Yaw instabilities produced by rapidly rotating, highly viscous liquids

A liquid-filled gyroscope was used to study the yaw instabilities for low Reynolds numbers. Control of physical variables produced a range in Reynolds number (Re) of 5 to 12 x 10 to the 3rd. The gyroscope is freely gimballed and spun at a constant rate by a dc motor. The logarithmic amplitude of the gyroscope motion grew linearly with time, and linear behavior was observed for precession angles smaller than 5 deg. The data suggested that the growth rates also varied linearly with the coning frequency, tau(R), of the liquid-solid parts. The strongest correlation for the amplitude growth rate of high viscosity liquids occurred for the product Re x tau(R). The experimental demonstration of growth rates proportional to the coning frequency is not consistent with the classical liquid-induced instability, which is based upon a resonant matching of a natural frequency of oscillation of the fluid and the coning frequency.