  Context. Large-scale equatorial Rossby modes have been observed on the Sun
over the last two solar cycles. Aims. We investigate the impact of the
time-varying zonal flows on the frequencies of Rossby modes. Methods. A
first-order perturbation theory approach is used to obtain an expression for
the expected shift in the mode frequencies due to perturbations in the internal
rotation rate. Results. Using the time-varying rotation from helioseismic
inversions we predict the changes in Rossby mode frequencies with azimuthal
orders from m = 1 to m = 15 over the last two solar cycles. The peak-to-peak
frequency change is less than 1 nHz for the m = 1 mode, grows with m, and
reaches 25 nHz for m = 15. Conclusions. Given the observational uncertainties
on mode frequencies due to the finite mode lifetimes, we find that the
predicted frequency shifts are near the limit of detectability.
