The flow in the surf zone: a fully nonlinear Boussinesq-type of approach

Musumeci, Rosaria Ester; Svendsen, Ib A.; Veeramony, J.

doi:10.1016/j.coastaleng.2005.02.007

Cited by 46 publications

(98 citation statements)

References 34 publications

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“…This is testified by figure 10, which illustrates the comparison between the results of the fully nonlinear model of Musumeci et al [19] and the experimental results collected by Cox et al [36] at the shoaling zone, at the breaking region and inside the surf zone of a laboratory planar beach. Not only is the water surface elevation reproduced fairly well, but also the computed vertical profiles of the horizontal velocity well match the experimental ones (this is different from most other breaking models, which, being characterized by self-similar vertical profiles, do not allow for a correct description of the 'undertow').…”

Section: (B) the 2000smentioning

confidence: 96%

“…In other words, a coupled model is built in which the vorticity transport equation can be solved either analytically [18,19] or numerically [20]. In any case, the solution is found to strongly depend on the surface vorticity ω s injected in the fluid body.…”

Section: (B) the 2000smentioning

confidence: 99%

“…Because of the derivation procedure, model equations require closures for both vorticity and turbulence. Solution of such extra equations can be pursued either by semi-analytical means [19] or by numerical calculations [20]. Derivation of this class of BTEs is achieved through the following main actions.…”

Section: (I) Equations For Irrotational Flowsmentioning

confidence: 99%

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A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

2013

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This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

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Section: (B) the 2000smentioning

confidence: 96%

Section: (B) the 2000smentioning

confidence: 99%

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A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

2013

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“…The numerical strategy consists in separating incident and outgoing waves on the basis of the quasi-hyperbolic form derived in the previous subsection. This kind of approach has been applied to Boussinesq-type equations in References [13,14] following the lines given by Van Dongeren and Svendsen [15] for fairly long waves. We will use a similar approach but without assuming that incident and outgoing waves are of small amplitude (weakly nonlinear) as is the case in the aforementioned works.…”

Section: Open Sea Boundary Conditionmentioning

confidence: 98%

A fourth‐order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq‐type equations. Part II: boundary conditions and validation

Cienfuegos

Barthélemy

Bonneton

2006

Numerical Methods in Fluids

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SUMMARYThis paper supplements the validation of the fourth-order compact finite volume Boussinesq-type model presented by Cienfuegos et al. (Int. J. Numer. Meth. Fluids 2006, in press). We discuss several issues related to the application of the model for realistic wave propagation problems where boundary conditions and uneven bathymetries must be considered. We implement a moving shoreline boundary condition following the lines given by Lynett et al. (Coastal Eng. 2002; 46:89-107), while an absorbing-generating seaward boundary and an impermeable vertical wall boundary are approximated using a characteristic decomposition of the Serre equations. Using several benchmark tests, both numerical and experimental, we show that the new finite volume model is able to correctly describe nonlinear wave processes from shallow waters and up to wavelengths which correspond to the theoretical deep water limit. The results compare favourably with those reported using former fully nonlinear and weakly dispersive Boussinesq-type solvers even when time integration is conducted with Courant numbers greater than 1.0. Furthermore, excellent nonlinear performance is observed when numerical computations are compared with several experimental tests on solitary waves shoaling over planar beaches up to breaking. A preliminary test including the wave-breaking parameterization described by Cienfuegos (Fifth International Symposium on Ocean Wave Measurement Analysis, Madrid, Spain, 2005) shows that the Boussinesq model can be extended to deal with surf zone waves. Finally, practical aspects related to the application of a high-order implicit filter as given by Gaitonde et al. (Int. J. Numer. Methods Engng 1999; 45:1849-1869 to damp out unphysical wavelengths, and the numerical robustness of the finite volume scheme are also discussed.

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“…The wave-breaking effects have to be parameterised by incorporating additional terms in the mass and momentum equations (e.g. Musumeci et al 2005;Cienfuegos et al, 2010;Bjørkavåg and Kalisch, 2011;Tissier et al, 2012, Kazolea et., 2014. The challenge is to take the breaking process into account to ensure an accurate description of the surf zone, including the wave height decay and the setup development.…”

Section: Introductionmentioning

confidence: 99%

Are breaking waves, bores, surges and jumps the same flow?

Lubin

Chanson

2016

Environ Fluid Mech

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The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.

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The flow in the surf zone: a fully nonlinear Boussinesq-type of approach

Cited by 46 publications

References 34 publications

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

A fourth‐order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq‐type equations. Part II: boundary conditions and validation

Are breaking waves, bores, surges and jumps the same flow?

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