cvmix_convection.tex

\chapter{\scshape Vertical convective mixing}
\label{chapter:cvmix_convection}

\minitoc
\vspace{.5cm}

The purpose of this chapter is to present the vertical convective
mixing scheme available in CVMix.  The following CVMix Fortran module
is directly connected to the material in this chapter:
\begin{align*} 
 &  {\tt cvmix\_convection.F90}.
\end{align*}


\section{Introduction to convective mixing}
\label{section:intro}

The hydrostatic approximation necessitates the use of a
parameterization of vertical overturning processes.  The original
parameterization used by Bryan in the 1960's was motivated largely
from ideas then used for modeling convection in stars
(\cite{Bryan1969}).  Work by Marshall and collaborators
(\cite{KlingerConvection}, \cite{MITmodel}) have largely supported the
basic ideas of vertical adjustment for purposes of large-scale ocean
circulation.

The \cite{CoxModel} implementation of convective adjustment (the
``NCON" scheme) may leave columns unstable after completing the code's
adjustment loop.  Various full convective schemes have come on-line,
with that from \cite{Rahmstorf1993} implemented in MOM.  An
alternative to the traditional form of convective adjustment is to
increase the vertical mixing coefficient to some large value (say $\ge
10 \mbox{m}^{2} \, \mbox{s}^{-1}$) in order to quickly diffuse
vertically unstable water columns.  Indeed, it is this form
recommended from the study of \cite{KlingerConvection}, and it is the
approach commonly used in boundary layer schemes such as \cite{PPvmix}
and \cite{LargeKPP}.  It is this vertical convective mixing approach
that is supported in CVMix.  


\section{Time-implicit vertical mixing}
\label{section:time-implicit-vmix}

An explicit treatment, especially with fine vertical grid resolution,
places an unreasonable limitation on the size of the time step
associated with vertical mixing processes.  The use of fine vertical
resolution with sophisticated mixed layer and/or neutral physics
schemes has prompted the near universal time-implicit treatment of
vertical mixing in ocean climate models.