Changeset 9393 for branches/2017/dev_merge_2017/DOC/tex_sub/chap_ZDF.tex
- Timestamp:
- 2018-03-13T15:00:56+01:00 (6 years ago)
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
branches/2017/dev_merge_2017/DOC/tex_sub/chap_ZDF.tex
r9392 r9393 18 18 % Vertical Mixing 19 19 % ================================================================ 20 \section{Vertical Mixing}20 \section{Vertical mixing} 21 21 \label{ZDF_zdf} 22 22 … … 42 42 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 43 43 These trends can be computed using either a forward time stepping scheme 44 (namelist parameter \ forcode{ln_zdfexp= .true.}) or a backward time stepping45 scheme (\ forcode{ln_zdfexp= .false.}) depending on the magnitude of the mixing44 (namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping 45 scheme (\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing 46 46 coefficients, and thus of the formulation used (see \S\ref{STP}). 47 47 … … 65 65 \end{align*} 66 66 67 These values are set through the \np{rn _avm0} and \np{rn_avt0} namelist parameters.67 These values are set through the \np{rn\_avm0} and \np{rn\_avt0} namelist parameters. 68 68 In all cases, do not use values smaller that those associated with the molecular 69 69 viscosity and diffusivity, that is $\sim10^{-6}~m^2.s^{-1}$ for momentum, … … 74 74 % Richardson Number Dependent 75 75 % ------------------------------------------------------------------------------------------------------------- 76 \subsection{Richardson Number Dependent (\protect\key{zdfric})}76 \subsection{Richardson number dependent (\protect\key{zdfric})} 77 77 \label{ZDF_ric} 78 78 … … 103 103 is the maximum value that can be reached by the coefficient when $Ri\leq 0$, 104 104 $a=5$ and $n=2$. The last three values can be modified by setting the 105 \np{rn _avmri}, \np{rn_alp} and \np{nn_ric} namelist parameters, respectively.105 \np{rn\_avmri}, \np{rn\_alp} and \np{nn\_ric} namelist parameters, respectively. 106 106 107 107 A simple mixing-layer model to transfer and dissipate the atmospheric 108 108 forcings (wind-stress and buoyancy fluxes) can be activated setting 109 the \np{ln _mldw} =.true.in the namelist.109 the \np{ln\_mldw}\forcode{ = .true.} in the namelist. 110 110 111 111 In this case, the local depth of turbulent wind-mixing or "Ekman depth" … … 125 125 126 126 is computed from the wind stress vector $|\tau|$ and the reference density $ \rho_o$. 127 The final $h_{e}$ is further constrained by the adjustable bounds \np{rn _mldmin} and \np{rn_mldmax}.127 The final $h_{e}$ is further constrained by the adjustable bounds \np{rn\_mldmin} and \np{rn\_mldmax}. 128 128 Once $h_{e}$ is computed, the vertical eddy coefficients within $h_{e}$ are set to 129 the empirical values \np{rn _wtmix} and \np{rn_wvmix} \citep{Lermusiaux2001}.129 the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{Lermusiaux2001}. 130 130 131 131 % ------------------------------------------------------------------------------------------------------------- 132 132 % TKE Turbulent Closure Scheme 133 133 % ------------------------------------------------------------------------------------------------------------- 134 \subsection{TKE Turbulent Closure Scheme (\protect\key{zdftke})}134 \subsection{TKE turbulent closure scheme (\protect\key{zdftke})} 135 135 \label{ZDF_tke} 136 136 … … 170 170 and diffusivity coefficients. The constants $C_k = 0.1$ and $C_\epsilon = \sqrt {2} /2$ 171 171 $\approx 0.7$ are designed to deal with vertical mixing at any depth \citep{Gaspar1990}. 172 They are set through namelist parameters \np{nn _ediff} and \np{nn_ediss}.172 They are set through namelist parameters \np{nn\_ediff} and \np{nn\_ediss}. 173 173 $P_{rt}$ can be set to unity or, following \citet{Blanke1993}, be a function 174 174 of the local Richardson number, $R_i$: … … 181 181 \end{align*} 182 182 Options are defined through the \ngn{namzdfy\_tke} namelist variables. 183 The choice of $P_{rt}$ is controlled by the \np{nn _pdl} namelist variable.183 The choice of $P_{rt}$ is controlled by the \np{nn\_pdl} namelist variable. 