\documentstyle [11pt]{article} \oddsidemargin 0.5in \evensidemargin 0.5in \topmargin -0.5in \headsep .5in \textheight 8.8in \textwidth 6in \parskip 3pt \parindent 0pt \def\baselinestretch{1.0} \begin{document} \begin{center} {\bf Appendix: Miami Ocean Model Features} \end{center} \vspace{5mm} (A) GENERAL: \begin{itemize} \item Isopycnic coordinates (equivalent to stack of shallow water models) \item Regular horizontal mesh on Mercator projection \item Arakawa C grid \item Variable bathymetry, irregular coastlines \item Kraus-Turner mixed layer exchanging mass with interior isopycnic layers \end{itemize} \vspace{5mm} (B) FORCING: \begin{itemize} \item Seasonally and latitudinally varying wind stress acting on mixed layer \item Surface heat flux: combination of imposed flux (radiation) and Newtonian forcing (sensible + latent heat) \item Salinity: imposed fresh-water flux \end{itemize} \vspace{5mm} (C) CONTINUITY EQUATION: \begin{itemize} \item All layers extend coast to coast; no internal bookkeeping of outcrop zones \item Layer thickness vanishes where layers outcrop into mixed layer or intersect ocean bottom \item Flux Corrected Transport scheme assures positive-definiteness of layer thickness \end{itemize} \vspace{5mm} (D) THERMODYNAMIC EQUATIONS: \begin{itemize} \item Nonlinear equation of state (3rd degree polynomial in T, linear in S) \item T,S advection by 3rd order Smolarkiewicz scheme \item ``Cabbeling" algorithm maintains reference density in isopycnal layers \item Turbulent T,S mixing based on constant eddy viscosity \item Layer thickness diffusion (and commensurate T,S diffusion) to account for Reynolds averaging of mass flux divergence term \item Conservative formulation of advection, lateral mixing, and time smoothing \end{itemize} \vspace{5mm} (E) MOMENTUM EQUATIONS: \begin{itemize} \item Primitive equations, fully nonlinear \item Potential-enstrophy conserving except in outcrop zones \item Deformation-dependent eddy viscosity \item One-sided pressure gradient formulation near bottom topography to avoid pressure field extrapolation to ``underground" grid points \item Velocity at massless grid points inferred from mass-carrying layers above or below \item Choice of free-slip or no-slip lateral boundary conditions \item Lateral boundary conditions imposed at ``submerged sidewalls" \end{itemize} \vspace{5mm} (F) TIME DIFFERENCING SCHEME: \begin{itemize} \item Split-explicit scheme replaces conventional rigid lid \item Long leapfrog time steps used in baroclinic equations; short forward-backward steps used in barotropic equations \item Explicit prediction of sea surface height \end{itemize} \end{document}