Changeset 2080
- Timestamp:
- 2010-09-09T15:11:04+02:00 (14 years ago)
- Location:
- branches/DEV_r1784_GLS/DOC/TexFiles
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branches/DEV_r1784_GLS/DOC/TexFiles/Biblio/Biblio.bib
r1225 r2080 85 85 86 86 @STRING{Tellus = {Tellus}} 87 88 @STRING{RGSP = {Rev. Geophys. Space Phys.} 87 89 88 90 @ARTICLE{Adcroft_Campin_OM04, … … 523 525 } 524 526 527 @ARTICLE{Canuto_2001, 528 author = {V. M. Canuto and A. Howard and Y. Cheng and M. S. Dubovikov}, 529 title = {Ocean turbulence. PartI: One-point closure model-momentum and heat vertical diffusivities}, 530 journal = JPO, 531 year = {2001}, 532 volume = {24, 12}, 533 pages = {2546-2559}, 534 owner = {gr}, 535 timestamp = {2010.09.09} 536 } 537 525 538 @ARTICLE{Cox1987, 526 539 author = {M. Cox}, … … 532 545 owner = {gm}, 533 546 timestamp = {2007.08.03} 547 } 548 549 @ARTICLE{Craig_Banner_1994, 550 author = {P. D. Banner and M. L. Banner}, 551 title = {Modeling wave-enhanced turbulence in the ocean surface layer}, 552 journal = JPO, 553 year = {1994}, 554 volume = {24, 12}, 555 pages = {2546-2559}, 556 owner = {g5}, 557 timestamp = {2010.09.09} 534 558 } 535 559 … … 705 729 owner = {gm}, 706 730 timestamp = {2007.08.04} 731 } 732 733 @ARTICLE{Galperin_1988, 734 author = {B. Galperin and L. H. Kantha and S. Hassid and A. Rosati}, 735 title = {A quasi-equilibrium turbulent energy model for geophysical flows}, 736 journal = JAS, 737 year = {1988}, 738 volume = {45}, 739 pages = {55-62}, 740 owner = {gr}, 741 timestamp = {2010.09.09} 707 742 } 708 743 … … 1083 1118 owner = {gm}, 1084 1119 timestamp = {2008.08.31} 1120 } 1121 1122 @ARTICLE{Kantha_Clayson_1994, 1123 author = {L. H. Kantha and C. A. Clayson}, 1124 title = {An improved mixed layer model for geophysical applications}, 1125 journal = JGR, 1126 year = {1994}, 1127 volume = {99}, 1128 pages = {25235-25266}, 1129 owner = {gr}, 1130 timestamp = {2010.09.09} 1085 1131 } 1086 1132 … … 1584 1630 } 1585 1631 1632 @ARTICLE{Mellor_Yamada_1982, 1633 author = {G. L. Mellor and T. Yamada}, 1634 title = {Development of a turbulence closure model for geophysical fluid problems}, 1635 journal = RGSP, 1636 year = {1982}, 1637 volume = {20}, 1638 pages = {851-875}, 1639 owner = {gr}, 1640 timestamp = {2010.09.09} 1641 } 1642 1586 1643 @ARTICLE{Merryfield1999, 1587 1644 author = {W. J. Merryfield and G. Holloway and A. E. Gargett}, … … 1791 1848 owner = {gm}, 1792 1849 timestamp = {2007.08.04} 1850 } 1851 1852 @ARTICLE{Rodi_1987, 1853 author = {W. Rodi}, 1854 title = {Examples of calculation methods for flow and mixing in stratified fluids}, 1855 journal = JGR, 1856 year = {1987}, 1857 volume = {92, C5}, 1858 pages = {5305-5328}, 1859 owner = {gr}, 1860 timestamp = {2010.09.09} 1793 1861 } 1794 1862 … … 2214 2282 } 2215 2283 2284 @ARTICLE{Umlauf_Burchard_2003, 2285 author = {L. Umlauf and H. Burchard}, 2286 title = {A generic length-scale equation for geophysical turbulence models}, 2287 journal = {Journal of Marine Systems}, 2288 year = {2003}, 2289 volume = {61}, 2290 pages = {235-265}, 2291 number = {2}, 2292 owner = {gr}, 2293 timestamp = {2010.09.09} 2294 } 2295 2216 2296 @BOOK{UNESCO1983, 2217 2297 title = {Algorithms for computation of fundamental property of sea water}, … … 2308 2388 owner = {gm}, 2309 2389 timestamp = {2007.08.04} 2390 } 2391 2392 @ARTICLE{Wilcox_1988, 2393 author = {D. C. Wilcox}, 2394 title = {Reassessment of the scale-determining equation for advanced turbulence models}, 2395 journal = {AIAA journal}, 2396 year = {1988}, 2397 volume = {26, 11}, 2398 pages = {1299-1310}, 2399 owner = {gr}, 2400 timestamp = {2010.09.09} 2310 2401 } 2311 2402 -
branches/DEV_r1784_GLS/DOC/TexFiles/Chapters/Chap_ZDF.tex