184 184 185 185 At the sea surface, the value of $\bar{e}$ is prescribed from the wind 186 stress field as $\bar{e}_o = e_{bb} |\tau| / \rho_o$, with $e_{bb}$ the \np{rn _ebb}186 stress field as $\bar{e}_o = e_{bb} |\tau| / \rho_o$, with $e_{bb}$ the \np{rn\_ebb} 187 187 namelist parameter. The default value of $e_{bb}$ is 3.75. \citep{Gaspar1990}), 188 188 however a much larger value can be used when taking into account the … … 191 191 The time integration of the $\bar{e}$ equation may formally lead to negative values 192 192 because the numerical scheme does not ensure its positivity. To overcome this 193 problem, a cut-off in the minimum value of $\bar{e}$ is used (\np{rn _emin}193 problem, a cut-off in the minimum value of $\bar{e}$ is used (\np{rn\_emin} 194 194 namelist parameter). Following \citet{Gaspar1990}, the cut-off value is set 195 195 to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$. This allows the subsequent formulations … … 199 199 instabilities associated with too weak vertical diffusion. They must be 200 200 specified at least larger than the molecular values, and are set through 201 \np{rn _avm0} and \np{rn_avt0} (namzdf namelist, see \S\ref{ZDF_cst}).201 \np{rn\_avm0} and \np{rn\_avt0} (namzdf namelist, see \S\ref{ZDF_cst}). 202 202 203 203 \subsubsection{Turbulent length scale} 204 204 For computational efficiency, the original formulation of the turbulent length 205 205 scales proposed by \citet{Gaspar1990} has been simplified. Four formulations 206 are proposed, the choice of which is controlled by the \np{nn _mxl} namelist206 are proposed, the choice of which is controlled by the \np{nn\_mxl} namelist 207 207 parameter. The first two are based on the following first order approximation 208 208 \citep{Blanke1993}: … … 212 212 which is valid in a stable stratified region with constant values of the Brunt- 213 213 Vais\"{a}l\"{a} frequency. The resulting length scale is bounded by the distance 214 to the surface or to the bottom (\np{nn _mxl} = 0) or by the local vertical scale factor215 (\np{nn _mxl} = 1). \citet{Blanke1993} notice that this simplification has two major214 to the surface or to the bottom (\np{nn\_mxl}\forcode{ = 0}) or by the local vertical scale factor 215 (\np{nn\_mxl}\forcode{ = 1}). \citet{Blanke1993} notice that this simplification has two major 216 216 drawbacks: it makes no sense for locally unstable stratification and the 217 217 computation no longer uses all the information contained in the vertical density 218 218 profile. To overcome these drawbacks, \citet{Madec1998} introduces the 219 \np{nn _mxl} = 2 or 3cases, which add an extra assumption concerning the vertical219 \np{nn\_mxl}\forcode{ = 2..3} cases, which add an extra assumption concerning the vertical 220 220 gradient of the computed length scale. So, the length scales are first evaluated 221 221 as in \eqref{Eq_tke_mxl0_1} and then bounded such that: … … 253 253 $i.e.$ $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$. 254 254 255 In the \np{nn _mxl}~=~2case, the dissipation and mixing length scales take the same255 In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same 256 256 value: $ l_k= l_\epsilon = \min \left(\ l_{up} \;,\; l_{dwn}\ \right)$, while in the 257 \np{nn _mxl}~=~3case, the dissipation and mixing turbulent length scales are give257 \np{nn\_mxl}\forcode{ = 3} case, the dissipation and mixing turbulent length scales are give 258 258 as in \citet{Gaspar1990}: 259 259 \begin{equation} \label{Eq_tke_mxl_gaspar} … … 264 264 \end{equation} 265 265 266 At the ocean surface, a non zero length scale is set through the \np{rn _mxl0} namelist266 At the ocean surface, a non zero length scale is set through the \np{rn\_mxl0} namelist 267 267 parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$ 268 268 where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness 269 269 parameter of the surface. Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94} 270 leads to a 0.04~m, the default value of \np{rn _mxl0}. In the ocean interior270 leads to a 0.04~m, the default value of \np{rn\_mxl0}. In the ocean interior 271 271 a minimum length scale is set to recover the molecular viscosity when $\bar{e}$ 272 272 reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). … … 296 296 citing observation evidence, and $\alpha_{CB} = 100$ the Craig and Banner's value. 297 297 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 298 with $e_{bb}$ the \np{rn _ebb} namelist parameter, setting \np{rn_ebb}~=~67.83corresponds299 to $\alpha_{CB} = 100$. Further setting \np{ln _mxl0} to true applies \eqref{ZDF_Lsbc}298 with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}\forcode{ = 67.83} corresponds 299 to $\alpha_{CB} = 100$. Further setting \np{ln\_mxl0} to true applies \eqref{ZDF_Lsbc} 300 300 as surface boundary condition on length scale, with $\beta$ hard coded to the Stacey's value. 