# Changeset 11684

Ignore:
Timestamp:
2019-10-11T00:16:15+02:00 (11 months ago)
Message:

chap_ZDF.tex now compiles

File:
1 edited

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 r11683 % ------------------------------------------------------------------------------------------------------------- \subsection[OSM: OSMOSIS boundary layer scheme (\forcode{ln_zdfosm = .true.})] {OSM: OSMOSIS boundary layer scheme (\protect\np{ln\_zdfosm}\forcode{ = .true.})} {OSM: OSMOSIS boundary layer scheme (\protect\np{ln_zdfosm}{ln\_zdfosm}\forcode{ = .true.})} \label{subsec:ZDF_osm} surface drift and penetration depth. There are three options: \begin{description} \item \np{nn\_osm\_wave=0} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is \item \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is assumed to be parallel to the surface wind stress, with magnitude consistent with a constant turbulent Langmuir number $\mathrm{La}_t=$ \np{rn\_m\_la} i.e.\ $u_{s0}=\tau/(\np{rn\_m\_la}^2\rho_0)$.  Default value of \np{rn\_m\_la} is 0.3. The Stokes penetration depth $\delta =$ \np{rn\_osm\_dstokes}; this has default value of \SI{5 m}. $\mathrm{La}_t=$ \protect\np{rn_m_la} {rn\_m\_la} i.e.\ $u_{s0}=\tau/(\mathrm{La}_t^2\rho_0)$.  Default value of \protect\np{rn_m_la}{rn\_m\_la} is 0.3. The Stokes penetration depth $\delta =$ \protect\np{rn_osm_dstokes}{rn\_osm\_dstokes}; this has default value of \SI{5}{m}. \item \np{nn\_osm\_wave=1} In this case the Stokes drift is \item \protect\np[=1]{nn_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is assumed to be parallel to the surface wind stress, with magnitude as in the classical Pierson-Moskowitz wind-sea depth, following the approach set out in Breivik(XXxx) \item \np{nn\_osm\_wave=2} In this case the Stokes drift is \item \protect\np[=2]{nn\_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is taken from  ECMWF wave model output, though only the component parallel to the wind stress is retained. Significant wave height and the surface boundary layer: \begin{description} \item \np{ln\_kpprimix}  Default is \np{.true.}. Switches on KPP-style Ri \#-dependent \item \protect\np{ln_kpprimix} {ln\_kpprimix}  Default is \np{.true.}. Switches on KPP-style Ri \#-dependent mixing below the surface boundary layer. If this is set \np{.true.}  the following variable settings are honoured: \item \np{rn\_riinfty} Critical value of local Ri \# below which \item \protect\np{rn_riinfty}{rn\_riinfty} Critical value of local Ri \# below which shear instability increases vertical mixing from background value. \item \np{rn\_difri} Maximum value of Ri \#-dependent mixing at $\mathrm{Ri}=0$. \item \np{ln\_convmix} If \texttt{.true.} then, where water column is unstable, specify diffusivity equal to \np{rn\_dif\_conv} (default value is 1 ms$^{-2}$). \item \protect\np{rn_difri} {rn\_difri} Maximum value of Ri \#-dependent mixing at $\mathrm{Ri}=0$. \item \protect\np{ln_convmix}{ln\_convmix} If \texttt{.true.} then, where water column is unstable, specify diffusivity equal to \protect\np{rn_dif_conv}{rn\_dif\_conv} (default value is 1 ms$^{-2}$). \end{description} Diagnostic output is controlled by: \begin{description} \item \np{ln\_dia\_osm} Default is \np{.false.}; allows XIOS output of OSMOSIS internal fields. \item \protect\np{ln_dia_osm}{ln\_dia\_osm} Default is \np{.false.}; allows XIOS output of OSMOSIS internal fields. \end{description} Obsolete namelist parameters include: \begin{description} \item \np{ln\_use\_osm\_la} With \np{nn\_osm\_wave=0}, \np{rn\_osm\_dstokes} is always used to specify the Stokes \item \protect\np{ln_use_osm_la}\np{ln\_use\_osm\_la} With \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave}, \protect\np{rn_osm_dstokes} {rn\_osm\_dstokes} is always used to specify the Stokes penetration depth. \item \np{nn\_ave} Choice of averaging method for KPP-style Ri# \item \protect\np{nn_ave} {nn\_ave} Choice of averaging method for KPP-style Ri \# mixing. Not taken account of. \item \np{rn\_osm\_hbl0} Depth of initial boundary layer is now set by a desnity criterion similar to that used in \item \protect\np{rn_osm_hbl0} {rn\_osm\_hbl0} Depth of initial boundary layer is now set by a density criterion similar to that used in calculating hmlp (output as mldr10_1) in zdfmxl.F90. \end{description} below should not be used with the OSMOSIS-OBL model: instabilities within the OSBL are part of the model, while instabilities below the ML are handled by the Ri # dependent scheme. ML are handled by the Ri \# dependent scheme. \subsubsection{Depth and velocity scales} but 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: \label{eq:composite-nu} \nu_{\ast}= \left\{ u_*^3 \left[1-\exp(-1.5 \mathrm{La}_t^2})\right]+w_{*L}^3\right\}^{1/3}. \nu_{\ast}= \left\{ u_*^3 \left[1-\exp(-.5 \mathrm{La}_t^2)\right]+w_{*L}^3\right\}^{1/3}. For 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: % The 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: \label{eq:diff-wml-base} \label{eq:L_L} L_L=-w_{*L}^3/\left<\overline{w^\prime b^\prime}\right>_L, 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 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 \label{eq:stable-av-buoy-flux} \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\right]. + 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] 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 $F(x)\equiv\tanh(x^{-1})^{0.69}$. 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 $F(x)\equiv\tanh(x^{-1})^{0.69}$. For the stable boundary layer, the equation for the depth of the OSBL is: