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Changeset 15574 for NEMO/branches/2021/dev_r14318_RK3_stage1/doc/latex/NEMO/subfiles/chap_ZDF.tex – NEMO

Ignore:
Timestamp:
2021-12-03T20:32:50+01:00 (3 years ago)
Author:
techene
Message:

#2605 #2715 trunk merged into dev_r14318_RK3_stage1

Location:
NEMO/branches/2021/dev_r14318_RK3_stage1
Files:
3 edited

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  • NEMO/branches/2021/dev_r14318_RK3_stage1

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  • NEMO/branches/2021/dev_r14318_RK3_stage1/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r14257 r15574  
    22 
    33\begin{document} 
    4  
    5 %% Custom aliases 
    6 \newcommand{\cf}{\ensuremath{C\kern-0.14em f}} 
    74 
    85\chapter{Vertical Ocean Physics (ZDF)} 
    … …  
    1714    Release & Author(s) & Modifications \\ 
    1815    \hline 
     16    {\em  next} & {\em A. Moulin, E. Clementi} & {\em Update of \autoref{subsec:ZDF_tke} in for wave coupling}\\[2mm] 
    1917    {\em   4.0} & {\em ...} & {\em ...} \\ 
    2018    {\em   3.6} & {\em ...} & {\em ...} \\ 
    … …  
    281279 
    282280%% ================================================================================================= 
    283 \subsubsection{Surface wave breaking parameterization} 
     281\subsubsection{Surface wave breaking parameterization (No information from an external wave model)} 
     282\label{subsubsec:ZDF_tke_wave}  
    284283 
    285284Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to 
    … …  
    309308with $e_{bb}$ the \np{rn_ebb}{rn\_ebb} namelist parameter, setting \np[=67.83]{rn_ebb}{rn\_ebb} corresponds 
    310309to $\alpha_{CB} = 100$. 
    311 Further setting  \np[=.true.]{ln_mxl0}{ln\_mxl0},  applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale, 
    312 with $\beta$ hard coded to the Stacey's value. 
    313 Note that a minimal threshold of \np{rn_emin0}{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the 
    314 surface $\bar{e}$ value. 
     310 
     311Further 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.\\ 
     312 
     313\subsubsection{Surface wave breaking parameterization (using information from an external wave model)} 
     314\label{subsubsec:ZDF_tke_waveco}  
     315 
     316Surface 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}).  
     317The 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. 
     318 
     319The surface TKE can be defined by a Dirichlet boundary condition setting $nn\_bc\_surf=0$ in \nam{zdf}{tke} namelist: 
     320\begin{equation} 
     321  \bar{e}_o  = \frac{1}{2}\,\left( 15.8 \, \frac{\Phi_o}{\rho_o}\right) ^{2/3} 
     322\end{equation} 
     323 
     324Nevertheless, 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}: 
     325 
     326\begin{equation} 
     327  \left(\frac{Km}{e_3}\,\partial_k e \right)_{z=z1} = \frac{\Phi_o}{\rho_o} 
     328\end{equation} 
     329 
     330 
     331The mixing length scale surface value $l_0$ can be estimated from the surface roughness length z0: 
     332\begin{equation} 
     333  l_o = \kappa \, \frac{ \left( C_k\,C_\epsilon \right) ^{1/4}}{C_k}\, z0 
     334\end{equation} 
     335where $z0$ 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. 
    315336 
    316337%% ================================================================================================= 
    317338\subsubsection{Langmuir cells} 
     339\label{subsubsec:ZDF_tke_langmuir} 
    318340 
    319341Langmuir circulations (LC) can be described as ordered large-scale vertical motions in 
    … …  
    338360\] 
    339361where $w_{LC}(z)$ is the vertical velocity profile of LC, and $H_{LC}$ is the LC depth. 
    340 With no information about the wave field, $w_{LC}$ is assumed to be proportional to 
    341 the Stokes drift $u_s = 0.377\,\,|\tau|^{1/2}$, where $|\tau|$ is the surface wind stress module 
    342 \footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as 
    343   $u_s =  0.016 \,|U_{10m}|$. 
    344   Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of 
    345   $1.5~10^{-3}$ give the expression used of $u_s$ as a function of the module of surface stress 
    346 }. 
     362 
    347363For the vertical variation, $w_{LC}$ is assumed to be zero at the surface as well as at 
    348364a finite depth $H_{LC}$ (which is often close to the mixed layer depth), 
    … …  
    352368  w_{LC}  = 
    353369  \begin{cases} 
    354     c_{LC} \,u_s \,\sin(- \pi\,z / H_{LC} )    &      \text{if $-z \leq H_{LC}$}    \\ 
     370    c_{LC} \,\|u_s^{LC}\| \,\sin(- \pi\,z / H_{LC} )    &      \text{if $-z \leq H_{LC}$}    \\ 
    355371    0                             &      \text{otherwise} 
    356372  \end{cases} 
    357373\] 
    358 where $c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data. 
    359 The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimeters per second. 
     374 
     375 
     376In the absence of information about the wave field, $w_{LC}$ is assumed to be proportional to 
     377the 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 
     378\footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as 
     379  $u_{s0} =  0.016 \,|U_{10m}|$. 
     380  Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of 
     381  $1.5~10^{-3}$ give the expression used of $u_{s0}$ as a function of the module of surface stress 
     382}. 
     383 
     384In 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. 
     385 
     386 
     387$c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data. 
     388The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimetres per second. 
    360389The value of $c_{LC}$ is set through the \np{rn_lc}{rn\_lc} namelist parameter, 
    361390having in mind that it should stay between 0.15 and 0.54 \citep{axell_JGR02}. 
    … …  
    365394converting its kinetic energy to potential energy, according to 
    366395\[ 
    367 - \int_{-H_{LC}}^0 { N^2\;z  \;dz} = \frac{1}{2} u_s^2 
     396- \int_{-H_{LC}}^0 { N^2\;z  \;dz} = \frac{1}{2} \|u_s^{LC}\|^2 
    368397\] 
    369398 
    … …  
    10831112  \label{lst:namdrg} 
    10841113\end{listing} 
     1114 
    10851115\begin{listing} 
    10861116  \nlst{namdrg_top} 
    … …  
    10881118  \label{lst:namdrg_top} 
    10891119\end{listing} 
     1120 
    10901121\begin{listing} 
    10911122  \nlst{namdrg_bot} 
    … …  
    14281459the Stokes Drift can be evaluated by setting \forcode{ln_sdw=.true.} 
    14291460(see \autoref{subsec:SBC_wave_sdw}) 
    1430 and the needed wave fields can be provided either in forcing or coupled mode 
     1461and the needed wave fields (significant wave height and mean wave number) can be provided either in forcing or coupled mode 
    14311462(for more information on wave parameters and settings see \autoref{sec:SBC_wave}) 
    14321463 
    … …  
    15621593by only a few extra physics choices namely: 
    15631594 
    1564 \begin{verbatim} 
     1595\begin{forlines} 
    15651596     ln_dynldf_OFF = .false. 
    15661597     ln_dynldf_lap = .true. 
    … …  
    15701601        nn_fct_h   =  2 
    15711602        nn_fct_v   =  2 
    1572 \end{verbatim} 
     1603\end{forlines} 
    15731604 
    15741605\noindent which were chosen to provide a slightly more stable and less noisy solution. The 
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