301 Note that a minimal threshold of \np{rn _emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters)301 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) 302 302 is applied on surface $\bar{e}$ value. 303 303 … … 317 317 of LC in an extra source terms of TKE, $P_{LC}$. 318 318 The presence of $P_{LC}$ in \eqref{Eq_zdftke_e}, the TKE equation, is controlled 319 by setting \np{ln _lc} to \textit{true} in the namtke namelist.319 by setting \np{ln\_lc} to \forcode{.true.} in the namtke namelist. 320 320 321 321 By making an analogy with the characteristic convective velocity scale … … 343 343 where $c_{LC} = 0.15$ has been chosen by \citep{Axell_JGR02} as a good compromise 344 344 to fit LES data. The chosen value yields maximum vertical velocities $w_{LC}$ of the order 345 of a few centimeters per second. The value of $c_{LC}$ is set through the \np{rn _lc}345 of a few centimeters per second. The value of $c_{LC}$ is set through the \np{rn\_lc} 346 346 namelist parameter, having in mind that it should stay between 0.15 and 0.54 \citep{Axell_JGR02}. 347 347 … … 366 366 ($i.e.$ near-inertial oscillations and ocean swells and waves). 367 367 368 When using this parameterization ($i.e.$ when \np{nn _etau}~=~1), the TKE input to the ocean ($S$)368 When using this parameterization ($i.e.$ when \np{nn\_etau}\forcode{ = 1}), the TKE input to the ocean ($S$) 369 369 imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized 370 370 by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: … … 379 379 and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely 380 380 covered by sea-ice). 381 The value of $f_r$, usually a few percents, is specified through \np{rn _efr} namelist parameter.382 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn _etau}~=~0)381 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter. 382 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}\forcode{ = 0}) 383 383 or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m 384 at high latitudes (\np{nn _etau}~=~1).385 386 Note that two other option existe, \np{nn _etau}~=~2, or 3. They correspond to applying384 at high latitudes (\np{nn\_etau}\forcode{ = 1}). 385 386 Note that two other option existe, \np{nn\_etau}\forcode{ = 2..3}. They correspond to applying 387 387 \eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part 388 388 of the stress to evaluate the fraction of TKE that penetrate the ocean. … … 508 508 % GLS Generic Length Scale Scheme 509 509 % ------------------------------------------------------------------------------------------------------------- 510 \subsection{GLS Generic Length Scale (\protect\key{zdfgls})}510 \subsection{GLS: Generic Length Scale (\protect\key{zdfgls})} 511 511 \label{ZDF_gls} 512 512 … … 558 558 The constants $C_1$, $C_2$, $C_3$, ${\sigma_e}$, ${\sigma_{\psi}}$ and the wall function ($Fw$) 559 559 depends of the choice of the turbulence model. Four different turbulent models are pre-defined 560 (Tab.\ref{Tab_GLS}). They are made available through the \np{nn _clo} namelist parameter.560 (Tab.\ref{Tab_GLS}). They are made available through the \np{nn\_clo} namelist parameter. 561 561 562 562 %--------------------------------------------------TABLE-------------------------------------------------- … … 567 567 % & \citep{Mellor_Yamada_1982} & \citep{Rodi_1987} & \citep{Wilcox_1988} & \\ 568 568 \hline \hline 569 \np{nn _clo} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} \\569 \np{nn\_clo} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} \\ 570 570 \hline 571 571 $( p , n , m )$ & ( 0 , 1 , 1 ) & ( 3 , 1.5 , -1 ) & ( -1 , 0.5 , -1 ) & ( 2 , 1 , -0.67 ) \\ … … 581 581 \caption{ \protect\label{Tab_GLS} 582 582 Set of predefined GLS parameters, or equivalently predefined turbulence models available 583 with \protect\key{zdfgls} and controlled by the \protect\np{nn _clos} namelist variable in \protect\ngn{namzdf\_gls} .}583 with \protect\key{zdfgls} and controlled by the \protect\np{nn\_clos} namelist variable in \protect\ngn{namzdf\_gls} .