Changeset 11677

Timestamp:

2019-10-11T00:15:29+02:00 (4 years ago)

Author:

agn

Message:

added structure figure

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex (modified) (1 diff)

NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

@@ -582 +582 @@
 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:
+\begin{equation}\label{eq:w_La}
+w_{*L}= \left(u_*^2 u_{s0}\right)^{1/3};
+\end{equation} 
+this is the 
+Where the mixed-layer is stable, a composite velocity scale is assumed:
+\begin{equation}\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}
+\end{equation} 
 \subsubsection{The flux gradient model}
 The flux-gradient relationships used in the OSMOSIS scheme take the form,