# Changeset 11677

Ignore:
Timestamp:
2019-10-11T00:15:29+02:00 (12 months ago)
Message:

 r11676 ML are handled by the Ri # dependent scheme. \subsubsection{The structure of the OSBL} Figure \ref{OSM1} \subsubsection{Depth and velocity scales} The model supposes a boundary layer of thickness $h_{\mathrm{bl}}$ enclosing a well-mixed layer of thickness $h_{\mathrm{ml}}$ and a relatively thin pycnocline at the base of thickness $\Delta h$; Fig.~\ref{fig: OSBL_structure} shows typical (a) buoyancy structure and (b) turbulent buoyancy flux profile for the unstable boundary layer (losing buoyancy at the surface; e.g.\ cooling). \begin{figure}[!t] \begin{center} \includegraphics[width=\textwidth]{Fig_ZDF_OSM_structure_of_OSBL} \caption{ \protect\label{fig: OSBL_structure} The structure of the entraining  boundary layer. (a) Mean buoyancy profile. (b) Profile of the buoyancy flux. } \end{center} \end{figure} The pycnocline is shallow but important, since here the turbulent OSBL interacts with the underlying ocean. In a finite difference model the pycnocline must be at least one model level thick. The pycnocline in the OSMOSIS scheme is assumed to have a finite thickness, and may include a number of model levels. This means that the OSMOSIS scheme must parametrize both the thickness of the pycnocline, and the turbulent fluxes within the pycnocline. Consideration of the power input by wind acting on the Stokes drift suggests the Langmuir velocity scale: \label{eq:w_La} w_{*L}= \left(u_*^2 u_{s0}\right)^{1/3}; this is the Where the mixed-layer is stable, a composite velocity scale is assumed: \label{eq:composite-nu} \nu_{\ast}= \left{}u_*^3 \left[\right]1-exp(-1.5 \mathrm{La}_t^2})\right]+w_{*L}^3\right}^{1/3} \subsubsection{The flux gradient model} The flux-gradient relationships used in the OSMOSIS scheme take the form,