Abstract
Nonlinear interactions between waves and turbulence cause systematic frequency shifts in Rossby waves. The frequency shifts in the inertial subranges of statistically steady β-plane turbulence were examined theoretically and numerically. The theoretical analysis is based on the Lagrangian closure called the Lagrangian renormalized approximation and predicts that when the β effect is small, the frequency shifts of Rossby waves are proportional to kx/k4/3 in the inverse energy transfer range, while they are proportional to kx with or without a log-correction term in the enstrophy transfer range, depending on the flow conditions, where kx is the wave number in the eastward direction. Numerical simulations using 10242 grid points of forced β-plane turbulence that exhibit the inertial subranges, show fairly good agreement with theoretical predictions.
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