Changeset 1224 for trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex
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- 2008-11-26T14:52:28+01:00 (16 years ago)
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trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex (modified) (18 diffs)
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trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex
r998 r1224 7 7 8 8 %gm% Add here a small introduction to ZDF and naming of the different physics (similar to what have been written for TRA and DYN. 9 \gmcomment{Steven remark : problem here with turbulent vs turbulence. I've changed "turbulent closure" to "turbulence closure", "turbulent mixing length" to "turbulence mixing length", but I've left "turbulent kinetic energy" alone - though I think it is an historical abberation! 10 Gurvan : I kept "turbulent closure"...} 11 \gmcomment{Steven bis : parameterization is the american spelling, parameterisation is the british} 9 \gmcomment{Steven remark (not taken into account : problem here with turbulent vs turbulence. I've changed "turbulent closure" to "turbulence closure", "turbulent mixing length" to "turbulence mixing length", but I've left "turbulent kinetic energy" alone - though I think it is an historical abberation! 10 Gurvan : I kept "turbulent closure etc "...} 12 11 13 12 … … 25 24 flux forcing is prescribed as a bottom boundary condition ($i.e.$ \key{trabbl} 26 25 defined, see \S\ref{TRA_bbc}), and specified through a bottom friction 27 parameteri zation for momentum (see \S\ref{ZDF_bfr}).26 parameterisation for momentum (see \S\ref{ZDF_bfr}). 28 27 29 28 In this section we briefly discuss the various choices offered to compute … … 84 83 large scale ocean structures. The hypothesis of a mixing mainly maintained by the 85 84 growth of Kelvin-Helmholtz like instabilities leads to a dependency between the 86 vertical turbulenceeddy coefficients and the local Richardson number ($i.e.$ the85 vertical eddy coefficients and the local Richardson number ($i.e.$ the 87 86 ratio of stratification to vertical shear). Following \citet{PacPhil1981}, the following 88 87 formulation has been implemented: … … 114 113 The vertical eddy viscosity and diffusivity coefficients are computed from a TKE 115 114 turbulent closure model based on a prognostic equation for $\bar {e}$, the turbulent 116 kinetic energy, and a closure assumption for the turbulen celength scales. This115 kinetic energy, and a closure assumption for the turbulent length scales. This 117 116 turbulent closure model has been developed by \citet{Bougeault1989} in the 118 117 atmospheric case, adapted by \citet{Gaspar1990} for the oceanic case, and … … 156 155 The choice of $P_{rt} $ is controlled by the \np{npdl} namelist parameter. 157 156 158 For computational efficiency, the original formulation of the turbulen celength157 For computational efficiency, the original formulation of the turbulent length 159 158 scales proposed by \citet{Gaspar1990} has been simplified. Four formulations 160 159 are proposed, the choice of which is controlled by the \np{nmxl} namelist … … 186 185 constraint, we introduce two additional length scales: $l_{up}$ and $l_{dwn}$, 187 186 the upward and downward length scales, and evaluate the dissipation and 188 mixing turbulen celength scales as (and note that here we use numerical187 mixing turbulent length scales as (and note that here we use numerical 189 188 indexing): 190 189 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 208 207 In the \np{nmxl}=2 case, the dissipation and mixing length scales take the same 209 208 value: $ l_k= l_\epsilon = \min \left(\ l_{up} \;,\; l_{dwn}\ \right)$, while in the 210 \np{nmxl}=2 case, the dissipation and mixing turbulencelength scales are give209 \np{nmxl}=2 case, the dissipation and mixing length scales are give 211 210 as in \citet{Gaspar1990}: 212 211 \begin{equation} \label{Eq_tke_mxl_gaspar} … … 243 242 %-------------------------------------------------------------------------------------------------------------- 244 243 245 The KKP scheme has been implemented by J. Chanut ... 244 The K-Profile Parametrization (KKP) developed by \cite{Large_al_RG94} has been 245 implemented in \NEMO by J. Chanut (PhD reference to be added here!). 246 246 247 247 \colorbox{yellow}{Add a description of KPP here.