Neither Boussinesq-type wave models nor non-hydrostatic wave-flow models can be directly
applied to details of breaking waves, since in both models essential processes such
as overturning, air-entrainment and wave generated turbulence, are absent. But,
if only the macro-scale effects of wave breaking are of interest, such as the effect
on the statistics of wave heights, details of the breaking process can be ignored.
By observing that both spilling and plunging breakers eventually evolve into a
quasi-steady bore, where the entire front-face of the wave is turbulent,
a breaking wave becomes analogous to a hydraulic jump.
Consequently, its integral properties (rate of energy dissipation, jump height) are
approximately captured by regarding the breaking wave as a discontinuity in the
flow variables (free surface, velocities). Proper treatment of such a discontinuity in
a non-hydrostatic model (conservation of mass and momentum) can therefore be
used to determine the energy dissipation of waves in the surf zone; see Section 5.4.4.

Though a vertical coarse resolution (1-3 layers) is sufficient to describe the wave
physics outside the surf zone (e.g. refraction, shoaling, diffraction, nonlinear wave-wave interactions),
dissipation due to wave
breaking requires a disproportional high vertical resolution (10-20).
A coarse resolution will
result in an underestimation of the horizontal velocities near the wave crest, and thus
an underestimation of the amplitude dispersion. This underestimation
implies that at low vertical resolution the influence of the non-hydrostatic
pressure gradient is overestimated. Consequently, the stabilizing dispersive effects
(i.e. the non-hydrostatic pressures) postpone the transition into the characteristic
saw-tooth shape and therefore also the onset of dissipation.

By enforcing a hydrostatic pressure distribution
at the front of a wave, we can locally reduce a non-hydrostatic wave-flow model to the
nonlinear shallow water equations. The wave then rapidly transitions into the characteristic
saw-tooth shape and, consistent with the high resolution approach, dissipation
is captured by ensuring momentum conservation over the resulting discontinuity.

The subsequent dissipation is well described by assuming depth uniform velocities
and a hydrostatic pressure distribution. In fact, these assumptions often form the
basis to derive dissipation formulations to account for depth-induced breaking in
energy balance type models, e.g. Battjes and Janssen (1978) among many others.
Hence, prescribing a hydrostatic pressure distribution in the model around the
discontinuity should result in the correct bulk dissipation.

There is no need to assume a hydrostatic pressure distribution if the vertical resolution
is sufficient (i.e. 10 to 20 layers). However, imposing a hydrostatic distribution resolutions at low
resolutions (1-3 layers) will ensure that, due the absence of dispersive effects, the front quickly
transitions into a bore like shape. Hence, it can be used to initiate the onset of
wave breaking, thus allowing for the use of low-vertical resolutions throughout the
domain. In practice this means that once a
grid point is in the front of a breaking wave, vertical accelerations are no longer
resolved, and the non-hydrostatic pressure is set to zero.

A grid point is therefore labelled for hydrostatic computation if
the local surface steepness
/*x* exceeds a predetermined
value . Equivalenty,
/*t* > .
Once labelled, a point only becomes non-hydrostatic again if the crest of the wave has
passed. This is assumed to occur when
/*t* < 0. Furthermore, because grid points
only become active again when the crest passes (where
*w* 0), vertical velocities *w*
are set to zero
on the front. To represent persistence of wave breaking, we locally reduce the
criterion to if a neighbouring grid point (in *x* - or *y* -direction) has been labelled
for hydrostatic computation. In this case a point is thus also labelled for hydrostatic
computation if
/*t* > , with
< . In all other grid points, the computations
are non-hydrostatic.
Based on calibration, the default value for the maximum steepness parameter is 0.6, while the persistence parameter
is set to 0.3.

To summarize, in case of a few layers (1-3) we must apply the command `BREAK` with optionally different values for and .
In case of a sufficient number of layers (>10) nothing needs to be specified with respect to wave breaking.