= Two-layer quasi-geostrophic energy conservation
{title2=$E=\tfrac12[\sum_iH_i|\nabla\psi_i|^2+(f_0^2/g\prime)(\psi_1-\psi_2)^2]$}
For inviscid unforced two-layer QG dynamics, $H_1F_1=H_2F_2=f_0^2/g\prime$ makes the coupling symmetric in the layer-depth inner product. Multiplication by $H_i\psi_i$ gives the positive energy $E=\tfrac12[\sum_iH_i|\nabla\psi_i|^2+(f_0^2/g\prime)(\psi_1-\psi_2)^2]$. It is conserved after integration when the lateral energy flux vanishes. The interface term is <available potential energy>; the gradient terms are <kinetic energy>.
Back to article page
