Incompressible Viscous Fluid as a 1/f Filter

Abstract

A discussion is given on a 1/f filter, which outputs a 1/f noise as a response to the white noise. It is shown theoretically and experimentally that, under proper conditions, an incompressible viscous fluid serves as the 1/f filter. Stimulated by the previous finding due to Mandelbrot et al. that the earth's pole motion involves the 1/f noise, a spherical shell enclosing a fluid is set in rotation about its diameter by a fluctuating external torque with the white spectrum, and its angular velocity is measured. It is found that, under the conditions predicted by the theory, the angular velocity involves the 1/f noise.