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.

On the vorticity transport due to dissipating or breaking waves in shallow-water flow

2000 ◽  
Vol 407 ◽  
pp. 235-263 ◽  
Author(s):  
OLIVER BÜHLER
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Small Scale ◽  
Practical Consideration ◽  
Mean Flow ◽  
Vorticity Transport

Theoretical and numerical results are presented on the transport of vorticity (or potential vorticity) due to dissipating gravity waves in a shallow-water system with background rotation and bottom topography. The results are obtained under the assumption that the flow can be decomposed into small-scale gravity waves and a large-scale mean flow. The particle-following formalism of ‘generalized Lagrangian-mean’ theory is then used to derive an ‘effective mean force’ that captures the vorticity transport due to the dissipating waves. This can be achieved without neglecting other, non-dissipative, effects which is an important practical consideration. It is then shown that the effective mean force obeys the so-called ‘pseudomomentum rule’, i.e. the force is approximately equal to minus the local dissipation rate of the wave's pseudomomentum. However, it is also shown that this holds only if the underlying dissipation mechanism is momentum-conserving. This requirement has important implications for numerical simulations, and these are discussed.The novelty of the results presented here is that they have been derived within a uniform theoretical framework, that they are not restricted to small wave amplitude, ray-tracing or JWKB-type approximations, and that they also include wave dissipation by breaking, or shock formation. The theory is tested carefully against shock-capturing nonlinear numerical simulations, which includes the detailed study of a wavetrain subject to slowly varying bottom topography. The theory is also cross-checked in the appropriate asymptotic limit against recently formulated weakly nonlinear theories. In addition to the general finite-amplitude theory, detailed small-amplitude expressions for the main results are provided in which the explicit appearance of Lagrangian fields can be avoided. The motivation for this work stems partly from an on-going study of high-altitude breaking of internal gravity waves in the atmosphere, and some preliminary remarks on atmospheric applications and on three-dimensional stratified versions of these results are given.

scholarly journals Shallow water equations for equatorial tsunami waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170100 ◽  
Author(s):  
Anna Geyer ◽  
Ronald Quirchmayr
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Water Model ◽  
Shallow Water Model ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Tsunami Waves ◽  
De Vries ◽  
Model Equations

We present derivations of shallow water model equations of Korteweg–de Vries and Boussinesq type for equatorial tsunami waves in the f -plane approximation and discuss their applicability. This article is part of the theme issue ‘Nonlinear water waves’.

A Coupled-Mode Technique for the Prediction of Wave-Induced Set-Up and Mean Flow in Variable Bathymetry Domains

2007 ◽  
Author(s):  
K. A. Belibassakis ◽  
Th. P. Gerostathis ◽  
G. A. Athanassoulis
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Environment ◽  
Wave Model ◽  
Mean Flow ◽  
Flow Equations ◽  
Coupled Mode ◽  
The Mean ◽  
Set Up ◽  
Wave Induced

In the present work, a complete, phase-resolving wave model is coupled with an iterative solver of the mean-flow equations in intermediate and shallow water depth, permitting an accurate calculation of wave set-up and wave-induced current in intermediate and shallow water environment with possibly steep bathymetric variations. The wave model is based on the consistent coupled-mode system of equations, developed by Athanassoulis & Belibassakis (1999) for the propagation of water waves in variable bathymetry regions. This model improves the predictions of the mild-slope equation, permitting the treatment of wave propagation in regions with steep bottom slope and/or large curvature. In addition, it supports the consistent calculation of wave velocity up to and including the bottom boundary. The above wave model has been further extended to include the effects of bottom friction and wave breaking, which are important factors for the calculation of radiation stresses on decreasing depth. The latter have been used as forcing terms to the mean flow equations in order to predict wave-induced set up and mean flow in open and closed domains. Numerical results obtained by the present model are presented and compared with predictions obtained by the mild-slope approximation (Massel & Gourlay 2000), and experimental data (Gourlay 1996).

scholarly journals Turbulence structure and interaction with steep breaking waves

2011 ◽  
Vol 674 ◽  
pp. 522-577 ◽  
Author(s):  
DJAMEL LAKEHAL ◽  
PETAR LIOVIC
Keyword(s):  
Fluid Flow ◽  
Water Waves ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Small Scale ◽  
Breaking Wave ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Scale Breaking ◽  
The Mean

Large-eddy and interface simulation using an interface tracking-based multi-fluid flow solver is conducted to investigate the breaking of steep water waves on a beach of constant bed slope. The present investigation focuses mainly on the ‘weak plunger’ breaking wave type and provides a detailed analysis of the two-way interaction between the mean fluid flow and the sub-modal motions, encompassing wave dynamics and turbulence. The flow is analysed from two points of views: mean to sub-modal exchange, and wave to turbulence interaction within the sub-modal range. Wave growth and propagation are due to energy transfer from the mean flow to the waves, and transport of mean momentum by these waves. The vigorous downwelling–upwelling patterns developing at the head and tail of each breaker are shown to generate both negative- and positive-signed energy exchange contributions in the thin sublayer underneath the water surface. The details of these exchange mechanisms are thoroughly discussed in this paper, together with the interplay between three-dimensional small-scale breaking associated with turbulence and the dominant two-dimensional wave motion. A conditional zonal analysis is proposed for the first time to understand the transient mechanisms of turbulent kinetic energy production, decay, diffusion and transport and their dependence and/or impact on surface wrinkling over the entire breaking process. The simulations provide a thorough picture of air–liquid coherent structures that develop over the breaking process, and link them to the transient mechanisms responsible for their local incidence.

