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Changeset 11690 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex – NEMO

2019-10-11T19:05:10+02:00 (5 years ago)

Update chapters according to previous commit

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

    r11685 r11690  
    249249  \centering 
    250   \includegraphics[width=0.66\textwidth]{Fig_mixing_length} 
     250  \includegraphics[width=0.66\textwidth]{ZDF_mixing_length} 
    251251  \caption[Mixing length computation]{Illustration of the mixing length computation} 
    252252  \label{fig:ZDF_mixing_length} 
    535535% ------------------------------------------------------------------------------------------------------------- 
    536 %        OSM OSMOSIS BL Scheme  
     536%        OSM OSMOSIS BL Scheme 
    537537% ------------------------------------------------------------------------------------------------------------- 
    538538\subsection[OSM: OSMOSIS boundary layer scheme (\forcode{ln_zdfosm = .true.})] 
    559559      depth $\delta = $ \protect\np{rn_osm_dstokes}{rn\_osm\_dstokes}; this has default value 
    560560      of 5~m. 
    562562  \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 
    566566      wave-mean period taken from this spectrum are used to calculate the Stokes penetration 
    567567      depth, following the approach set out in  \citet{breivik.janssen.ea_JPO14}. 
    569569    \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 
    585585    \item \protect\np{rn_difri} {rn\_difri} Maximum value of Ri \#-dependent mixing at $\mathrm{Ri}=0$. 
    586586    \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 m~s$^{-2}$).  
     587       diffusivity equal to \protect\np{rn_dif_conv}{rn\_dif\_conv} (default value is 1 m~s$^{-2}$). 
    588588 \end{description} 
    589589 Diagnostic output is controlled by: 
    618618parameterization (KPP) scheme of \citet{large.ea_RG97}. 
    619619A specified shape of diffusivity, scaled by the (OSBL) depth 
    620 $h_{\mathrm{BL}}$ and a turbulent velocity scale, is imposed throughout the  
     620$h_{\mathrm{BL}}$ and a turbulent velocity scale, is imposed throughout the 
    621621boundary layer 
    622622$-h_{\mathrm{BL}}<z<\eta$. The turbulent closure model 
    627627as in KPP, it is set by a prognostic equation that is informed by 
    628628energy budget considerations reminiscent of the classical mixed layer 
    629 models of \citet{kraus.turner_tellus67}.  
     629models of \citet{kraus.turner_tellus67}. 
    630630The model also includes an explicit parametrization of the structure 
    631631of the pycnocline (the stratified region at the bottom of the OSBL). 
    644644  \begin{center} 
    645     \includegraphics[width=0.7\textwidth]{Fig_ZDF_OSM_structure_of_OSBL} 
     645    %\includegraphics[width=0.7\textwidth]{ZDF_OSM_structure_of_OSBL} 
    646646    \caption{ 
    647647      \protect\label{fig: OSBL_structure} 
    656656w_{*L}= \left(u_*^2 u_{s\,0}\right)^{1/3}; 
    657 \end{equation}  
    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: 
    690690where $\beta_d$ and $\beta_\nu$ are parameters that are determined by matching Eqs \ref{eq:diff-unstable} and \ref{eq:visc-unstable} to the eddy diffusivity and viscosity at the base of the well-mixed layer, given by 
    692 \begin{equation}\label{eq:diff-wml-base}  
    693693K_{d,\mathrm{ml}}=K_{\nu,\mathrm{ml}}=\,0.16\,\omega_* \Delta h. 
    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:L_L}  
    705705  L_L=-w_{*L}^3/\left<\overline{w^\prime b^\prime}\right>_L, 
    746746\max\left(\Delta B_{bl},\frac{w_{*L}^2}{h_\mathrm{bl}}\right)\frac{\partial h_\mathrm{bl}}{\partial t} = \left(0.06 + 0.52\,\frac{ h_\mathrm{bl}}{L_L}\right) \frac{w_{*L}^3}{h_\mathrm{bl}} +\left<\overline{w^\prime b^\prime}\right>_L. 
    747 \end{equation}  
    749749Equation. \ref{eq:dhdt-unstable} always leads to the depth of the entraining OSBL increasing (ignoring the effect of the mean vertical motion), but the change in the thickness of the stable OSBL given by Eq. \ref{eq:dhdt-stable} can be positive or negative, depending on the magnitudes of $\left<\overline{w^\prime b^\prime}\right>_L$ and $h_\mathrm{bl}/L_L$. The rate at which the depth of the OSBL can decrease is limited by choosing an effective buoyancy $w_{*L}^2/h_\mathrm{bl}$, in place of $\Delta B_{bl}$ which will be $\approx 0$ for the collapsing OSBL. 
    757757  \centering 
    758   \includegraphics[width=0.66\textwidth]{Fig_ZDF_TKE_time_scheme} 
     758  \includegraphics[width=0.66\textwidth]{ZDF_TKE_time_scheme} 
    759759  \caption[Subgrid kinetic energy integration in GLS and TKE schemes]{ 
    760760    Illustration of the subgrid kinetic energy integration in GLS and TKE schemes and 
    869869  \centering 
    870   \includegraphics[width=0.66\textwidth]{Fig_npc} 
     870  \includegraphics[width=0.66\textwidth]{ZDF_npc} 
    871871  \caption[Unstable density profile treated by the non penetrative convective adjustment algorithm]{ 
    872872    Example of an unstable density profile treated by 
    10141014  \centering 
    1015   \includegraphics[width=0.66\textwidth]{Fig_zdfddm} 
     1015  \includegraphics[width=0.66\textwidth]{ZDF_ddm} 
    10161016  \caption[Diapycnal diffusivities for temperature and salt in regions of salt fingering and 
    10171017  diffusive convection]{ 
    14921492  \centering 
    1493   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_coeff} 
     1493  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_coeff} 
    14941494  \caption[Partitioning coefficient used to partition vertical velocities into parts]{ 
    14951495    The value of the partitioning coefficient (\cf) used to partition vertical velocities into 
    15321532  \centering 
    1533   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_overflow_frames} 
     1533  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_overflow_frames} 
    15341534  \caption[OVERFLOW: time-series of temperature vertical cross-sections]{ 
    15351535    A time-series of temperature vertical cross-sections for the OVERFLOW test case. 
    16121612  \centering 
    1613   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_overflow_all_rdt} 
     1613  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_overflow_all_rdt} 
    16141614  \caption[OVERFLOW: sample temperature vertical cross-sections from mid- and end-run]{ 
    16151615    Sample temperature vertical cross-sections from mid- and end-run using 
    16251625  \centering 
    1626   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_maxCf} 
     1626  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_maxCf} 
    16271627  \caption[OVERFLOW: maximum partitioning coefficient during a series of test runs]{ 
    16281628    The maximum partitioning coefficient during a series of test runs with 
    16361636  \centering 
    1637   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_maxCf_loc} 
     1637  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_maxCf_loc} 
    16381638  \caption[OVERFLOW: maximum partitioning coefficient for the case overlaid]{ 
    16391639    The maximum partitioning coefficient for the \forcode{nn_rdt=10.0} case overlaid with 
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