Turbulence under breaking surface waves

In this scenario, it is demonstrated how the effect of breaking surface waves is parameterised in one- and two-equation models. This is usually done by injecting turbulent kinetic energy (TKE) at the surface, see Craig and Banner (1994) and Craig (1996). The rate of TKE injected is proportional to the surface friction velocity cubed, as defined in (211). Injection of TKE at the surface leads to a thin surface boundary layer, in which the vertical transport of TKE and its dissipation approximately balance. This layer is sometimes called the transport layer. Even though there can be considerable shear in this layer, shear-production of turbulence is negligible by definition (also see section 4.7.4).

Different types of models are available in GOTM for the wave-breaking scenario. The key change in gotmturb.nml for runs with TKE injection is to set ubc_type = 2, telling GOTM to set the type of the upper boundary to TKE injection. The decay rates of the TKE and the dissipation rate in the wave-affected layer are then an natural outcome of the model. Note that with the KPP model, this scenario cannot be run.

In all cases a surface-stress of $ \tau_x= 1.027$ Nm$ ^{-2}$ was applied. After a runtime of 2 days, a steady-state with a constant stress over the whole water column of 20 m depth is reached. The wave affected layer can be found in the uppermost meter or so, and because of the strong gradients in this region we used a refined grid close to the surface. The parameters for such a `zoomed grid' can be set in the input file gotmmean.nml according to the decription in section 3.3. If you want to compare the computed profiles with the analytical solutions in (110), you'll need a specification of the parameter $ K$. This parameter is computed in k_bc() to be found in turbulence.F90, where you can add a few FORTRAN lines to write it out.

Karsten Bolding 2012-12-28