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NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex
r10414 r10442 35 35 The alternative is to use diffusive schemes such as upstream or flux corrected schemes. 36 36 This last option was rejected because we prefer a complete handling of the model diffusion, 37 i.e.of the model physics rather than letting the advective scheme produces its own implicit diffusion without37 \ie of the model physics rather than letting the advective scheme produces its own implicit diffusion without 38 38 controlling the space and time structure of this implicit diffusion. 39 39 Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required. … … 60 60 \textbf{* relative, planetary and total vorticity term:} 61 61 62 Let us define as either the relative, planetary and total potential vorticity, i.e. ?, ?, and ?, respectively.62 Let us define as either the relative, planetary and total potential vorticity, \ie, ?, and ?, respectively. 63 63 The continuous formulation of the vorticity term satisfies following integral constraints: 64 64 \[ … … 122 122 This properties is satisfied locally with the choice of discretization we have made (property (II.1.9)~). 123 123 In addition, when the equation of state is linear 124 ( i.e.when an advective-diffusive equation for density can be derived from those of temperature and salinity)124 (\ie when an advective-diffusive equation for density can be derived from those of temperature and salinity) 125 125 the change of horizontal kinetic energy due to the work of pressure forces is balanced by the change of 126 126 potential energy due to buoyancy forces: … … 164 164 165 165 In continuous formulation, the advective terms of the tracer equations conserve the tracer content and 166 the quadratic form of the tracer, $i.e.$166 the quadratic form of the tracer, \ie 167 167 \[ 168 168 % \label{eq:tra_tra2} … … 283 283 In discrete form, all these properties are satisfied in $z$-coordinate (see Appendix C). 284 284 In $s$-coordinates, only first order properties can be demonstrated, 285 $i.e.$the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence.285 \ie the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence. 286 286 287 287 % ------------------------------------------------------------------------------------------------------------- … … 294 294 the heat and salt contents are conserved (equations in flux form, second order centred finite differences). 295 295 As a form flux is used to compute the temperature and salinity, 296 the quadratic form of these quantities ( i.e.their variance) globally tends to diminish.296 the quadratic form of these quantities (\ie their variance) globally tends to diminish. 297 297 As for the advective term, there is generally no strict conservation of mass even if, 298 298 in practice, the mass is conserved with a very good accuracy. … … 309 309 \] 310 310 311 \textbf{* vertical physics: }conservation of tracer, dissipation of tracer variance, $i.e.$311 \textbf{* vertical physics: }conservation of tracer, dissipation of tracer variance, \ie 312 312 313 313 \[ … … 330 330 \biblio 331 331 332 \pindex 333 332 334 \end{document}
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