Changeset 15548 for NEMO/branches/2021/ticket2632_r14588_theta_sbcblk/doc/latex/NEMO/subfiles/chap_ZDF.tex

Timestamp:

2021-11-28T18:59:49+01:00 (3 years ago)

Author:

gsamson

Message:

update branch to the head of the trunk (r15547); ticket #2632

Location:

NEMO/branches/2021/ticket2632_r14588_theta_sbcblk

Files:

• . (modified) (1 prop)
• doc/latex/NEMO/subfiles/chap_ZDF.tex (modified) (6 diffs)

NEMO/branches/2021/ticket2632_r14588_theta_sbcblk

@@ -9 +9 @@
 
 # SETTE
-^/utils/CI/sette@14244        sette
+^/utils/CI/sette@HEAD        sette
+

@@ -9 +9 @@
 
 # SETTE
-^/utils/CI/sette@14244        sette
+^/utils/CI/sette@HEAD        sette
+

NEMO/branches/2021/ticket2632_r14588_theta_sbcblk/doc/latex/NEMO/subfiles/chap_ZDF.tex

@@ -278 +278 @@
 
 %% =================================================================================================
-\subsubsection{Surface wave breaking parameterization}
+\subsubsection{Surface wave breaking parameterization (No information from an external wave model)}
+\label{subsubsec:ZDF_tke_wave} 
 
 Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to
@@ -306 +307 @@
 with $e_{bb}$ the \np{rn_ebb}{rn\_ebb} namelist parameter, setting \np[=67.83]{rn_ebb}{rn\_ebb} corresponds
 to $\alpha_{CB} = 100$.
-Further setting  \np[=.true.]{ln_mxl0}{ln\_mxl0},  applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale,
-with $\beta$ hard coded to the Stacey's value.
-Note that a minimal threshold of \np{rn_emin0}{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the
-surface $\bar{e}$ value.
+
+Further setting  \np[=.true.]{ln_mxl0}{ln\_mxl0},  applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale, with $\beta$ hard coded to the Stacey's value. Note that a minimal threshold of \np{rn_emin0}{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the surface $\bar{e}$ value.\\
+
+\subsubsection{Surface wave breaking parameterization (using information from an external wave model)}
+\label{subsubsec:ZDF_tke_waveco} 
+
+Surface boundary conditions for the turbulent kinetic energy, the mixing length scale and the dissipative length scale can be defined using wave fields provided from an external wave model (see \autoref{chap:SBC}, \autoref{sec:SBC_wave}). 
+The injection of turbulent kinetic energy at the surface can be given by the dissipation of the wave field usually dominated by wave breaking. In coupled mode, the wave to ocean energy flux term ($\Phi_o$) from an external wave model can be provided and then converted into an ocean turbulence source by setting ln\_phioc=.true.
+
+The surface TKE can be defined by a Dirichlet boundary condition setting $nn\_bc\_surf=0$ in \nam{zdf}{tke} namelist:
+\begin{equation}
+  \bar{e}_o  = \frac{1}{2}\,\left( 15.8 \, \frac{\Phi_o}{\rho_o}\right) ^{2/3}
+\end{equation}
+
+Nevertheless, due to the definition of the computational grid, the TKE flux is not applied at the free surface but at the centre of the topmost grid cell ($z = z1$). To be more accurate, a Neumann boundary condition amounting to interpreter the half-grid cell at the top as a constant flux layer (consistent with the surface layer Monin–Obukhov theory) can be applied setting $nn\_bc\_surf=1$ in  \nam{zdf}{tke} namelist \citep{couvelard_2020}:
+
+\begin{equation}
+  \left(\frac{Km}{e_3}\,\partial_k e \right)_{z=z1} = \frac{\Phi_o}{\rho_o}
+\end{equation}
+
+
+The mixing length scale surface value $l_0$ can be estimated from the surface roughness length z0:
+\begin{equation}
+  l_o = \kappa \, \frac{ \left( C_k\,C_\epsilon \right) ^{1/4}}{C_k}\, z0
+\end{equation}
+where $z0$ is directly estimated from the significant wave height ($Hs$) provided by the external wave model as $z0=1.6Hs$. To use this option ln\_mxhsw as well as ln\_wave and ln\_sdw have to be set to .true.
 