} 584 584 \end{center} \end{table} 585 585 %-------------------------------------------------------------------------------------------------------------- … … 589 589 value near physical boundaries (logarithmic boundary layer law). $C_{\mu}$ and $C_{\mu'}$ 590 590 are calculated from stability function proposed by \citet{Galperin_al_JAS88}, or by \citet{Kantha_Clayson_1994} 591 or one of the two functions suggested by \citet{Canuto_2001} (\np{nn _stab_func} = 0, 1, 2 or 3, resp.).591 or one of the two functions suggested by \citet{Canuto_2001} (\np{nn\_stab\_func}\forcode{ = 0..3}, resp.). 592 592 The value of $C_{0\mu}$ depends of the choice of the stability function. 593 593 594 594 The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated 595 thanks to Dirichlet or Neumann condition through \np{nn _tkebc_surf} and \np{nn_tkebc_bot}, resp.596 As for TKE closure , the wave effect on the mixing is considered when \np{ln _crban}~=~true597 \citep{Craig_Banner_JPO94, Mellor_Blumberg_JPO04}. The \np{rn _crban} namelist parameter598 is $\alpha_{CB}$ in \eqref{ZDF_Esbc} and \np{rn _charn} provides the value of $\beta$ in \eqref{ZDF_Lsbc}.595 thanks to Dirichlet or Neumann condition through \np{nn\_tkebc\_surf} and \np{nn\_tkebc\_bot}, resp. 596 As for TKE closure , the wave effect on the mixing is considered when \np{ln\_crban}\forcode{ = .true.} 597 \citep{Craig_Banner_JPO94, Mellor_Blumberg_JPO04}. The \np{rn\_crban} namelist parameter 598 is $\alpha_{CB}$ in \eqref{ZDF_Esbc} and \np{rn\_charn} provides the value of $\beta$ in \eqref{ZDF_Lsbc}. 599 599 600 600 The $\psi$ equation is known to fail in stably stratified flows, and for this reason … … 606 606 stably stratified situations, and that its value has to be chosen in accordance 607 607 with the algebraic model for the turbulent fluxes. The clipping is only activated 608 if \ forcode{ln_length_lim = .true.}, and the $c_{lim}$ is set to the \np{rn_clim_galp} value.608 if \np{ln\_length\_lim}\forcode{ = .true.}, and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value. 609 609 610 610 The time and space discretization of the GLS equations follows the same energetic … … 615 615 % OSM OSMOSIS BL Scheme 616 616 % ------------------------------------------------------------------------------------------------------------- 617 \subsection{OSM OSMOSIS Boundary Layer scheme (\protect\key{zdfosm})}617 \subsection{OSM: OSMOSIS boundary layer scheme (\protect\key{zdfosm})} 618 618 \label{ZDF_osm} 619 619 … … 646 646 % Non-Penetrative Convective Adjustment 647 647 % ------------------------------------------------------------------------------------------------------------- 648 \subsection [Non-Penetrative Convective Adjustment (\protect\np{ln_tranpc})]649 {Non-Penetrative Convective Adjustment (\protect\np{ln_tranpc}=.true.)}648 \subsection[Non-penetrative convective adjmt (\protect\np{ln\_tranpc}\forcode{ = .true.})] 649 {Non-penetrative convective adjustment (\protect\np{ln\_tranpc}\forcode{ = .true.})} 650 650 \label{ZDF_npc} 651 651 … … 671 671 672 672 Options are defined through the \ngn{namzdf} namelist variables. 673 The non-penetrative convective adjustment is used when \np{ln _zdfnpc}~=~\textit{true}.674 It is applied at each \np{nn _npc} time step and mixes downwards instantaneously673 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}\forcode{ = .true.}. 674 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously 675 675 the statically unstable portion of the water column, but only until the density 676 676 structure becomes neutrally stable ($i.e.$ until the mixed portion of the water … … 713 713 % Enhanced Vertical Diffusion 714 714 % ------------------------------------------------------------------------------------------------------------- 715 \subsection [Enhanced Vertical Diffusion (\protect\np{ln_zdfevd})] 716 {Enhanced Vertical Diffusion (\protect\forcode{ln_zdfevd = .true.})} 715 \subsection{Enhanced vertical diffusion (\protect\np{ln\_zdfevd}\forcode{ = .true.})} 717 716 \label{ZDF_evd} 718 717 … … 722 721 723 722 Options are defined through the \ngn{namzdf} namelist variables. 724 The enhanced vertical diffusion parameterisation is used when \ forcode{ln_zdfevd= .true.}.723 The enhanced vertical diffusion parameterisation is used when \np{ln\_zdfevd}\forcode{ = .true.}. 725 724 In this case, the vertical eddy mixing coefficients are assigned very large values 726 725 (a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable 727 726 ($i.e.