= Cubic-time resistive damping in a differentially rotating cell
{title2=$a\sim a_0\exp[-\eta m^2(\Omega')^2t^3/3]$}
In a smooth interior region with locally constant shear $\Omega'$, a wound azimuthal <Fourier mode> has radial <wavenumber> $k_s\simeq-m\Omega't$. Integrating its resistive damping rate $\eta k_s^2$ gives the <exponential decay> in the title. The characteristic time is $\tau_c=[3/(\eta m^2\Omega'^2)]^{1/3}$. For $m=1$ and $\Omega'=-\Omega_0/d$, $\Omega_0\tau_c=(3\mathrm{Rm})^{1/3}$, where $\mathrm{Rm}=\Omega_0d^2/\eta$. This is a high-<magnetic Reynolds number> interior transient on a time long compared with the rotation time but short compared with $d^2/\eta$. Physical <magnetic field> components may have additional algebraic factors from taking <derivatives> of the wound <magnetic vector potential>. A maintained exterior field, an axial core and a circulation-edge <boundary layer> prevent interpreting this estimate as an exact, uniform, infinite-time solution.
Back to article page
