More on background mixing.

src/parameterizations/vertical/_Internal_tides.dox

@@ -4,7 +4,7 @@ Two parameterizations of vertical mixing due to internal tides are
 available with the option INT_TIDE_DISSIPATION. The first is that of
 \cite st_laurent2002 while the second is that of \cite polzin2009. Choose
 between them with the INT_TIDE_PROFILE option. There are other relevant
-paramters which can be seen in MOM_parameter_doc.all once the main tidal
+parameters which can be seen in MOM_parameter_doc.all once the main tidal
 dissipation switch is turned on.
 
 \section section_st_laurent St Laurent et al.
@@ -69,7 +69,7 @@ case the maximum of all the contributions is used.
 
 The vertical diffusion profile of \cite polzin2009 is a WKB-stretched
 algebraic decay profile. It is based on a radiation balance equation,
-which links the dissipation profile associtated with internal breaking to
+which links the dissipation profile associated with internal breaking to
 the finescale internal wave shear producing that dissipation. The vertical
 profile of internal-tide driven energy dissipation can then vary in time
 and space, and evolve in a changing climate (\cite melet2012). \cite melet2012
@@ -135,9 +135,9 @@ at the ocean floor, so that in both formulations:
    \int_{0}^{H} \epsilon (z) dz = \frac{qE}{\rho} .
 \f]
 
-Whereas \cite polzin2009 assumed tthat the total dissipation was locally in balance with the
+Whereas \cite polzin2009 assumed that the total dissipation was locally in balance with the
 barotropic to baroclinic energy conversion rate \f$(q=1)\f$, here we use the \cite simmons2004 value
-of \f$q=1/3\f$ to retain as much consistency as passible between both parameterizations.
+of \f$q=1/3\f$ to retain as much consistency as possible between both parameterizations.
 
 \subsection subsection_vertical_decay_scale Vertical decay-scale reformulation
 
@@ -221,7 +221,7 @@ the implementation in MOM6, it is required that you provide an estimate
 of the TKE loss due to the Lee waves which is then applied with either
 the St. Laurent or the Polzin vertical profile.
 
-IS THERE A SCRIPT to produce this somewhere or what???
+\todo Is there a script to produce this somewhere or what???
 
 */
 

src/parameterizations/vertical/_V_diffusivity.dox

@@ -3,8 +3,8 @@
 Sets the interior vertical diffusion of scalars due to the following processes:
 
 -# Shear-driven mixing: two options, \cite jackson2008 and KPP interior;
--# Background mixing via CVMix (Bryan-Lewis profile) or the scheme described by
-   \cite harrison2008.
+-# Background mixing via CVMix (Bryan-Lewis profile), the scheme described by
+   \cite harrison2008, or that in \cite danabasoglu2012.
 -# Double-diffusion, old method and new method via CVMix;
 -# Tidal mixing: many options available, see \ref Internal_Tidal_Mixing.
 
@@ -50,11 +50,31 @@ parameterization of \cite large1994 is as follows, where the diffusivity \f$\kap
 is given by
 
 \f[
-   \kappa = \kappa_0 \left[ 1 - \min \left( 1, \frac{\mbox{Ri}}{\mbox{Ri}_c} \right) ^2 \right] ^3 ,
+   \kappa = \kappa_0 \left[ 1 - \min \left( 1, \frac{\mbox{Ri}}{\mbox{Ri}_c} \right) ^2 \right] ^3 ,\
 \f]
 
 with \f$\kappa_0 = 5 \times 10^{-3}\, \mbox{m}^2 \,\mbox{s}^{-1}\f$ and \f$\mbox{Ri}_c = 0.7\f$.
 
