A TECHNIQUE FOR DIRECT MEASUREMENT OF TIME-DEPENDENT COMPLEX EIGENFREQUENCIES OF WAVES IN FLUIDS

A method is developed for obtaining best estimates of slowly varying time-dependent complex eigenfrequencies of waves in fluids. The procedure is to excite the wave motion of interest in a fluid by a mechanical forcing and to subsequently switch off this forcing when resonance has been reached so that the fluid is free to oscillate at its natural complex eigenfrequency. The pressure response of the freely decaying waves is modeled with frequencies and decay rates represented as power series expansions in time up to the linear term. Estimates are obtained using a least-squares method after linearization about initial estimates of the parameters. The performance of the method was compared with the theoretical bounds (i.e., Cramer-Rao lower bounds) and was verified by inversion of simulated records that included pseudorandom noise. Applications of the method using real data were made by recovering slowly varying time-dependent complex eigenfrequencies of inertial waves in a rotating fluid during spin-up of the fluid from rest, confirming the merits of this technique. Methods developed in this work will find application in the recovery of frequencies and decay rates for fluid oscillations of the Earth's fluid core.