On the available free energy in drift wave turbulence

We report a variational formalism to calculate how much free energy can be released in a drift wave turbulence system, through which estimating the upper limit of the zonal flow intensity becomes possible. This formalism is rooted in the same structure between the wave kinetic equation and the particle kinetic equation, i.e., both following a Liouville equation. The minimal energy state is approached by rearranging the “quasi-particles” (i.e., wave packets) in their phase space. Taking the Charney–Hasegawa–Mima system as a prototype, we analytically derived an upper limit of the available free energy for a Gaussian initial distribution of the wave action. For more general scenarios, by developing an algorithm of rearrangement, we numerically calculated the available free energy. Through direct numerical simulations, it is further verified that the total energy of the zonal flow does not exceed the upper bound set by the variational principle.