Changeset 11684
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 20191011T00:16:15+02:00 (11 months ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
r11683 r11684 537 537 %  538 538 \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.})} 540 540 \label{subsec:ZDF_osm} 541 541 … … 551 551 surface drift and penetration depth. There are three options: 552 552 \begin{description} 553 \item \ np{nn\_osm\_wave=0} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is553 \item \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is 554 554 assumed to be parallel to the surface wind stress, with 555 555 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 of558 \ np{rn\_m\_la} is 0.3. The Stokes penetration559 depth $\delta = $ \ np{rn\_osm\_dstokes}; this has default value560 of \SI{5 556 $\mathrm{La}_t=$ \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}. 561 561 562 \item \ np{nn\_osm\_wave=1} In this case the Stokes drift is562 \item \protect\np[=1]{nn_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is 563 563 assumed to be parallel to the surface wind stress, with 564 564 magnitude as in the classical PiersonMoskowitz windsea … … 567 567 depth, following the approach set out in Breivik(XXxx) 568 568 569 \item \ np{nn\_osm\_wave=2} In this case the Stokes drift is569 \item \protect\np[=2]{nn\_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is 570 570 taken from ECMWF wave model output, though only the component parallel 571 571 to the wind stress is retained. Significant wave height and … … 578 578 the surface boundary layer: 579 579 \begin{description} 580 \item \ np{ln\_kpprimix} Default is \np{.true.}. Switches on KPPstyle Ri \#dependent580 \item \protect\np{ln_kpprimix} {ln\_kpprimix} Default is \np{.true.}. Switches on KPPstyle Ri \#dependent 581 581 mixing below the surface boundary layer. If this is set 582 582 \np{.true.} the following variable settings are honoured: 583 \item \ np{rn\_riinfty} Critical value of local Ri \# below which583 \item \protect\np{rn_riinfty}{rn\_riinfty} Critical value of local Ri \# below which 584 584 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, specify587 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$^{2}$). 588 588 \end{description} 589 589 Diagnostic output is controlled by: 590 590 \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. 592 592 \end{description} 593 593 Obsolete namelist parameters include: 594 594 \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 Stokes595 \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 597 597 penetration depth. 598 \item \ np{nn\_ave} Choice of averaging method for KPPstyle Ri#598 \item \protect\np{nn_ave} {nn\_ave} Choice of averaging method for KPPstyle Ri \# 599 599 mixing. Not taken account of. 600 \item \ np{rn\_osm\_hbl0} Depth of initial boundary layer is now set601 by a de snity criterion similar to that used in600 \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. 602 602 \end{description} 603 603 … … 637 637 below should not be used with the OSMOSISOBL model: instabilities 638 638 within the OSBL are part of the model, while instabilities below the 639 ML are handled by the Ri # dependent scheme.639 ML are handled by the Ri \# dependent scheme. 640 640 641 641 \subsubsection{Depth and velocity scales} … … 658 658 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: 659 659 \begin{equation}\label{eq:compositenu} 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}. 661 661 \end{equation} 662 662 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: … … 702 702 % 703 703 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: 704 \begin{equation}\label{eq: diffwmlbase}704 \begin{equation}\label{eq:L_L} 705 705 L_L=w_{*L}^3/\left<\overline{w^\prime b^\prime}\right>_L, 706 706 \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 $I(z)$ by707 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 708 708 \begin{equation} \label{eq:stableavbuoyflux} 709 709 \left<\overline{w^\prime b^\prime}\right>_L = \tfrac{1}{2} {\overline{w^\prime b^\prime}}_0g\alpha_E\left[\tfrac{1}{2}(I(0)+I(h))\left<I\right>\right]. … … 729 729 + 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] 730 730 \end{equation} 731 where the factor $G\equiv 1  \mathrm{e}^ {25\delta/h_{\mathrm{bl}}}(14\delta/h_{\mathrm{bl}})$ models the lesser efficiency of Langmuir mixing when the boundarylayer 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 $F(x)\equiv\tanh(x^{1})^{0.69}$.731 where the factor $G\equiv 1  \mathrm{e}^ {25\delta/h_{\mathrm{bl}}}(14\delta/h_{\mathrm{bl}})$ models the lesser efficiency of Langmuir mixing when the boundarylayer 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 $F(x)\equiv\tanh(x^{1})^{0.69}$. 732 732 733 733 For the stable boundary layer, the equation for the depth of the OSBL is:
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