In decaying two-dimensional Navier–Stokes turbulence, Batchelor's similarity
hypothesis fails due to the existence of coherent vortices. However, it is shown that
decaying two-dimensional turbulence governed by the Charney–Hasegawa–Mima (CHM)
equation
(∂/∂t)(∇2φ−λ2φ)
+J(φ, ∇2φ) = D,
where D is a damping, is described well by Batchelor's similarity hypothesis for wave
numbers k [Lt ] λ (the so-called AM regime). It is argued that CHM turbulence in the
AM regime is a more ‘ideal’ form of two-dimensional turbulence than is Navier–Stokes
turbulence itself.