1993
DOI: 10.1016/0378-3839(93)90001-o
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A Boussinesq model for waves breaking in shallow water

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Cited by 307 publications
(196 citation statements)
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“…A common parameterisation is L r = 2.91h r (Haller and Catalan, 2009), although the re-analysis of large-scale experiments suggests L r /h r  1 to 8 ( Figure 5). In Figure 5, steady breaker, stationary hydraulic jump and tidal bore data are compared; 4. the mean front slope angle ɸ (Schäffer et al, 1993), typically between 8° to 30° for the termination and initiation of the breaking event respectively; 5. the roller celerity (or celerity of the breaking wave); 6. the energy dissipation in the roller region; 7. the bubble size distributions, often improperly estimated based upon Hinze's (1955) model developed in the case of a single droplet under non-coalescecing conditions (!). To estimate most of these quantities, flow analogies have been considered, but some limitations are clearly identified and some modifications, based on new experimental data analysis, are proposed in the following sections.…”
Section: Current State Of Practice In Numerical Modelling and Limitatmentioning
confidence: 99%
“…A common parameterisation is L r = 2.91h r (Haller and Catalan, 2009), although the re-analysis of large-scale experiments suggests L r /h r  1 to 8 ( Figure 5). In Figure 5, steady breaker, stationary hydraulic jump and tidal bore data are compared; 4. the mean front slope angle ɸ (Schäffer et al, 1993), typically between 8° to 30° for the termination and initiation of the breaking event respectively; 5. the roller celerity (or celerity of the breaking wave); 6. the energy dissipation in the roller region; 7. the bubble size distributions, often improperly estimated based upon Hinze's (1955) model developed in the case of a single droplet under non-coalescecing conditions (!). To estimate most of these quantities, flow analogies have been considered, but some limitations are clearly identified and some modifications, based on new experimental data analysis, are proposed in the following sections.…”
Section: Current State Of Practice In Numerical Modelling and Limitatmentioning
confidence: 99%
“…Wave breaking is introduced in the Boussinesq equations on the basis of the surface roller concept for spilling breakers as described by Schaffer et al (1993) and Madsen et al (1997aMadsen et al ( , 1997b. The basic principle is that the surface roller is considered as a volume of water carried by the wave with the wave celerity.…”
Section: Breaker Model Based On the Roller Conceptmentioning
confidence: 99%
“…Schaffer et al, 1993;Madsen et al, 1997a,b;Sorensen et al, 1998) we have studied and modelled surf zone dynamics such as the shoaling, breaking and runup of regular and irregular waves, the generation and release of low frequency waves, wave-induced rip-currents and circulation cells behind detached breakwaters. For this purpose we have until recently applied a timedomain Boussinesq model (I) in terms of the depth-integrated velocity and including lowest order nonlinearity and Pade [2,2] dispersion characteristics.…”
Section: Introductionmentioning
confidence: 99%
“…(1)- (4) the subscript t denotes differentiation with respect to time, d is still the water depth, U is the horizontal velocity vector U = (U, V ) with U and V being the depth-averaged horizontal velocities along the x and y directions, respectively; ζ is the surface elevation, h the total depth (h = d + ζ ), g is the gravitational acceleration, τ b = (τ bx , τ by ) is the bottom friction term (shear stress components approximated by the use of the quadratic law according to Ribberink (1998), δ is the roller thickness (determined geometrically according to Schäffer et al, 1993). E is the eddy viscosity term (according to Chen et al, 2000), and u o is the bottom velocity vector u o = (u o , v o ) with u o and v o being the instantaneous bottom velocities along the x and y directions respectively.…”
Section: Boussinesq Equations For Breaking/non-breaking Waves and Tsumentioning
confidence: 99%