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]