} … … 262 262 quickly re-establish the static stability of the water column. These 263 263 processes have been removed from the model via the hydrostatic 264 assumption so they must be parameterized. Three parameteri zations264 assumption so they must be parameterized. Three parameterisations 265 265 are available to deal with convective processes: a non-penetrative 266 266 convective adjustment or an enhanced vertical diffusion, or/and the … … 354 354 %-------------------------------------------------------------------------------------------------------------- 355 355 356 The enhanced vertical diffusion parameteri zation is used when \np{ln\_zdfevd}=true.356 The enhanced vertical diffusion parameterisation is used when \np{ln\_zdfevd}=true. 357 357 In this case, the vertical eddy mixing coefficients are assigned very large values 358 358 (a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable … … 364 364 if \np{n\_evdm}=1, the four neighbouring $A_u^{vm} \;\mbox{and}\;A_v^{vm}$ 365 365 values also, are set equal to the namelist parameter \np{avevd}. A typical value 366 for $avevd$ is between 1 and $100~m^2.s^{-1}$. This parameteri zation of366 for $avevd$ is between 1 and $100~m^2.s^{-1}$. This parameterisation of 367 367 convective processes is less time consuming than the convective adjustment 368 368 algorithm presented above when mixing both tracers and momentum in the … … 384 384 $A_u^{vm} {and}\;A_v^{vm}$ (up to $1\;m^2s^{-1})$. These large values 385 385 restore the static stability of the water column in a way similar to that of the 386 enhanced vertical diffusion parameteri zation (\S\ref{ZDF_evd}). However,386 enhanced vertical diffusion parameterisation (\S\ref{ZDF_evd}). However, 387 387 in the vicinity of the sea surface (first ocean layer), the eddy coefficients 388 computed by the turbulen ce scheme do not usually exceed $10^{-2}m.s^{-1}$,388 computed by the turbulent closure scheme do not usually exceed $10^{-2}m.s^{-1}$, 389 389 because the mixing length scale is bounded by the distance to the sea surface 390 390 (see \S\ref{ZDF_tke}). It can thus be useful to combine the enhanced vertical … … 412 412 to diffusive convection. Double-diffusive phenomena contribute to diapycnal 413 413 mixing in extensive regions of the ocean. \citet{Merryfield1999} include a 414 parameteri zation of such phenomena in a global ocean model and show that414 parameterisation of such phenomena in a global ocean model and show that 415 415 it leads to relatively minor changes in circulation but exerts significant regional 416 416 influences on temperature and salinity. … … 422 422 \end{align*} 423 423 where subscript $f$ represents mixing by salt fingering, $d$ by diffusive convection, 424 and $o$ by processes other than double diffusion. The rates of double-diffusive mixing depend on the buoyancy ratio $R_\rho = \alpha \partial_z T / \beta \partial_z S$, 424 and $o$ by processes other than double diffusion. The rates of double-diffusive mixing 425 depend on the buoyancy ratio $R_\rho = \alpha \partial_z T / \beta \partial_z S$, 425 426 where $\alpha$ and $\beta$ are coefficients of thermal expansion and saline 426 427 contraction (see \S\ref{TRA_eos}). To represent mixing of $S$ and $T$ by salt … … 443 444 $A^{\ast v} = 10^{-4}~m^2.s^{-1}$ ; (b) diapycnal diffusivities $A_d^{vT}$ and 444 445 $A_d^{vS}$ for temperature and salt in regions of diffusive convection. Heavy 445 curves denote the Federov parameteri zation and thin curves the Kelley446 parameteri zation. The latter is not implemented in \NEMO. }446 curves denote the Federov parameterisation and thin curves the Kelley 447 parameterisation. The latter is not implemented in \NEMO. } 447 448 \end{center} \end{figure} 448 449 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 453 454 we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$. 454 455 455 To represent mixing of S and T by diffusive layering, the diapycnal diffusivities suggested by Federov (1988) is used: 456 To represent mixing of S and T by diffusive layering, the diapycnal diffusivities suggested 457 by Federov (1988) is used: 456 458 \begin{align} \label{Eq_zdfddm_d} 457 459 A_d^{vT} &= \begin{cases} … … 525 527 \label{ZDF_bfr_linear} 526 528 527 The linear bottom friction parameteri zation assumes that the bottom friction529 The linear bottom friction parameterisation assumes that the bottom friction 528 530 is proportional to the interior velocity (i.e. the velocity of the last model level): 529 531 \begin{equation} \label{Eq_zdfbfr_linear} … … 571 573 \label{ZDF_bfr_nonlinear} 572 574 573 The non-linear bottom friction parameteri zation assumes that the bottom575 The non-linear bottom friction parameterisation assumes that the bottom 574 576 friction is quadratic: 575 577 \begin{equation} \label{Eq_zdfbfr_nonlinear}
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