Merge pull request #508 from geodynamics/illorenzo7-patch-4

Fairly certain there's a missing c_7 in ohmic heating

doc/source/User_Guide/physics_math_overview.rst

@@ -151,7 +151,7 @@ respectively. The evolution of :math:`\Theta` is described by
        c_6\,\boldsymbol{\nabla}\cdot\left[\mathrm{f}_1(r)\,\mathrm{f}_4(r)\,\mathrm{f}_5(r)\,\boldsymbol{\nabla}\Theta \right] \\
         +\ c_{10}\,\mathrm{f}_6(r)
         + c_8\,\Phi(r,\theta,\phi)
-        + c_9\,\mathrm{f}_7(r)|\boldsymbol{\nabla}\times\boldsymbol{B}|^2,
+        + c_8\,c_4\,c_7\,\mathrm{f}_7(r)|\boldsymbol{\nabla}\times\boldsymbol{B}|^2,
 
 where the viscous heating :math:`\Phi` is given by
 
@@ -161,6 +161,8 @@ where the viscous heating :math:`\Phi` is given by
        \Phi(r,\theta,\phi) = c_5\,\mathcal{D}_{ij}e_{ij} &= 2\,c_5\,\mathrm{f}_1(r)\mathrm{f}_3(r)\left[e_{ij}e_{ij} - \frac{1}{3}\left(\boldsymbol{\nabla}\cdot\boldsymbol{v}\right)^2\right] \\
        &= 2\,c_5\,\mathrm{f}_1(r)\mathrm{f}_3(r)\left[e_{ij} - \frac{1}{3}\left(\boldsymbol{\nabla}\cdot\boldsymbol{v}\right)\delta_{ij}\right]^2.
 
+For historical consistency, we also define :math:`c_9\,\equiv c_8\,c_4\,c_7`. 
+
 Finally, the evolution of :math:`\boldsymbol{B}` is described by the
 induction equation