profiles, maximum runup and overtopping volumes agree very well with the measured values.

Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms

2014 ◽  
Vol 178 (3) ◽  
pp. 278-298 ◽  
Author(s):  
Yu. A. Chirkunov ◽  
S. Yu. Dobrokhotov ◽  
S. B. Medvedev ◽  
D. S. Minenkov
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
One Dimensional ◽  
Nonlinear Shallow Water Equations

Wave-driven currents and vortex dynamics on barred beaches

2001 ◽  
Vol 449 ◽  
pp. 313-339 ◽  
Author(s):  
OLIVER BÜHLER ◽  
TIVON E. JACOBSON
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Wave Breaking ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Vortex Structures ◽  
Water Model ◽  
Mean Flow ◽  
The Mean

We present a theoretical and numerical investigation of longshore currents driven by breaking waves on beaches, especially barred beaches. The novel feature considered here is that the wave envelope is allowed to vary in the alongshore direction, which leads to the generation of strong dipolar vortex structures where the waves are breaking. The nonlinear evolution of these vortex structures is studied in detail using a simple analytical theory to model the effect of a sloping beach. One of our findings is that the vortex evolution provides a robust mechanism through which the preferred location of the longshore current can move shorewards from the location of wave breaking. Such current dislocation is an often-observed (but ill-understood) phenomenon on real barred beaches.To underpin our results, we present a comprehensive theoretical description of the relevant wave–mean interaction theory in the context of a shallow-water model for the beach. Therein we link the radiation-stress theory of Longuet-Higgins & Stewart to recently established results concerning the mean vorticity generation due to breaking waves. This leads to detailed results for the entire life-cycle of the mean-flow vortex evolution, from its initial generation by wave breaking until its eventual dissipative decay due to bottom friction.In order to test and illustrate our theory we also present idealized nonlinear numerical simulations of both waves and vortices using the full shallow-water equations with bottom topography. In these simulations wave breaking occurs through shock formation of the shallow-water waves. We note that because the shallow-water equations also describe the two-dimensional flow of a homentropic perfect gas, our theoretical and numerical results can also be applied to nonlinear acoustics and sound–vortex interactions.

scholarly journals Wave Breaking and Propagation Speed for a Class of One-Dimensional Shallow Water Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Zaihong Jiang ◽  
Sevdzhan Hakkaev
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Time ◽  
Wave Breaking ◽  
Blow Up ◽  
Propagation Speed ◽  
One Dimensional ◽  
General Family ◽  
Infinite Propagation Speed

We investigate a more general family of one-dimensional shallow water equations. Analogous to the Camassa-Holm equation, these new equations admit blow-up phenomenon and infinite propagation speed. First, we establish blow-up results for this family of equations under various classes of initial data. It turns out that it is the shape instead of the size and smoothness of the initial data which influences breakdown in finite time. Then, infinite propagation speed for the shallow water equations is proved in the following sense: the corresponding solutionu(t,x)with compactly supported initial datumu0(x)does not have compactx-support any longer in its lifespan.

Purely erosional cyclic and solitary steps created by flow over a cohesive bed

2000 ◽  
Vol 419 ◽  
pp. 203-238 ◽  
Author(s):  
GARY PARKER ◽  
NORIHIRO IZUMI
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Shallow Water Equations ◽  
Hydraulic Jump ◽  
Water Surface ◽  
Migration Speed ◽  
One Dimensional ◽  
Surface Profiles ◽  
Cohesive Bed ◽  
Cohesive Material

An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.

A shock solution for the nonlinear shallow water equations

2010 ◽  
Vol 658 ◽  
pp. 166-187 ◽  
Author(s):  
MATTEO ANTUONO
Keyword(s):  
Shock Wave ◽  
General Solution ◽  
Theoretical Analysis ◽  
Asymptotic Behaviour ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Boundary Data ◽  
Depth Analysis ◽  
Nonlinear Shallow Water Equations ◽  
Shock Solution

A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the main quantities along and behind the bore. The theoretical analysis is then applied to the specific case in which the water at the front of the shock wave is still. A comparison with the Shen & Meyer (J. Fluid Mech., vol. 16, 1963, p. 113) solution reveals that such a solution can be regarded as a specific case of the more general solution proposed here. The results obtained can be regarded as a useful benchmark for numerical solvers based on the NSWEs.

scholarly journals LABORATORY EXPERIMENTS ON THE INFLUENCE OF WIND ON NEARSHORE WAVE BREAKING

1988 ◽  
Vol 1 (21) ◽  
pp. 46
Author(s):  
Scott L. Douglass ◽  
J. Richard Weggel
Keyword(s):  
Wind Direction ◽  
Wave Breaking ◽  
Laboratory Experiments ◽  
Surf Zone ◽  
Breaking Waves ◽  
Wave Tank ◽  
Zone Width

The influence of wind on nearshore breaking waves was investigated in a laboratory wave tank. Breaker location, geometry, and type depended upon the wind acting on the wave as it broke. Onshore winds tended to cause waves to break earlier, in deeper water, and to spill: offshore winds tended to cause waves to break later, in shallower water, and to plunge. A change in wind direction from offshore to onshore increased the surf zone width by up to 100%. Wind's effect was greatest for waves which were near the transition between breaker types in the absence of wind. For onshore winds, it was observed that microscale breaking can initiate spilling breaking by providing a perturbation on the crest of the underlying wave as it shoals.

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