From 7bc229a13da38d4c215c1c0533a9817f33a93708 Mon Sep 17 00:00:00 2001 From: Bradley Hindman Date: Fri, 16 Jun 2023 09:43:39 -0600 Subject: [PATCH] Update physics_math_overview.rst There are two typos in equation (16) which expresses the radial velocity component in terms of the streamfunctions: 1) The first term should be proportional to 1/r^2, not 1/r 2) The second term should involve the W streamfunction instead of the Z streamfunction. There are two completely equivalent errors in Equation (22) which expresses the radial component of the magnetic field in terms of the fluxfunctions. --- doc/source/User_Guide/physics_math_overview.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/source/User_Guide/physics_math_overview.rst b/doc/source/User_Guide/physics_math_overview.rst index 98746e6d..33081b27 100644 --- a/doc/source/User_Guide/physics_math_overview.rst +++ b/doc/source/User_Guide/physics_math_overview.rst @@ -473,7 +473,7 @@ where *W* and *Z* are referred to as the poloidal and toroidal stream functions .. math:: :label: vrstream - \mathrm{f_1}v_r = - \frac{1}{r\mathrm{sin}\theta}\frac{\partial}{\partial\theta}\left(\mathrm{sin}\theta\frac{\partial W}{\partial\theta} \right)-\frac{1}{r^2\mathrm{sin}^2\theta}\frac{\partial^2 Z}{\partial\phi^2}, + \mathrm{f_1}v_r = - \frac{1}{r^2\mathrm{sin}\theta}\frac{\partial}{\partial\theta}\left(\mathrm{sin}\theta\frac{\partial W}{\partial\theta} \right)-\frac{1}{r^2\mathrm{sin}^2\theta}\frac{\partial^2 W}{\partial\phi^2}, .. math:: :label: vtstream @@ -513,7 +513,7 @@ where *C* and *A* are the poloidal and toroidal flux functions respectively. Si .. math:: :label: Brstream - B_r = - \frac{1}{r\mathrm{sin}\theta}\frac{\partial}{\partial\theta}\left(\mathrm{sin}\theta\frac{\partial C}{\partial\theta} \right)-\frac{1}{r^2\mathrm{sin}^2\theta}\frac{\partial^2 A}{\partial\phi^2}, + B_r = - \frac{1}{r^2\mathrm{sin}\theta}\frac{\partial}{\partial\theta}\left(\mathrm{sin}\theta\frac{\partial C}{\partial\theta} \right)-\frac{1}{r^2\mathrm{sin}^2\theta}\frac{\partial^2 C}{\partial\phi^2}, .. math:: :label: Btstream