$ when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) 728 727 \citep{Lazar_PhD97, Lazar_al_JPO99}. This is done either on tracers only 729 (\ forcode{nn_evdm = 0}) or on both momentum and tracers (\forcode{nn_evdm= 1}).728 (\np{nn\_evdm}\forcode{ = 0}) or on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}). 730 729 731 730 In practice, where $N^2\leq 10^{-12}$, $A_T^{vT}$ and $A_T^{vS}$, and 732 if \ forcode{nn_evdm= 1}, the four neighbouring $A_u^{vm} \;\mbox{and}\;A_v^{vm}$733 values also, are set equal to the namelist parameter \np{rn _avevd}. A typical value731 if \np{nn\_evdm}\forcode{ = 1}, the four neighbouring $A_u^{vm} \;\mbox{and}\;A_v^{vm}$ 732 values also, are set equal to the namelist parameter \np{rn\_avevd}. A typical value 734 733 for $rn\_avevd$ is between 1 and $100~m^2.s^{-1}$. This parameterisation of 735 734 convective processes is less time consuming than the convective adjustment 736 735 algorithm presented above when mixing both tracers and momentum in the 737 736 case of static instabilities. It requires the use of an implicit time stepping on 738 vertical diffusion terms (i.e. \ forcode{ln_zdfexp= .false.}).737 vertical diffusion terms (i.e. \np{ln\_zdfexp}\forcode{ = .false.}). 739 738 740 739 Note that the stability test is performed on both \textit{before} and \textit{now} … … 745 744 % Turbulent Closure Scheme 746 745 % ------------------------------------------------------------------------------------------------------------- 747 \subsection[Turbulent Closure Scheme (\protect\key{zdf\{tke, gls, osm\}})]{Turbulent Closure Scheme (\protect\key{zdftke}, \protect\key{zdfgls} or \protect\key{zdfosm})}746 \subsection[Turbulent closure scheme (\protect\key{zdf}\{tke,gls,osm\})]{Turbulent Closure Scheme (\protect\key{zdftke}, \protect\key{zdfgls} or \protect\key{zdfosm})} 748 747 \label{ZDF_tcs} 749 748 … … 761 760 because the mixing length scale is bounded by the distance to the sea surface. 762 761 It can thus be useful to combine the enhanced vertical 763 diffusion with the turbulent closure scheme, $i.e.$ setting the \np{ln _zdfnpc}762 diffusion with the turbulent closure scheme, $i.e.$ setting the \np{ln\_zdfnpc} 764 763 namelist parameter to true and defining the turbulent closure CPP key all together. 765 764 766 765 The KPP turbulent closure scheme already includes enhanced vertical diffusion 767 766 in the case of convection, as governed by the variables $bvsqcon$ and $difcon$ 768 found in \mdl{zdfkpp}, therefore \ forcode{ln_zdfevd= .false.} should be used with the KPP767 found in \mdl{zdfkpp}, therefore \np{ln\_zdfevd}\forcode{ = .false.} should be used with the KPP 769 768 scheme. %gm% + one word on non local flux with KPP scheme trakpp.F90 module... 770 769 … … 772 771 % Double Diffusion Mixing 773 772 % ================================================================ 774 \section [Double Diffusion Mixing (\protect\key{zdfddm})] 775 {Double Diffusion Mixing (\protect\key{zdfddm})} 773 \section{Double diffusion mixing (\protect\key{zdfddm})} 776 774 \label{ZDF_ddm} 777 775 … … 855 853 % Bottom Friction 856 854 % ================================================================ 857 \section [Bottom and Top Friction (\textit{zdfbfr})] {Bottom and Top Friction (\protect\mdl{zdfbfr} module)}855 \section{Bottom and top friction (\protect\mdl{zdfbfr})} 858 856 \label{ZDF_bfr} 859 857 … … 918 916 % Linear Bottom Friction 919 917 % ------------------------------------------------------------------------------------------------------------- 920 \subsection{Linear Bottom Friction (\protect\np{nn_botfr} = 0 or 1)}918 \subsection{Linear bottom friction (\protect\np{nn\_botfr}\forcode{ = 0..1})} 921 919 \label{ZDF_bfr_linear} 922 920 … … 940 938 $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 941 939 This is the default value used in \NEMO. It corresponds to a decay time scale 942 of 115~days. It can be changed by specifying \np{rn _bfri1} (namelist parameter).940 of 115~days. It can be changed by specifying \np{rn\_bfri1} (namelist parameter). 943 941 944 942 For the linear friction case the coefficients defined in the general … … 950 948 \end{split} 951 949 \end{equation} 952 When \ forcode{nn_botfr = 1}, the value of $r$ used is \np{rn_bfri1}.953 Setting \ forcode{nn_botfr= 0} is equivalent to setting $r=0$ and leads to a free-slip950 When \np{nn\_botfr}\forcode{ = 1}, the value of $r$ used is \np{rn\_bfri1}. 