diff --git a/doc/source/User_Guide/physics_math_overview.rst b/doc/source/User_Guide/physics_math_overview.rst index a641a34c..2799035d 100644 --- a/doc/source/User_Guide/physics_math_overview.rst +++ b/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