An Exact Gaussian Solution for the Two-Dimensional Ideal Incompressible Magnetohydrodynamic Turbulence

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  • Exact Gaussian Solution for the Two Dim

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An exact solution associated with a stationary Gaussian distribution is obtained for two-dimensional ideal incompressible magnetohydrodynamic turbulence by using the Wiener-Hermite expansion with a time-dependent ideal random function. The spectra are given by ⟨\ ildeφ(p:t)\ ildeφ(q:t)⟩∝q−2δ(p+q) and ⟨\ ildeA(p:t)\ ildeA(q:t)⟩∝(q2+γ)−1δ(p+q) where \ ildeφ and \ ildeA are the Fourier transforms of the stream function and the electro-magnetic potential respectively. A remarkable result is that the two-time correlation function ⟨\ ildeφ(k:t)\ ildeA(p:0)⟩=0 for an arbitrary t, but this does not necessarily mean the statistically independence of \ ildeφ and \ ildeA.

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