Geoscience Reference
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thermocline depth can be modelled. 1 Inertial oscillations can, at times, dominate obser-
vations of current shear (Palmer, Rippeth, et al., 2008 ) .Models are able to represent this,
though achieving the correct mixing at the thermocline depends on having sufficient
vertical resolution and on the temporal resolution of the driving winds. Simulating
mixing by internal waves is more problematic. At present, large-scale models of shelf
seas do not have the horizontal resolution to allow the proper representation of the
internal waves, which can have components with wavelengths of 1 km or less whichmay
invalidate the hydrostatic assumption. Only models covering limited domains and time
scales are able to cope with the computational effort required for such small-scale
processes (Lamb, 1994 ). Moreover, the sensitivity of internal wave mixing to changes
in the slope of the seabed means that high-quality bathymetric information is required.
As an interim solution to the problem, models often 'parameterise' the impacts of
unresolved processes. The challenge then is to represent the mixing impact of a
process, based preferably on some broadly applicable relationships arising from
observations of the process. For the case of interior mixing driven by internal waves
or by meteorological variability, the simplest parameterisation is to limit the lowest
allowable eddy diffusivity and viscosity (Sharples and Tett, 1994 ) ; this is the approach
taken in our coupled physics-biogeochemistry model ( www.cambridge.org/shelfseas ) .
Physics summary box
In order to obtain a more complete picture of vertical exchange than that provided
by the TML model of Chapter 6 , we need to represent turbulent processes more
explicitly in our numerical models.
Such models require a 'turbulence closure' scheme which relates the eddy viscosity
and diffusivity to mean properties.
Measurements of turbulent energy dissipation by shear profilers provide a direct
test of the ability of the models to simulate turbulent mixing.
Sharp density gradients (pycnoclines) can severely limit the ability of turbulence to mix
water properties into and across them, an effect which can be quantified by relating
diffusivities to the gradient Richardson number using a turbulence closure scheme.
Knowledge of the eddy diffusivity is fundamental to quantifying turbulent fluxes
of, for instance, heat, nutrients and carbon. Measurements of dissipation rates and
water column stability can be combined to estimate eddy diffusivities (e.g.
Equation 7.11 ).
Typical values of eddy diffusivity within a pycnocline can be 10 4 -10 6 m 2 s 1 .
A wind-mixed surface layer might have values of 10 2 -10 4 m 2 s 1 , while the
1 This is a difficult process to observe in the real ocean; the spring-neap signal needs to be separated
from internal mixing mechanisms, and from the tidal advection of a horizontally variable thermocline
structure. Numerical modelling (Sharples, 2008 ) suggests that the base of the thermocline only changes
by 3-5 metres, implying that a model requires a vertical resolution of 1 metre or less in order to simulate
this process.
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