A0_TZ_factor

multiplicative factor that multiplies \(A_0^2\) to compute quasigeostrophic enstrophy.

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Description

Real valued property with dimensions \((j,kl)\) and units of \(m^{-1} s^{-2}\).

Discussion

These coefficients multiply \(A_0^2\) to give a horizontally-averaged depth-integrated total quasigeostrophic enstrophy.

For \(j>0\), both the geostrophic (\(K_h>0\)) and mean-density anomaly (\(K_h=0\)) modes have coefficients computed with

\[\textrm{TZ}^{klj} = \frac{g}{2} \left( K^2 + L_r^{-2} \right)^2 L_r^2\]

where \(L_r^2 = \frac{g h}{f_0^2}\) is the squared Rossby radius of deformation for each mode. In the case of a rigid-lid there exists a the barotropic mode with no vortex stretching and thus,

\[\textrm{TZ}^{kl0} = \frac{g}{2} K^4 \frac{g L_z}{f_0^2}\]

for the \(j=0\) barotropic mode.