Frequency shifts of Rossby waves in the inertial subranges of β-plane turbulence

Nonlinear interactions between waves and turbulence cause systematic frequency shifts in Rossby waves. The frequency shifts in the inertial subranges of statistically steady beta -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 beta effect is small, the frequency shifts of Rossby waves are proportional to k(x)/k(4/3) in the inverse energy transfer range, while they are proportional to k(x) with or without a log-correction term in the enstrophy transfer range, depending on the flow conditions, where k(x) is the wave number in the eastward direction. Numerical simulations using 1024(2) grid points of forced beta -plane turbulence that exhibit the inertial subranges, show fairly good agreement with theoretical predictions. (C) 2001 American Institute of Physics.