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.

scholarly journals The "shallow-waterness" of the wave climate in European coastal regions

2016 ◽  
Author(s):  
Kai Håkon Christensen ◽  
Ana Carrasco ◽  
Jean-Raymond Bidlot ◽  
Øyvind Breivik
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Wave Energy ◽  
Water Waves ◽  
Bottom Topography ◽  
Mean Flow ◽  
Momentum Exchange ◽  
Shallow Water Waves ◽  
Coastal Regions ◽  
Deep Water Waves

Abstract. In contrast to deep water waves, shallow water waves are influenced by bottom topography, which has consequences for the propagation of wave energy as well as for the energy and momentum exchange between the waves and the mean flow. The ERA-Interim reanalysis is used to assess the fraction of wave energy associated with shallow water waves in coastal regions in Europe. We show maps of the distribution of this fraction as well as time series statistics from 8 selected stations. There is a strong seasonal dependence and high values are typically associated with winter storms, indicating that shallow water wave effects can occasionally be important even in the deeper parts of the shelf seas otherwise dominated by deep water waves.

scholarly journals The “shallow-waterness” of the wave climate in European coastal regions

Ocean Science ◽  
2017 ◽  
Vol 13 (4) ◽  
pp. 589-597
Author(s):  
Kai Håkon Christensen ◽  
Ana Carrasco ◽  
Jean-Raymond Bidlot ◽  
Øyvind Breivik
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Wave Energy ◽  
Water Waves ◽  
Bottom Topography ◽  
Mean Flow ◽  
Momentum Exchange ◽  
Shallow Water Waves ◽  
Coastal Regions ◽  
Deep Water Waves

Abstract. In contrast to deep water waves, shallow water waves are influenced by bottom topography, which has consequences for the propagation of wave energy as well as for the energy and momentum exchange between the waves and the mean flow. The ERA-Interim reanalysis is used to assess the fraction of wave energy associated with shallow water waves in coastal regions in Europe. We show maps of the distribution of this fraction as well as time series statistics from eight selected stations. There is a strong seasonal dependence and high values are typically associated with winter storms, indicating that shallow water wave effects can occasionally be important even in the deeper parts of the shelf seas otherwise dominated by deep water waves.

Driven Nonlinear Potential Flow With Wave Breaking at Shallow-Water Beaches

2017 ◽  
Author(s):  
Floriane Gidel ◽  
Onno Bokhove ◽  
Mark Kelmanson
Keyword(s):  
Shallow Water ◽  
Potential Flow ◽  
Water Waves ◽  
Wave Breaking ◽  
Equations Of Motion ◽  
Water Model ◽  
Dispersive Waves ◽  
Variational Structure ◽  
Nonlinear Potential ◽  
Nonlinear Equations Of Motion

We introduce a new model of nonlinear dispersive waves generated by wavemakers in deep water, coupled to a shallow-water model with wave breaking, modelled as hydraulics bores, in the shore zone. Coupling of deep- and shallow-water models requires the formulation of an advanced space-time technology able to stably capture the free-surface dynamics. Our approach comprises the direct discretisation of the variational principle for the continuum modelling of potential-flow water-wave dynamics. Preservation of the variational structure in the discretisation ensures that important conservation properties of the original continuum system are inherited to a high degree by the discrete system. The nonlinear equations of motion resulting from the coupling of the potential-flow water-waves and the (breaking) shallow-water waves are solved in unison. By construction, this process results in a stable and robust numerical scheme that is well suited to demanding maritime applications.

scholarly journals A numerical model for simulation of near-shore waves and wave induced currents using the depth-averaged non-hydrostatic shallow water equations with an improvement of wave energy dissipation

2020 ◽  
Vol 20 (2) ◽  
pp. 155-172
Author(s):  
Phung Dang Hieu ◽  
Phan Ngoc Vinh
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Wave Height ◽  
Shallow Water Equations ◽  
Wave Breaking ◽  
Water Model ◽  
Height Distribution ◽  
Time Duration ◽  
Wave Energy Dissipation ◽  
Near Shore

This study proposes a numerical model based on the depth-integrated non-hydrostatic shallow water equations with an improvement of wave breaking dissipation. Firstly, studies of parameter sensitivity were carried out using the proposed numerical model for simulation of wave breaking to understand the effects of the parameters of the breaking model on wave height distribution. The simulated results of wave height near the breaking point were very sensitive to the time duration parameter of wave breaking. The best value of the onset breaking parameter is around 0.3 for the non-hydrostatic shallow water model in the simulation of wave breaking. The numerical results agreed well with the published experimental data, which confirmed the applicability of the present model to the simulation of waves in near-shore areas.

Sign in / Sign up

Export Citation Format

Share Document