 %% =================================================================================================
 \subsubsection{Langmuir cells}
+\label{subsubsec:ZDF_tke_langmuir}
 
 Langmuir circulations (LC) can be described as ordered large-scale vertical motions in
@@ -335 +359 @@
 \]
 where $w_{LC}(z)$ is the vertical velocity profile of LC, and $H_{LC}$ is the LC depth.
-With no information about the wave field, $w_{LC}$ is assumed to be proportional to
-the Stokes drift $u_s = 0.377\,\,|\tau|^{1/2}$, where $|\tau|$ is the surface wind stress module
-\footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as
-  $u_s =  0.016 \,|U_{10m}|$.
-  Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of
-  $1.5~10^{-3}$ give the expression used of $u_s$ as a function of the module of surface stress
-}.
+
 For the vertical variation, $w_{LC}$ is assumed to be zero at the surface as well as at
 a finite depth $H_{LC}$ (which is often close to the mixed layer depth),
@@ -349 +367 @@
   w_{LC}  =
   \begin{cases}
-    c_{LC} \,u_s \,\sin(- \pi\,z / H_{LC} )    &      \text{if $-z \leq H_{LC}$}    \\
+    c_{LC} \,\|u_s^{LC}\| \,\sin(- \pi\,z / H_{LC} )    &      \text{if $-z \leq H_{LC}$}    \\
     0                             &      \text{otherwise}
   \end{cases}
 \]
-where $c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data.
-The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimeters per second.
+
+
+In the absence of information about the wave field, $w_{LC}$ is assumed to be proportional to
+the surface Stokes drift ($u_s^{LC}=u_{s0} $) empirically estimated by $ u_{s0} = 0.377\,\,|\tau|^{1/2}$, where $|\tau|$ is the surface wind stress module
+\footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as
+  $u_{s0} =  0.016 \,|U_{10m}|$.
+  Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of
+  $1.5~10^{-3}$ give the expression used of $u_{s0}$ as a function of the module of surface stress
+}.
+
+In case of online coupling with an external wave model (see \autoref{chap:SBC} \autoref{sec:SBC_wave}), $w_{LC}$ is proportional to the component of the Stokes drift aligned with the wind \citep{couvelard_2020} and $ u_s^{LC}  = \max(u_{s0}.e_\tau,0)$ where $e_\tau$ is the unit vector in the wind stress direction and $u_{s0}$ is the surface Stokes drift provided by the external wave model.
+
+
+$c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data.
+The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimetres per second.
 The value of $c_{LC}$ is set through the \np{rn_lc}{rn\_lc} namelist parameter,
 having in mind that it should stay between 0.15 and 0.54 \citep{axell_JGR02}.
@@ -362 +393 @@
 converting its kinetic energy to potential energy, according to
 \[
-- \int_{-H_{LC}}^0 { N^2\;z  \;dz} = \frac{1}{2} u_s^2
+- \int_{-H_{LC}}^0 { N^2\;z  \;dz} = \frac{1}{2} \|u_s^{LC}\|^2
 \]
 
@@ -1427 +1458 @@
 the Stokes Drift can be evaluated by setting \forcode{ln_sdw=.true.}
 (see \autoref{subsec:SBC_wave_sdw})
-and the needed wave fields can be provided either in forcing or coupled mode
+and the needed wave fields (significant wave height and mean wave number) can be provided either in forcing or coupled mode
 (for more information on wave parameters and settings see \autoref{sec:SBC_wave})
 

@@ -9 +9 @@
 
 # SETTE
-^/utils/CI/sette@14244        sette
+^/utils/CI/sette@HEAD        sette
+