951 Setting \np{nn\_botfr}\forcode{ = 0} is equivalent to setting $r=0$ and leads to a free-slip 954 952 bottom boundary condition. These values are assigned in \mdl{zdfbfr}. 955 953 From v3.2 onwards there is support for local enhancement of these values 956 via an externally defined 2D mask array (\ forcode{ln_bfr2d= .true.}) given954 via an externally defined 2D mask array (\np{ln\_bfr2d}\forcode{ = .true.}) given 957 955 in the \ifile{bfr\_coef} input NetCDF file. The mask values should vary from 0 to 1. 958 956 Locations with a non-zero mask value will have the friction coefficient increased 959 by $mask\_value$*\np{rn _bfrien}*\np{rn_bfri1}.957 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}. 960 958 961 959 % ------------------------------------------------------------------------------------------------------------- 962 960 % Non-Linear Bottom Friction 963 961 % ------------------------------------------------------------------------------------------------------------- 964 \subsection{Non- Linear Bottom Friction (\protect\np{nn_botfr} = 2)}962 \subsection{Non-linear bottom friction (\protect\np{nn\_botfr}\forcode{ = 2})} 965 963 \label{ZDF_bfr_nonlinear} 966 964 … … 977 975 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} 978 976 uses $C_D = 1.4\;10^{-3}$ and $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 979 The CME choices have been set as default values (\np{rn _bfri2} and \np{rn_bfeb2}977 The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} 980 978 namelist parameters). 981 979 … … 993 991 994 992 The coefficients that control the strength of the non-linear bottom friction are 995 initialised as namelist parameters: $C_D$= \np{rn _bfri2}, and $e_b$ =\np{rn_bfeb2}.993 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 996 994 Note for applications which treat tides explicitly a low or even zero value of 997 \np{rn _bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible998 via an externally defined 2D mask array (\ forcode{ln_bfr2d= .true.}). This works in the same way995 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible 996 via an externally defined 2D mask array (\np{ln\_bfr2d}\forcode{ = .true.}). This works in the same way 999 997 as for the linear bottom friction case with non-zero masked locations increased by 1000 $mask\_value$*\np{rn _bfrien}*\np{rn_bfri2}.998 $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}. 1001 999 1002 1000 % ------------------------------------------------------------------------------------------------------------- 1003 1001 % Bottom Friction Log-layer 1004 1002 % ------------------------------------------------------------------------------------------------------------- 1005 \subsection[Log-layer Bottom Friction enhancement (\protect\np{ln_loglayer} = .true.)]{Log-layer Bottom Friction enhancement (\protect\np{nn_botfr} = 2, \protect\np{ln_loglayer} = .true.)} 1003 \subsection[Log-layer btm frict enhncmnt (\protect\np{nn\_botfr}\forcode{ = 2}, \protect\np{ln\_loglayer}\forcode{ = .true.})] 1004 {Log-layer bottom friction enhancement (\protect\np{nn\_botfr}\forcode{ = 2}, \protect\np{ln\_loglayer}\forcode{ = .true.})} 1006 1005 \label{ZDF_bfr_loglayer} 1007 1006 1008 1007 In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally 1009 enhanced using a "law of the wall" scaling. If \np{ln _loglayer} = .true., $C_D$ is no1008 enhanced using a "law of the wall" scaling. If \np{ln\_loglayer} = .true., $C_D$ is no 1010 1009 longer constant but is related to the thickness of the last wet layer in each column by: 1011 1010 … … 1014 1013 \end{equation} 1015 1014 1016 \noindent where $\kappa$ is the von-Karman constant and \np{rn _bfrz0} is a roughness1015 \noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness 1017 1016 length provided via the namelist. 1018 1017 1019 1018 For stability, the drag coefficient is bounded such that it is kept greater or equal to 1020 the base \np{rn _bfri2} value and it is not allowed to exceed the value of an additional1021 namelist parameter: \np{rn _bfri2_max}, i.e.:1019 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional 1020 namelist parameter: \np{rn\_bfri2\_max}, i.e.: 1022 1021 1023 1022 \begin{equation} … … 1026 1025 1027 1026 \noindent Note also that a log-layer enhancement can also be applied to the top boundary 1028 friction if under ice-shelf cavities are in use (\np{ln _isfcav}=.true.). In this case, the1029 relevant namelist parameters are \np{rn _tfrz0}, \np{rn_tfri2}1030 and \np{rn _tfri2_max}.1027 friction if under ice-shelf cavities are in use (\np{ln\_isfcav}\forcode{ = .true.