Changeset 6289 for trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex
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trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex
r5120 r6289 34 34 coefficients can be assumed to be either constant, or a function of the local 35 35 Richardson number, or computed from a turbulent closure model (either 36 TKE or KPPformulation). The computation of these coefficients is initialized36 TKE or GLS formulation). The computation of these coefficients is initialized 37 37 in the \mdl{zdfini} module and performed in the \mdl{zdfric}, \mdl{zdftke} or 38 \mdl{zdf kpp} modules. The trends due to the vertical momentum and tracer38 \mdl{zdfgls} modules. The trends due to the vertical momentum and tracer 39 39 diffusion, including the surface forcing, are computed and added to the 40 40 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. … … 355 355 %--------------------------------------------------------------% 356 356 357 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}. 357 Vertical mixing parameterizations commonly used in ocean general circulation models 358 tend to produce mixed-layer depths that are too shallow during summer months and windy conditions. 359 This bias is particularly acute over the Southern Ocean. 360 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}. 361 The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations, 362 but rather is meant to account for observed processes that affect the density structure of 363 the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme 364 ($i.e.$ near-inertial oscillations and ocean swells and waves). 365 366 When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$) 367 imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized 368 by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: 369 \begin{equation} \label{ZDF_Ehtau} 370 S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau} 371 \end{equation} 372 where 373 $z$ is the depth, 374 $e_s$ is TKE surface boundary condition, 375 $f_r$ is the fraction of the surface TKE that penetrate in the ocean, 376 $h_\tau$ is a vertical mixing length scale that controls exponential shape of the penetration, 377 and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely 378 covered by sea-ice). 379 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter. 380 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}~=~0) 381 or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m 382 at high latitudes (\np{nn\_etau}~=~1). 383 384 Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying 385 \eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part 386 of the stress to evaluate the fraction of TKE that penetrate the ocean. 387 Those two options are obsolescent features introduced for test purposes. 388 They will be removed in the next release. 389 390 359 391 360 392 % 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). 393 % the most critical process not reproduced by statistical turbulence models is the activity of 394 % internal waves and their interaction with turbulence. After the Reynolds decomposition, 395 % internal waves are in principle included in the RANS equations, but later partially 396 % excluded by the hydrostatic assumption and the model resolution. 397 % Thus far, the representation of internal wave mixing in ocean models has been relatively crude 398 % (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 362 399 363 400 … … 573 610 Examples of performance of the 4 turbulent closure scheme can be found in \citet{Warner_al_OM05}. 574 611 575 % -------------------------------------------------------------------------------------------------------------576 % K Profile Parametrisation (KPP)577 % -------------------------------------------------------------------------------------------------------------578 \subsection{K Profile Parametrisation (KPP) (\key{zdfkpp}) }579 \label{ZDF_kpp}580 581 %--------------------------------------------namkpp--------------------------------------------------------582 \namdisplay{namzdf_kpp}583 %--------------------------------------------------------------------------------------------------------------584 585 The KKP scheme has been implemented by J. Chanut ...586 Options are defined through the \ngn{namzdf\_kpp} namelist variables.587 588 \colorbox{yellow}{Add a description of KPP here.}589 590 612 591 613 % ================================================================ … … 636 658 637 659 Options are defined through the \ngn{namzdf} namelist variables. 638 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc} =true.660 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}. 639 661 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously 640 662 the statically unstable portion of the water column, but only until the density … … 644 666 (Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is 645 667 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 are668 $k$ and $k+1$. The temperature and salinity in the two levels are 647 669 vertically mixed, conserving the heat and salt contents of the water column. 648 670 The new density is then computed by a linear approximation. If the new … … 664 686 \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 665 687 666 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}. 688 The current implementation has been modified in order to deal with any non linear 689 equation of seawater (L. Brodeau, personnal communication). 690 Two main differences have been introduced compared to the original algorithm: 691 $(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency 692 (not the the difference in potential density) ; 693 $(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients 694 are vertically mixed in the same way their temperature and salinity has been mixed. 695 These two modifications allow the algorithm to perform properly and accurately 696 with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each 697 mixing iteration. 686 698 687 699 % ------------------------------------------------------------------------------------------------------------- … … 689 701 % ------------------------------------------------------------------------------------------------------------- 690 702 \subsection [Enhanced Vertical Diffusion (\np{ln\_zdfevd})] 691 703 {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 692 704 \label{ZDF_evd} 693 705
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