scholarly journals BORE-INDUCED MACROVORTICES OVER A PLANAR BEACH: THE CROSS-SEA CONDITION CASE

2012 ◽  
Vol 1 (33) ◽  
pp. 18
Author(s):  
Matteo Postacchini ◽  
Maurizio Brocchini ◽  
Luciano Soldini
Keyword(s):  
Shallow Water Equations ◽  
Wave Breaking ◽  
Ad Hoc ◽  
Rip Currents ◽  
Positive Interaction ◽  
Wave Ray ◽  
Nonlinear Shallow Water Equations ◽  
Fair Comparison ◽  
Wave Trains ◽  
Vorticity Generation

Wave breaking over submerged topographic obstacles leads to vorticity generation and, at times, to the generation of strong offshore-directed rip currents. The generation of finite-length breakers may also be induced by the positive interaction of wave trains propagating to shore with a relative angle. Such an interaction gives rise to a short-crested system, this, in turn, generating both breakers of finite crossflow length and an intense associated vorticity. We here analyze such a vorticity generation mechanism specifically focusing on the location where wave breaking occurs. To this purpose we use both a simple theoretical approach, based on the well-known theory of wave ray propagation, and ad-hoc numerical simulations, by means of a NSWE (Nonlinear Shallow Water Equations) solver. A fair comparison between such preliminary theoretical and numerical results suggests that the present work can be used as the basis for future analyses of vorticity generation by cross seas.

Vorticity generation due to cross-sea

2014 ◽  
Vol 744 ◽  
pp. 286-309 ◽  
Author(s):  
M. Postacchini ◽  
M. Brocchini ◽  
L. Soldini
Keyword(s):  
Ad Hoc ◽  
Flow Characteristics ◽  
Cross Flow ◽  
Shallow Waters ◽  
Wave Forcing ◽  
Flow Length ◽  
Nonlinear Shallow Water Equations ◽  
Flow Evolution ◽  
Wave Trains ◽  
Vorticity Generation

AbstractSimilarly to shore-parallel waves interacting with submerged obstacles, two wave trains, approaching the shore with different angles, generate breakers of finite cross-flow length and an intense vorticity at their edges. The dynamics of crossing wave trains in shallow waters is studied by means of a simple theoretical approach that is used to inspect the flow characteristics at breaking. The post-breaking dynamics, with specific focus on the vorticity generation and evolution processes, is described on the basis of the analytical results of Brocchini et al. (J. Fluid Mech., vol. 507, 2004, pp. 289–307). Ad hoc numerical simulations, performed by means of a nonlinear shallow-water equations (NSWE) solver, are used to support the analytical findings and detail the post-breaking flow evolution. Comparisons between numerical and analytical findings confirm that: (i) the cross-sea theory successfully predicts the breaking position when a finite-length breaker stems from two crossing wave trains and (ii) the dynamics induced by such a breaking (i.e. vorticity generation, mutual-advection and self-advection mechanisms) is similar to that occurring after the breaking event of a shore-parallel wave over a submerged obstacle: vortices generated at the breaker edges are first subjected to wave forcing and self-advection, these pushing the vortices shoreward; then, oppositely-signed vortices pair and the mutual interaction enables them to invert the motion and move seaward. Useful relationships have been found to describe the main features of such a dynamics (i.e. breaker length, vortex trajectories, etc.).

scholarly journals A Two-Layer Hydrostatic-Reconstruction Method for High-Resolution Solving of the Two-Layer Shallow-Water Equations over Uneven Bed Topography

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Jiang Lin ◽  
Bing Mao ◽  
Xinhua Lu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Ad Hoc ◽  
Finite Volume Methods ◽  
Reconstruction Method ◽  
Riemann Solver ◽  
Robust Solutions ◽  
Bed Topography ◽  
Benchmark Tests ◽  
Nonlinear Shallow Water Equations

In this study, attention is focused on numerically solving the two-dimensional, two-layer nonlinear shallow-water equations (2LSWEs) over uneven bed topography. A two-layer hydrostatic-reconstruction method (2LHRM) is proposed for face value reconstructions. A numerical model is then developed based on the 2LHRM in the framework of finite-volume methods using the slope-limited centered (SLIC) approximate Riemann solver for flux evaluations. The validations against various benchmark tests show that the 2LHRM by working with the SLIC scheme predicts robust solutions around large gradients and is able to simulate lake-at-rest solutions without using any ad-hoc techniques.

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.

Numerical Investigation of Wave Period Influence on Long Wave Run-Up on Slope With Rigid Vegetation

2016 ◽  
Author(s):  
Jun Tang ◽  
Yongming Shen
Keyword(s):  
Shallow Water Equations ◽  
Water Wave ◽  
Wave Period ◽  
Coastal Vegetation ◽  
Coastal Structures ◽  
Rigid Vegetation ◽  
Comparison With Experiment ◽  
Long Wave ◽  
Nonlinear Shallow Water Equations ◽  
Run Up

Coastal vegetation can not only provide shade to coastal structures but also reduce wave run-up. Study of long water wave climb on vegetation beach is fundamental to understanding that how wave run-up may be reduced by planted vegetation along coastline. The present study investigates wave period influence on long wave run-up on a partially-vegetated plane slope via numerical simulation. The numerical model is based on an implementation of Morison’s formulation for rigid structures induced inertia and drag stresses in the nonlinear shallow water equations. The numerical scheme is validated by comparison with experiment results. The model is then applied to investigate long wave with diverse periods propagating and run-up on a partially-vegetated 1:20 plane slope, and the sensitivity of run-up to wave period is investigated based on the numerical results.

scholarly journals Vorticity generation by short‐crested wave breaking

2012 ◽  
Vol 39 (24) ◽  
Author(s):  
David B. Clark ◽  
Steve Elgar ◽  
Britt Raubenheimer
Keyword(s):  
Wave Breaking ◽  
Vorticity Generation

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 Non-breaking and breaking solitary wave run-up

2002 ◽  
Vol 456 ◽  
pp. 295-318 ◽  
Author(s):  
YING LI ◽  
FREDRIC RAICHLEN
Keyword(s):  
Numerical Model ◽  
Solitary Wave ◽  
Wave Breaking ◽  
Ad Hoc ◽  
Mapping Technique ◽  
Breaking Wave ◽  
Good Prediction ◽  
Computational Domain ◽  
Domain Mapping ◽  
Run Up

The run-up of non-breaking and breaking solitary waves on a uniform plane beach connected to a constant-depth wave tank was investigated experimentally and numerically. If only the general characteristics of the run-up process and the maximum run-up are of interest, for the case of a breaking wave the post-breaking condition can be simplified and represented as a propagating bore. A numerical model using this bore structure to treat the process of wave breaking and subsequent shoreward propagation was developed. The nonlinear shallow water equations (NLSW) were solved using the weighted essentially non-oscillatory (WENO) shock capturing scheme employed in gas dynamics. Wave breaking and post-breaking propagation are handled automatically by this scheme and ad hoc terms are not required. A computational domain mapping technique was used to model the shoreline movement. This numerical scheme was found to provide a relatively simple and reasonably good prediction of various aspects of the run-up process. The energy dissipation associated with wave breaking of solitary wave run-up (excluding the effects of bottom friction) was also estimated using the results from the numerical model.

scholarly journals Modelling coastal wave trains and wave breaking

2020 ◽  
Vol 147 ◽  
pp. 101581
Author(s):  
A. Duran ◽  
G.L. Richard
Keyword(s):  
Wave Breaking ◽  
Wave Trains
Sign in / Sign up

Export Citation Format

Share Document