Changeset 11684


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Timestamp:
2019-10-11T00:16:15+02:00 (11 months ago)
Author:
agn
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chap_ZDF.tex now compiles

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1 edited

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

    r11683 r11684  
    537537% ------------------------------------------------------------------------------------------------------------- 
    538538\subsection[OSM: OSMOSIS boundary layer scheme (\forcode{ln_zdfosm = .true.})] 
    539 {OSM: OSMOSIS boundary layer scheme (\protect\np{ln\_zdfosm}\forcode{ = .true.})} 
     539{OSM: OSMOSIS boundary layer scheme (\protect\np{ln_zdfosm}{ln\_zdfosm}\forcode{ = .true.})} 
    540540\label{subsec:ZDF_osm} 
    541541 
     
    551551surface drift and penetration depth. There are three options: 
    552552\begin{description} 
    553   \item \np{nn\_osm\_wave=0} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is 
     553  \item \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is 
    554554      assumed to be parallel to the surface wind stress, with 
    555555      magnitude consistent with a constant turbulent Langmuir number 
    556     $\mathrm{La}_t=$ \np{rn\_m\_la} i.e.\ 
    557     $u_{s0}=\tau/(\np{rn\_m\_la}^2\rho_0)$.  Default value of 
    558     \np{rn\_m\_la} is 0.3. The Stokes penetration 
    559       depth $\delta = $ \np{rn\_osm\_dstokes}; this has default value 
    560       of \SI{5 m}. 
     556    $\mathrm{La}_t=$ \protect\np{rn_m_la} {rn\_m\_la} i.e.\ 
     557    $u_{s0}=\tau/(\mathrm{La}_t^2\rho_0)$.  Default value of 
     558    \protect\np{rn_m_la}{rn\_m\_la} is 0.3. The Stokes penetration 
     559      depth $\delta = $ \protect\np{rn_osm_dstokes}{rn\_osm\_dstokes}; this has default value 
     560      of \SI{5}{m}. 
    561561  
    562   \item \np{nn\_osm\_wave=1} In this case the Stokes drift is 
     562  \item \protect\np[=1]{nn_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is 
    563563      assumed to be parallel to the surface wind stress, with 
    564564      magnitude as in the classical Pierson-Moskowitz wind-sea 
     
    567567      depth, following the approach set out in Breivik(XXxx) 
    568568  
    569     \item \np{nn\_osm\_wave=2} In this case the Stokes drift is 
     569    \item \protect\np[=2]{nn\_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is 
    570570      taken from  ECMWF wave model output, though only the component parallel 
    571571      to the wind stress is retained. Significant wave height and 
     
    578578    the surface boundary layer: 
    579579\begin{description} 
    580    \item \np{ln\_kpprimix}  Default is \np{.true.}. Switches on KPP-style Ri \#-dependent 
     580   \item \protect\np{ln_kpprimix} {ln\_kpprimix}  Default is \np{.true.}. Switches on KPP-style Ri \#-dependent 
    581581     mixing below the surface boundary layer. If this is set 
    582582     \np{.true.}  the following variable settings are honoured: 
    583     \item \np{rn\_riinfty} Critical value of local Ri \# below which 
     583    \item \protect\np{rn_riinfty}{rn\_riinfty} Critical value of local Ri \# below which 
    584584      shear instability increases vertical mixing from background value. 
    585     \item \np{rn\_difri} Maximum value of Ri \#-dependent mixing at $\mathrm{Ri}=0$. 
    586     \item \np{ln\_convmix} If \texttt{.true.} then, where water column is unstable, specify 
    587        diffusivity equal to \np{rn\_dif\_conv} (default value is 1 ms$^{-2}$).  
     585    \item \protect\np{rn_difri} {rn\_difri} Maximum value of Ri \#-dependent mixing at $\mathrm{Ri}=0$. 
     586    \item \protect\np{ln_convmix}{ln\_convmix} If \texttt{.true.} then, where water column is unstable, specify 
     587       diffusivity equal to \protect\np{rn_dif_conv}{rn\_dif\_conv} (default value is 1 ms$^{-2}$).  
    588588 \end{description} 
    589589 Diagnostic output is controlled by: 
    590590  \begin{description} 
    591     \item \np{ln\_dia\_osm} Default is \np{.false.}; allows XIOS output of OSMOSIS internal fields. 
     591    \item \protect\np{ln_dia_osm}{ln\_dia\_osm} Default is \np{.false.}; allows XIOS output of OSMOSIS internal fields. 
    592592  \end{description} 
    593593Obsolete namelist parameters include: 
    594594\begin{description} 
    595    \item \np{ln\_use\_osm\_la} With \np{nn\_osm\_wave=0}, 
    596       \np{rn\_osm\_dstokes} is always used to specify the Stokes 
     595   \item \protect\np{ln_use_osm_la}\np{ln\_use\_osm\_la} With \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave}, 
     596      \protect\np{rn_osm_dstokes} {rn\_osm\_dstokes} is always used to specify the Stokes 
    597597      penetration depth. 
    598    \item \np{nn\_ave} Choice of averaging method for KPP-style Ri# 
     598   \item \protect\np{nn_ave} {nn\_ave} Choice of averaging method for KPP-style Ri \# 
    599599      mixing. Not taken account of. 
    600    \item \np{rn\_osm\_hbl0} Depth of initial boundary layer is now set 
    601      by a desnity criterion similar to that used in   
     600   \item \protect\np{rn_osm_hbl0} {rn\_osm\_hbl0} Depth of initial boundary layer is now set 
     601     by a density criterion similar to that used in calculating hmlp (output as mldr10_1) in zdfmxl.F90. 
    602602\end{description} 
    603603 
     
