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branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_ZDF.tex
r5120 r6275 33 33 points, respectively (see \S\ref{TRA_zdf} and \S\ref{DYN_zdf}). These 34 34 coefficients can be assumed to be either constant, or a function of the local 35 Richardson number, or computed from a turbulent closure model (either 36 TKE or KPP formulation). The computation of these coefficients is initialized 37 in the \mdl{zdfini} module and performed in the \mdl{zdfric}, \mdl{zdftke} or 38 \mdl{zdfkpp} modules. The trends due to the vertical momentum and tracer 39 diffusion, including the surface forcing, are computed and added to the 40 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 35 Richardson number, or computed from a turbulent closure model (TKE, GLS or KPP formulation). 36 The computation of these coefficients is initialized in the \mdl{zdfini} module 37 and performed in the \mdl{zdfric}, \mdl{zdftke}, \mdl{zdfgls} or \mdl{zdfkpp} modules. 38 The trends due to the vertical momentum and tracer diffusion, including the surface forcing, 39 are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 41 40 These trends can be computed using either a forward time stepping scheme 42 41 (namelist parameter \np{ln\_zdfexp}=true) or a backward time stepping … … 355 354 %--------------------------------------------------------------% 356 355 357 To be add here a description of "penetration of TKE" and the associated namelist parameters 358 \np{nn\_etau}, \np{rn\_efr} and \np{nn\_htau}. 356 Vertical mixing parameterizations commonly used in ocean general circulation models 357 tend to produce mixed-layer depths that are too shallow during summer months and windy conditions. 358 This bias is particularly acute over the Southern Ocean. 359 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}. 360 The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations, 361 but rather is meant to account for observed processes that affect the density structure of 362 the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme 363 ($i.e.$ near-inertial oscillations and ocean swells and waves). 364 365 When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$) 366 imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized 367 by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: 368 \begin{equation} \label{ZDF_Ehtau} 369 S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau} 370 \end{equation} 371 where 372 $z$ is the depth, 373 $e_s$ is TKE surface boundary condition, 374 $f_r$ is the fraction of the surface TKE that penetrate in the ocean, 375 $h_\tau$ is a vertical mixing length scale that controls exponential shape of the penetration, 376 and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely 377 covered by sea-ice). 378 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter. 379 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}~=~0) 380 or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m 381 at high latitudes (\np{nn\_etau}~=~1). 382 383 Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying 384 \eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part 385 of the stress to evaluate the fraction of TKE that penetrate the ocean. 386 Those two options are obsolescent features introduced for test purposes. 387 They will be removed in the next release. 388 389 359 390 360 391 % from Burchard et al OM 2008 : 361 % the most critical process not reproduced by statistical turbulence models is the activity of internal waves and their interaction with turbulence. After the Reynolds decomposition, internal waves are in principle included in the RANS equations, but later partially excluded by the hydrostatic assumption and the model resolution. Thus far, the representation of internal wave mixing in ocean models has been relatively crude (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 392 % the most critical process not reproduced by statistical turbulence models is the activity of 393 % internal waves and their interaction with turbulence. After the Reynolds decomposition, 394 % internal waves are in principle included in the RANS equations, but later partially 395 % excluded by the hydrostatic assumption and the model resolution. 396 % Thus far, the representation of internal wave mixing in ocean models has been relatively crude 397 % (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 362 398 363 399 … … 586 622 Options are defined through the \ngn{namzdf\_kpp} namelist variables. 587 623 588 \colorbox{yellow}{Add a description of KPP here.} 624 Note that KPP is an obsolescent feature of the \NEMO system. 625 It will be removed in the next release (v3.7 and followings). 589 626 590 627 … … 636 673 637 674 Options are defined through the \ngn{namzdf} namelist variables. 638 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc} =true.675 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}. 639 676 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously 640 677 the statically unstable portion of the water column, but only until the density … … 644 681 (Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is 645 682 found. Assume in the following that the instability is located between levels 646 $k$ and $k+1$. The potentialtemperature and salinity in the two levels are683 $k$ and $k+1$. The temperature and salinity in the two levels are 647 684 vertically mixed, conserving the heat and salt contents of the water column. 648 685 The new density is then computed by a linear approximation. If the new … … 664 701 \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 665 702 666 Note that in the current implementation of this algorithm presents several 667 limitations. First, potential density referenced to the sea surface is used to 668 check whether the density profile is stable or not. This is a strong 669 simplification which leads to large errors for realistic ocean simulations. 670 Indeed, many water masses of the world ocean, especially Antarctic Bottom 671 Water, are unstable when represented in surface-referenced potential density. 672 The scheme will erroneously mix them up. Second, the mixing of potential 673 density is assumed to be linear. This assures the convergence of the algorithm 674 even when the equation of state is non-linear. Small static instabilities can thus 675 persist due to cabbeling: they will be treated at the next time step. 676 Third, temperature and salinity, and thus density, are mixed, but the 677 corresponding velocity fields remain unchanged. When using a Richardson 678 Number dependent eddy viscosity, the mixing of momentum is done through 679 the vertical diffusion: after a static adjustment, the Richardson Number is zero 680 and thus the eddy viscosity coefficient is at a maximum. When this convective 681 adjustment algorithm is used with constant vertical eddy viscosity, spurious 682 solutions can occur since the vertical momentum diffusion remains small even 683 after a static adjustment. In that case, we recommend the addition of momentum 684 mixing in a manner that mimics the mixing in temperature and salinity 685 \citep{Speich_PhD92, Speich_al_JPO96}. 703 The current implementation has been modified in order to deal with any non linear 704 equation of seawater (L. Brodeau, personnal communication). 705 Two main differences have been introduced compared to the original algorithm: 706 $(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency 707 (not the the difference in potential density) ; 708 $(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients 709 are vertically mixed in the same way their temperature and salinity has been mixed. 710 These two modifications allow the algorithm to perform properly and accurately 711 with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each 712 mixing iteration. 686 713 687 714 % ------------------------------------------------------------------------------------------------------------- … … 689 716 % ------------------------------------------------------------------------------------------------------------- 690 717 \subsection [Enhanced Vertical Diffusion (\np{ln\_zdfevd})] 691 718 {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 692 719 \label{ZDF_evd} 693 720
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