r2055 r2080 233 233 234 234 % ------------------------------------------------------------------------------------------------------------- 235 % GLS Generic Length Scale Scheme 236 % ------------------------------------------------------------------------------------------------------------- 237 \subsection{GLS Generic Length Scale (\key{zdfgls})} 238 \label{ZDF_gls} 239 240 %--------------------------------------------namgls--------------------------------------------------------- 241 \namdisplay{namgls} 242 %-------------------------------------------------------------------------------------------------------------- 243 244 The model allows to resolve two prognostic equations for turbulent 245 kinetic energy $\bar {e}$ and a generic length scale \citep{Umlauf_Burchard_2003}. Thanks to the latter, commonly 246 used closures can be retrieved: $k-kl$ \citep{Mellor_Yamada_1982}, $k-{\epsilon }$ \citep{Rodi_1987} and $k-{\omega }$ 247 \citep{Wilcox_1988}. These equations could be written in a generic form with the incorporation 248 of a new variable : ${\psi} = (C^{0}_{\mu})^{p} \ {\bar{e}}^{m} \ l^{n}$. 249 250 \begin{equation} \label{Eq_zdfgls_e} 251 \frac{\partial \bar{e}}{\partial t} = 252 \frac{A^{vm}}{{\sigma_e} {e_3} }\;\left[ {\left( {\frac{\partial u}{\partial k}} \right)^2 253 +\left( {\frac{\partial v}{\partial k}} \right)^2} \right] 254 -A^{vT}\,N^2 255 +\frac{1}{e_3} \;\frac{\partial }{\partial k}\left[ {\frac{A^{vm}}{e_3 } 256 \;\frac{\partial \bar{e}}{\partial k}} \right] 257 - \epsilon \; 258 \end{equation} 259 260 \begin{equation} \label{Eq_zdfgls_psi} 261 \frac{\partial \psi}{\partial t} = \frac{\psi}{\bar{e}} 262 (\frac{{C_1}A^{vm}}{{\sigma_{\psi}} {e_3} }\;\left[ {\left( {\frac{\partial u}{\partial k}} \right)^2 263 +\left( {\frac{\partial v}{\partial k}} \right)^2} \right] 264 -{C_3}A^{vT}\,N^2- C_2{\epsilon}Fw) 265 +\frac{1}{e_3} \;\frac{\partial }{\partial k}\left[ {\frac{A^{vm}}{e_3 } 266 \;\frac{\partial \psi}{\partial k}} \right]\; 267 \end{equation} 268 269 \begin{equation} \label{Eq_zdfgls_kz} 270 \begin{split} 271 A^{vm} &= C_{\mu} \ \sqrt {\bar{e}} \ l \\ 272 A^{vT} &= C_{\mu'}\ \sqrt {\bar{e}} \ l 273 \end{split} 274 \end{equation} 275 276 \begin{equation} \label{Eq_zdfgls_eps} 277 {\epsilon} = (C^{0}_{\mu}) \frac{\bar {e}^{3/2}}{l} \; 278 \end{equation} 279 where $N$ is the local Brunt-Vais\"{a}l\"{a} frequency (see \S\ref{TRA_bn2}) and $\epsilon$ the dissipation rate. 280 In function of the parameters k, m and n, common turbulent closure could be retrieved. 281 The constants C1, C2, C3, ${\sigma_e}$, ${\sigma_{\psi}}$ and the wall function (Fw) depends of the choice of the turbulence model. 282 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 283 \begin{figure}[!h] 284 \centering 285 \includegraphics[scale=0.7]{./TexFiles/Figures/tabgls.png} 286 \caption {Values of the parameters in function of the model of turbulence.} 287 \label{tabgls} 288 \end{figure} 289 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 290 291 About the Mellor-Yamada model, the negativity of n allows to use a wall function to force 292 the convergence of the mixing length towards Kzb (K: Kappa and zb: rugosity length) value 293 near physical boundaries (logarithmic boundary layer law). $C_{\mu}$ and $C_{\mu'}$ are calculated from stability functions 294 of \citet{Galperin_1988}, \citet{Kantha_Clayson_1994} or \citet{Canuto_2001}. 295 $C^{0}_{\mu}$ depends of the choice of the stability function. 296 297 The boundary condition at the surface and the bottom could be calculated thanks to Diriclet or Neumann condition. 298 The wave effect on the mixing could be also being considered \citep{Craig_Banner_1994}. 299 300 ------------------------------------------------------------------------------------------------------------- 235 301 % K Profile Parametrisation (KPP) 236 302 % ------------------------------------------------------------------------------------------------------------- … … 247 313 \colorbox{yellow}{Add a description of KPP here.} 248 314 249 % -------------------------------------------------------------------------------------------------------------250 % GLS Vertical scheme251 % -------------------------------------------------------------------------------------------------------------252 \subsection{Generic length-scale equation model of Umlauf and Burchard (2003) (\key{zdfgls}) }253 \label{ZDF_gls}254 255 %--------------------------------------------namgls--------------------------------------------------------256 \namdisplay{namgls}257 %--------------------------------------------------------------------------------------------------------------258 The model allows to resolve two prognostic equations for turbulent kinetic energy and a generic length scale.259 260 \colorbox{yellow}{More explanations, with equations, will come soon. }261 315 262 316 % ================================================================
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