    637637below should not be used with the OSMOSIS-OBL model: instabilities 
    638638within the OSBL are part of the model, while instabilities below the 
    639 ML are handled by the Ri # dependent scheme. 
     639ML are handled by the Ri \# dependent scheme. 
    640640 
    641641\subsubsection{Depth and velocity scales} 
     
    658658but at times the Stokes drift may be weak due to e.g.\ ice cover, short fetch, misalignment with the surface stress, etc.\ so  a composite velocity scale is assumed for the stable (warming) boundary layer: 
    659659\begin{equation}\label{eq:composite-nu} 
    660   \nu_{\ast}= \left\{ u_*^3 \left[1-\exp(-1.5 \mathrm{La}_t^2})\right]+w_{*L}^3\right\}^{1/3}. 
     660  \nu_{\ast}= \left\{ u_*^3 \left[1-\exp(-.5 \mathrm{La}_t^2)\right]+w_{*L}^3\right\}^{1/3}. 
    661661\end{equation} 
    662662For the unstable boundary layer this is merged with the standard convective velocity scale $w_{*C}=\left(\overline{w^\prime b^\prime}_0 \,h_\mathrm{ml}\right)^{1/3}$, where $\overline{w^\prime b^\prime}_0$ is the upwards surface buoyancy flux, to give: 
     
    702702% 
    703703The shape of the eddy viscosity and diffusivity profiles is the same as the shape in the unstable OSBL. The eddy diffusivity/viscosity depends on the stability parameter $h_{\mathrm{bl}}/{L_L}$ where $ L_L$ is analogous to the Obukhov length, but for Langmuir turbulence: 
    704 \begin{equation}\label{eq:diff-wml-base}  
     704\begin{equation}\label{eq:L_L}  
    705705  L_L=-w_{*L}^3/\left<\overline{w^\prime b^\prime}\right>_L, 
    706706\end{equation} 
    707 with the mean turbulent buoyancy flux averaged over the boundary layer given in terms of its surface value $\overline{w^\prime b^\prime}}_0$ and (downwards) )solar irradiance $I(z)$ by 
     707with the mean turbulent buoyancy flux averaged over the boundary layer given in terms of its surface value $\overline{w^\prime b^\prime}_0$ and (downwards) )solar irradiance $I(z)$ by 
    708708\begin{equation} \label{eq:stable-av-buoy-flux} 
    709709\left<\overline{w^\prime b^\prime}\right>_L = \tfrac{1}{2} {\overline{w^\prime b^\prime}}_0-g\alpha_E\left[\tfrac{1}{2}(I(0)+I(-h))-\left<I\right>\right]. 
     
    729729  + G\left(\delta/h_{\mathrm{ml}} \right)\left[\alpha_{\mathrm{S}}e^{-1.5\, \mathrm{La}_t}-\alpha_{\mathrm{L}} \frac{w_{\mathrm{*L}}^3}{h_{\mathrm{ml}}}\right] 
    730730\end{equation} 
    731 where the factor $G\equiv 1 - \mathrm{e}^ {-25\delta/h_{\mathrm{bl}}}(1-4\delta/h_{\mathrm{bl}})$ models the lesser efficiency of Langmuir mixing when the boundary-layer depth is much greater than the Stokes depth, and $\alpha_{\mathrm{B}}$, $\alpha_{S}$  and $\alpha_{\mathrm{L}}$ depend on the ratio of the appropriate eddy turnover time to the inertial timescale $f^{-1}$. Results from the LES suggest $\alpha_{\mathrm{B}}=0.18 F(fh_{\mathrm{bl}}/w_{*C})$, $\alpha_{S}=0.15 F(fh_{\mathrm{bl}}/u_*}$  and $\alpha_{\mathrm{L}}=0.035 F(fh_{\mathrm{bl}}/u_{*L})$, where $F(x)\equiv\tanh(x^{-1})^{0.69}$. 
     731where the factor $G\equiv 1 - \mathrm{e}^ {-25\delta/h_{\mathrm{bl}}}(1-4\delta/h_{\mathrm{bl}})$ models the lesser efficiency of Langmuir mixing when the boundary-layer depth is much greater than the Stokes depth, and $\alpha_{\mathrm{B}}$, $\alpha_{S}$  and $\alpha_{\mathrm{L}}$ depend on the ratio of the appropriate eddy turnover time to the inertial timescale $f^{-1}$. Results from the LES suggest $\alpha_{\mathrm{B}}=0.18 F(fh_{\mathrm{bl}}/w_{*C})$, $\alpha_{S}=0.15 F(fh_{\mathrm{bl}}/u_*$  and $\alpha_{\mathrm{L}}=0.035 F(fh_{\mathrm{bl}}/u_{*L})$, where $F(x)\equiv\tanh(x^{-1})^{0.69}$. 
    732732 
    733733For the stable boundary layer, the equation for the depth of the OSBL is: 
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