}). In this case, the 1028 relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} 1029 and \np{rn\_tfri2\_max}. 1031 1030 1032 1031 % ------------------------------------------------------------------------------------------------------------- 1033 1032 % Bottom Friction stability 1034 1033 % ------------------------------------------------------------------------------------------------------------- 1035 \subsection{Bottom Friction stability considerations}1034 \subsection{Bottom friction stability considerations} 1036 1035 \label{ZDF_bfr_stability} 1037 1036 … … 1082 1081 % Implicit Bottom Friction 1083 1082 % ------------------------------------------------------------------------------------------------------------- 1084 \subsection [Implicit Bottom Friction (\protect\np{ln_bfrimp})]{Implicit Bottom Friction (\protect\np{ln_bfrimp}$=$\textit{T})}1083 \subsection{Implicit bottom friction (\protect\np{ln\_bfrimp}\forcode{ = .true.})} 1085 1084 \label{ZDF_bfr_imp} 1086 1085 1087 1086 An optional implicit form of bottom friction has been implemented to improve 1088 1087 model stability. We recommend this option for shelf sea and coastal ocean applications, especially 1089 for split-explicit time splitting. This option can be invoked by setting \np{ln _bfrimp}1090 to \ textit{true} in the \textit{nambfr} namelist. This option requires \np{ln_zdfexp} to be \textit{false}1088 for split-explicit time splitting. This option can be invoked by setting \np{ln\_bfrimp} 1089 to \forcode{.true.} in the \textit{nambfr} namelist. This option requires \np{ln\_zdfexp} to be \forcode{.false.} 1091 1090 in the \textit{namzdf} namelist. 1092 1091 … … 1135 1134 % Bottom Friction with split-explicit time splitting 1136 1135 % ------------------------------------------------------------------------------------------------------------- 1137 \subsection[Bottom Friction with split-explicit time splitting]{Bottom Friction with split-explicit time splitting (\protect\np{ln_bfrimp})} 1136 \subsection[Bottom friction w/ split-explicit time splitting (\protect\np{ln\_bfrimp})] 1137 {Bottom friction with split-explicit time splitting (\protect\np{ln\_bfrimp})} 1138 1138 \label{ZDF_bfr_ts} 1139 1139 … … 1144 1144 \key{dynspg\_flt}). Extra attention is required, however, when using 1145 1145 split-explicit time stepping (\key{dynspg\_ts}). In this case the free surface 1146 equation is solved with a small time step \np{rn _rdt}/\np{nn_baro}, while the three1146 equation is solved with a small time step \np{rn\_rdt}/\np{nn\_baro}, while the three 1147 1147 dimensional prognostic variables are solved with the longer time step 1148 of \np{rn _rdt} seconds. The trend in the barotropic momentum due to bottom1148 of \np{rn\_rdt} seconds. The trend in the barotropic momentum due to bottom 1149 1149 friction appropriate to this method is that given by the selected parameterisation 1150 1150 ($i.e.$ linear or non-linear bottom friction) computed with the evolving velocities … … 1176 1176 limiting is thought to be having a major effect (a more likely prospect in coastal and shelf seas 1177 1177 applications) then the fully implicit form of the bottom friction should be used (see \S\ref{ZDF_bfr_imp} ) 1178 which can be selected by setting \np{ln _bfrimp} $=$ \textit{true}.1178 which can be selected by setting \np{ln\_bfrimp} $=$ \forcode{.true.}. 1179 1179 1180 1180 Otherwise, the implicit formulation takes the form: … … 1192 1192 % Tidal Mixing 1193 1193 % ================================================================ 1194 \section{Tidal Mixing (\protect\key{zdftmx})}1194 \section{Tidal mixing (\protect\key{zdftmx})} 1195 1195 \label{ZDF_tmx} 1196 1196 … … 1220 1220 and $F(z)$ the vertical structure function. 1221 1221 1222 The mixing efficiency of turbulence is set by $\Gamma$ (\np{rn _me} namelist parameter)1222 The mixing efficiency of turbulence is set by $\Gamma$ (\np{rn\_me} namelist parameter) 1223 1223 and is usually taken to be the canonical value of $\Gamma = 0.2$ (Osborn 1980). 