+One can instead select the \cite pacanowski1981 scheme within CVMix. Unlike
+the \cite large1994 scheme, they propose that the\ vertical shear
+viscosity \f$\nu_{\mbox{shear}}\nf$ be different from the vertical shear
+diffusivity \f$\kappa_{\mbox{shear}}\f$. For gravitationally stable
+profiles (i.e., \f$N^2 > 0\f$), they chose
+
+\f[
+   \nu_{\mbox{shear}} = \frac{\nu_0}{(1 + a \mbox{Ri})^n}
+\f]
+
+\f[
+   \kappa_{\mbox{shear}} = \frac{\nu_0}{(1 + a \mbox{Ri})^{n+1}}
+\f]
+
+where \f$\nu_0\f$, \f$a\f$ and \f$n\f$ are adjustable parameters. Common settings are \f$a = 5\f$
+and \f$n = 2\f$.
+
+For both CVMix shear mixing schemes, the mixing coefficients are set to
+a large value for gravitationally unstable profiles.
+
 \subsection subsection_kappa_shear Shear-driven mixing in Jackson
 
 While the above parameterization works well enough in the equatorial
@@ -117,10 +137,10 @@ that the TKE reaches a quasi-steady state faster than the flow is evolving
 and faster than it can be affected by mean-flow advection so that \f$DQ/Dt =
 0\f$. Since this parameterization is meant to be used in climate models
 with low horizontal resolution and large time steps compared to the
-mixing time scales, this is a reasonable assumtion. The most tenuous
+mixing time scales, this is a reasonable assumption. The most tenuous
 assumption is in the form of the dissipation \f$\epsilon = Q(C_N N +
 c_S S)\f$ (where \f$c_N\f$ and \f$c_S\f$ are to be determined),
-which is assumed to be dependent on the buoyancy frequeny (through loss
+which is assumed to be dependent on the buoyancy frequency (through loss
 of energy to internal waves) and the velocity shear (through the energy
 cascade to smaller scales).
 
@@ -138,7 +158,7 @@ diffusivity, the second term as a source, and the final two as sinks.
 This equation with \eqref{eq:Jackson_11} are simple enough to solve quickly
 using an iterative technique.
 
-We also need boundary contitions for \eqref{eq:Jackson_10}
+We also need boundary conditions for \eqref{eq:Jackson_10}
 and \eqref{eq:Jackson_11}. For the turbulent diffusivity we use
 \f$\kappa = 0\f$ since our diffusivity is numerically defined on
 layer interfaces. This ensures that there is no turbulent flux across
@@ -189,7 +209,7 @@ The background vertical mixing in \cite bryan1979 is of the form:
    \kappa = C_1 + C_2 \mbox{atan} [ C_3 ( |z| - C_4 )]
 \f]
 
-where the contants are runtime parameters as shown here:
+where the constants are runtime parameters as shown here:
 
 <table>
 <caption id="bryan_lewis_parms">Bryan Lewis parameters</caption>
@@ -227,7 +247,10 @@ the diffusivity is
 
 where \f$H_t = 2500\, \mbox{m}\f$, \f$\delta_t = 222\, \mbox{m}\f$, and
 \f$\kappa_d\f$ is the deep ocean diffusivity of \f$10^{-4}\, \mbox{m}^2
-\, \mbox{s}^{-1}\f$.
+\, \mbox{s}^{-1}\f$. Note that this is the vertical structure described
+in \cite harrison2008, but that isn't what is in the code. Instead, the surface
+value is propagated down, with the assumption that the tidal mixing parameterization
+will provide the deep mixing: \ref Internal_Tidal_Mixing.
 
 There is also a "new" Henyey version, taking into account the effect of stratification on
 TKE dissipation,
@@ -248,6 +271,14 @@ The original version concentrates buoyancy work in regions of strong stratificat
 
 \subsection subsection_danabasoglu_back Danabasoglu background mixing
 
+The shape of the \cite danabasoglu background mixing has a uniform background value, with a dip
+at the equator and a bump at \f$\pm 30^{\circ}$ degrees latitude. The form is shown in this figure
+
+\image html background_varying.png "Form of the vertically uniform background mixing in \cite danabasoglu2012. The values are symmetric about the equator."
+\imagelatex{background_varying.png,Form of the vertically uniform background mixing in \cite danabasoglu2012. The values are symmetric about the equator.,\includegraphics[width=\textwidth\,height=\textheight/2\,keepaspectratio=true]}
+
+Some parameters of this curve are set in the input file, some are hard-coded in calculate_bkgnd_mixing.
+
 \section section_Double_Diff Double Diffusion
 
 */