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It should also be remembered that the wind generates surface waves which can
contribute to mixing near the surface through the turbulence which is induced by
wave breaking. Moreover, if the water is shallow enough, waves, especially long
period swells, may have orbital motions which extend down to the seabed and
induce bottom stresses which promote vertical mixing. To separate the effect of
stirring by the surface wind stress and the contribution from wave motions is
difficult and requires independent wind and wave data from local direct measure-
ments, as in an extreme shallow case studied by Wiles, et al., 2006 .
9.7
Modelling the physics of ROFIs
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It should be clear from the forgoing sections that ROFIs are host to a diverse
range of interacting physical processes. While we have seen that analytical
models can represent the key aspects of the individual processes, numerical methods
are needed if we are to try and simulate the full complexity of ROFI behaviour
and thus test the extent of our understanding of the way they work. Because of
the range of processes involved, their interactions and the multiple dynamic feed-
backs involved, ROFIs constitute a demanding challenge to the skill of numerical
models.
While the ultimate goal must be prognostic full physics 3D models, much
progress to date has been made with 1D simulations at a point, using a turbulence
closure scheme similar to the approach described in Chapter 7 . In addition to
specified forcing by tides and winds, it is also necessary, in a 1D ROFI model,
to prescribe the horizontal gradients of density which must be determined
from observations. If a full suite of forcing is available, these 1D models can
give a satisfactory first order simulation of the evolution of density structure
and flow in a ROFI (Sharples and Simpson, 1995 ) and can reproduce the
enhanced dissipation (e.g. as seen in Fig. 9.9c ) resulting from tidally forced
convection (Simpson et al., 2002 ) . The focus in 1D models on vertical exchange
processes makes them a useful test-bed for evaluating turbulence closure schemes.
A flexible 1D model framework for comparing different closure schemes is avail-
able in the General Ocean Turbulence Model (GOTM; see: http://www.gotm.net/
index.php ).
A 3D full physics model involves much greater freedom than is the case of a 1D
model, as it is forced only by inputs at the boundaries (i.e. tidal elevations and
freshwater input at the lateral boundaries, heat and wind stress at the surface). To
properly determine the evolution of the system, a 3D model must accurately repre-
sent the vertical mixing of buoyancy and momentum at each point in the model
domain. Any deficiency in calculating the mixing rates here will cause errors in the
horizontal density gradients which will modify the circulation and hence the velocity
shear. This in turn will cause further misrepresentation of the vertical mixing. The
effect of tight feedback loops of this kind is particularly acute in ROFIs where such a
complex suite of processes is operating.
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