1224 The tidal dissipation efficiency is given by the parameter $q$ (\np{rn _tfe} namelist parameter)1224 The tidal dissipation efficiency is given by the parameter $q$ (\np{rn\_tfe} namelist parameter) 1225 1225 represents the part of the internal wave energy flux $E(x, y)$ that is dissipated locally, 1226 1226 with the remaining $1-q$ radiating away as low mode internal waves and … … 1229 1229 The vertical structure function $F(z)$ models the distribution of the turbulent mixing in the vertical. 1230 1230 It is implemented as a simple exponential decaying upward away from the bottom, 1231 with a vertical scale of $h_o$ (\np{rn _htmx} namelist parameter, with a typical value of $500\,m$) \citep{St_Laurent_Nash_DSR04},1231 with a vertical scale of $h_o$ (\np{rn\_htmx} namelist parameter, with a typical value of $500\,m$) \citep{St_Laurent_Nash_DSR04}, 1232 1232 \begin{equation} \label{Eq_Fz} 1233 1233 F(i,j,k) = \frac{ e^{ -\frac{H+z}{h_o} } }{ h_o \left( 1- e^{ -\frac{H}{h_o} } \right) } … … 1238 1238 diffusivity assuming a Prandtl number of 1, $i.e.$ $A^{vm}_{tides}=A^{vT}_{tides}$. 1239 1239 In the limit of $N \rightarrow 0$ (or becoming negative), the vertical diffusivity 1240 is capped at $300\,cm^2/s$ and impose a lower limit on $N^2$ of \np{rn _n2min}1240 is capped at $300\,cm^2/s$ and impose a lower limit on $N^2$ of \np{rn\_n2min} 1241 1241 usually set to $10^{-8} s^{-2}$. These bounds are usually rarely encountered. 1242 1242 … … 1266 1266 % Indonesian area specific treatment 1267 1267 % ------------------------------------------------------------------------------------------------------------- 1268 \subsection{Indonesian area specific treatment (\protect\np{ln _zdftmx_itf})}1268 \subsection{Indonesian area specific treatment (\protect\np{ln\_zdftmx\_itf})} 1269 1269 \label{ZDF_tmx_itf} 1270 1270 1271 1271 When the Indonesian Through Flow (ITF) area is included in the model domain, 1272 1272 a specific treatment of tidal induced mixing in this area can be used. 1273 It is activated through the namelist logical \np{ln _tmx_itf}, and the user must provide1273 It is activated through the namelist logical \np{ln\_tmx\_itf}, and the user must provide 1274 1274 an input NetCDF file, \ifile{mask\_itf}, which contains a mask array defining the ITF area 1275 1275 where the specific treatment is applied. 1276 1276 1277 When \ forcode{ln_tmx_itf= .true.}, the two key parameters $q$ and $F(z)$ are adjusted following1277 When \np{ln\_tmx\_itf}\forcode{ = .true.}, the two key parameters $q$ and $F(z)$ are adjusted following 1278 1278 the parameterisation developed by \citet{Koch-Larrouy_al_GRL07}: 1279 1279 … … 1285 1285 So it is assumed that $q = 1$, $i.e.$ all the energy generated is available for mixing. 1286 1286 Note that for test purposed, the ITF tidal dissipation efficiency is a 1287 namelist parameter (\np{rn _tfe_itf}). A value of $1$ or close to is1287 namelist parameter (\np{rn\_tfe\_itf}). A value of $1$ or close to is 1288 1288 this recommended for this parameter. 1289 1289 … … 1329 1329 \end{equation} 1330 1330 where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution 1331 of the energy available for mixing. If the \np{ln _mevar} namelist parameter is set to false,1331 of the energy available for mixing. If the \np{ln\_mevar} namelist parameter is set to false, 1332 1332 the mixing efficiency is taken as constant and equal to 1/6 \citep{Osborn_JPO80}. 1333 1333 In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter … … 1338 1338 1339 1339 In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary 1340 as a function of $Re_b$ by setting the \np{ln _tsdiff} parameter to true, a recommended choice).1340 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice). 1341 1341 This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014}, 1342 1342 is implemented as in \cite{de_lavergne_JPO2016_efficiency}. … … 1356 1356 h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz' } \; , 1357 1357 \end{equation*} 1358 The $n_p$ parameter (given by \np{nn _zpyc} in \ngn{namzdf\_tmx\_new} namelist) controls the stratification-dependence of the pycnocline-intensified dissipation.1358 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist) controls the stratification-dependence of the pycnocline-intensified dissipation. 1359 1359 It can take values of 1 (recommended) or 2. 1360 1360 Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of
Note: See TracChangeset
for help on using the changeset viewer.
