Changeset 10442 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
r10414 r10442 25 25 At the surface they are prescribed from the surface forcing (see \autoref{chap:SBC}), 26 26 while at the bottom they are set to zero for heat and salt, 27 unless a geothermal flux forcing is prescribed as a bottom boundary condition ( $i.e.$\key{trabbl} defined,27 unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \key{trabbl} defined, 28 28 see \autoref{subsec:TRA_bbc}), and specified through a bottom friction parameterisation for momentum 29 29 (see \autoref{sec:ZDF_bfr}). … … 86 86 The hypothesis of a mixing mainly maintained by the growth of Kelvin-Helmholtz like instabilities leads to 87 87 a dependency between the vertical eddy coefficients and the local Richardson number 88 ( $i.e.$the ratio of stratification to vertical shear).88 (\ie the ratio of stratification to vertical shear). 89 89 Following \citet{Pacanowski_Philander_JPO81}, the following formulation has been implemented: 90 90 \[ … … 254 254 \end{aligned} 255 255 \] 256 where $l^{(k)}$ is computed using \autoref{eq:tke_mxl0_1}, $i.e.$$l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$.256 where $l^{(k)}$ is computed using \autoref{eq:tke_mxl0_1}, \ie $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$. 257 257 258 258 In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value: … … 326 326 \forcode{.true.} in the namtke namelist. 327 327 328 By making an analogy with the characteristic convective velocity scale ( $e.g.$, \citet{D'Alessio_al_JPO98}),328 By making an analogy with the characteristic convective velocity scale (\eg, \citet{D'Alessio_al_JPO98}), 329 329 $P_{LC}$ is assumed to be : 330 330 \[ … … 369 369 This bias is particularly acute over the Southern Ocean. 370 370 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}. 371 The parameterization is an empirical one, $i.e.$not derived from theoretical considerations,371 The parameterization is an empirical one, \ie not derived from theoretical considerations, 372 372 but rather is meant to account for observed processes that affect the density structure of 373 373 the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme 374 ( $i.e.$near-inertial oscillations and ocean swells and waves).375 376 When using this parameterization ( $i.e.$when \np{nn\_etau}\forcode{ = 1}),374 (\ie near-inertial oscillations and ocean swells and waves). 375 376 When using this parameterization (\ie when \np{nn\_etau}\forcode{ = 1}), 377 377 the TKE input to the ocean ($S$) imposed by the winds in the form of near-inertial oscillations, 378 378 swell and waves is parameterized by \autoref{eq:ZDF_Esbc} the standard TKE surface boundary condition, … … 403 403 % excluded by the hydrostatic assumption and the model resolution. 404 404 % Thus far, the representation of internal wave mixing in ocean models has been relatively crude 405 % ( e.g.Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002).405 % (\eg Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 406 406 407 407 % ------------------------------------------------------------------------------------------------------------- … … 654 654 %-------------------------------------------------------------------------------------------------------------- 655 655 656 Static instabilities ( i.e.light potential densities under heavy ones) may occur at particular ocean grid points.656 Static instabilities (\ie light potential densities under heavy ones) may occur at particular ocean grid points. 657 657 In nature, convective processes quickly re-establish the static stability of the water column. 658 658 These processes have been removed from the model via the hydrostatic assumption so they must be parameterized. … … 699 699 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously the statically unstable portion of 700 700 the water column, but only until the density structure becomes neutrally stable 701 ( $i.e.$until the mixed portion of the water column has \textit{exactly} the density of the water just below)701 (\ie until the mixed portion of the water column has \textit{exactly} the density of the water just below) 702 702 \citep{Madec_al_JPO91}. 