If the star is ellipsoid instead a sphere, the wave should be rich of harmonics, not only (2*orbital frequency). Can these harmonics behave the same way, i.e. they appear/disappear together and drift (if they can drift) toward the same direction? Or any of the harmonics can behave independently, e.g.: fundamental frequency remain the same and the 2nd harmonic drift to higher frequency? If they can behave independently, what is the reason that can cause such behaviour? Consider the star has precession and nutation movement.