Entrainment

The entrainment scenario is similar to the Couette scenario, except that the water column is now stably stratified by a vertically constant density gradient. Also in this scenario, the effect of Earth’s rotation is ignored. The entrainment scenario  is ideally suited to benchmark the model performance in stress-driven entrainment situations against available experiments (see Umlauf and Burchard, 2005) The results shown in the figure below illustrate that after the onset of the constant surface stress in the x-direction, a thin near-surface layer is accelerated (panel a), and slowly entrains into the stratified, non-turbulent interior region. Shear-driven turbulence in this region is mirrored in the large turbulent diffusivities shown in panel ©, which generate a nearly well-mixed surface layer  that is separated from the interior by a pycnocline of gradually increasing strength (panel b). The white dashed line indicates the solution suggested by Price (1979) for shear-driven entrainment into a linearly stratified fluid [see Eq. (53) in Umlauf and Burchard, 2005]. The numerical solution shown in the figure has been obtained with the k-ε model. Solutions for other two-equation models available in GOTM look similar. You can easily check this by modifying the GOTM namelist files to run the k-ω model (Umlauf et al., 2003) or the GLS (generic length scale) model described in Umlauf and Burchard (2003). Technical details for this GOTM scenario may be found in the GOTM documentation. We now also provide the MATLAB script used to generate the figure below. Note that only MATLAB 2015a and higher supports direct reading of NetCDF output. [caption id=“attachment_217” align=“alignnone” width=“500”] Temporal variability of (a) velocity, (b) stratification, and © turbulent diffusivity for the entrainment scenario. The white dashed line shows the entrainment depth according to Price (1979).[/caption]