703 703 The associated algorithm is an iterative process used in the following way (\autoref{fig:npc}): … … 748 748 In this case, the vertical eddy mixing coefficients are assigned very large values 749 749 (a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable 750 ( $i.e.$when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}.750 (\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}. 751 751 This is done either on tracers only (\np{nn\_evdm}\forcode{ = 0}) or 752 752 on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}). … … 760 760 momentum in the case of static instabilities. 761 761 It requires the use of an implicit time stepping on vertical diffusion terms 762 ( i.e. \np{ln\_zdfexp}\forcode{ = .false.}).762 (\ie np{ln\_zdfexp}\forcode{ = .false.}). 763 763 764 764 Note that the stability test is performed on both \textit{before} and \textit{now} values of $N^2$. … … 784 784 because the mixing length scale is bounded by the distance to the sea surface. 785 785 It can thus be useful to combine the enhanced vertical diffusion with the turbulent closure scheme, 786 $i.e.$setting the \np{ln\_zdfnpc} namelist parameter to true and786 \ie setting the \np{ln\_zdfnpc} namelist parameter to true and 787 787 defining the turbulent closure CPP key all together. 788 788 … … 855 855 856 856 The factor 0.7 in \autoref{eq:zdfddm_f_T} reflects the measured ratio $\alpha F_T /\beta F_S \approx 0.7$ of 857 buoyancy flux of heat to buoyancy flux of salt ( $e.g.$, \citet{McDougall_Taylor_JMR84}).857 buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{McDougall_Taylor_JMR84}). 858 858 Following \citet{Merryfield1999}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$. 859 859 … … 955 955 956 956 The linear bottom friction parameterisation (including the special case of a free-slip condition) assumes that 957 the bottom friction is proportional to the interior velocity ( i.e.the velocity of the last model level):957 the bottom friction is proportional to the interior velocity (\ie the velocity of the last model level): 958 958 \[ 959 959 % \label{eq:zdfbfr_linear} … … 1049 1049 For stability, the drag coefficient is bounded such that it is kept greater or equal to 1050 1050 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional namelist parameter: 1051 \np{rn\_bfri2\_max}, i.e.:1051 \np{rn\_bfri2\_max}, \ie 1052 1052 \[ 1053 1053 rn\_bfri2 \leq C_D \leq rn\_bfri2\_max … … 1135 1135 and update it with the latest value. 1136 1136 On the other hand, the bottom friction contributed by the other terms 1137 ( e.g.the advection term, viscosity term) has been included in the 3-D momentum equations and1137 (\eg the advection term, viscosity term) has been included in the 3-D momentum equations and 1138 1138 should not be added in the 2-D barotropic mode. 1139 1139 … … 1175 1175 while the three dimensional prognostic variables are solved with the longer time step of \np{rn\_rdt} seconds. 1176 1176 The trend in the barotropic momentum due to bottom friction appropriate to this method is that given by 1177 the selected parameterisation ( $i.e.$linear or non-linear bottom friction) computed with1177 the selected parameterisation (\ie linear or non-linear bottom friction) computed with 1178 1178 the evolving velocities at each barotropic timestep. 1179 1179 … … 1264 1264 1265 1265 The associated vertical viscosity is calculated from the vertical diffusivity assuming a Prandtl number of 1, 1266 $i.e.$$A^{vm}_{tides}=A^{vT}_{tides}$.1266 \ie $A^{vm}_{tides}=A^{vT}_{tides}$. 1267 1267 In the limit of $N \rightarrow 0$ (or becoming negative), the vertical diffusivity is capped at $300\,cm^2/s$ and 1268 1268 impose a lower limit on $N^2$ of \np{rn\_n2min} usually set to $10^{-8} s^{-2}$. … … 1312 1312 Once generated, internal tides remain confined within this semi-enclosed area and hardly radiate away. 1313 1313 Therefore all the internal tides energy is consumed within this area. 1314 So it is assumed that $q = 1$, $i.e.$all the energy generated is available for mixing.1314 So it is assumed that $q = 1$, \ie all the energy generated is available for mixing. 1315 1315 Note that for test purposed, the ITF tidal dissipation efficiency is a namelist parameter (\np{rn\_tfe\_itf}). 1316 1316 A value of $1$ or close to is this recommended for this parameter. … … 1401 1401 \biblio 1402 1402 1403 \pindex 1404 1403 1405 \end{document}
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