Analytical study of the water surface fluctuations induced by grid-stirred turbulence

Through calibration and with some working assumptions, the radius of the blobs is shown to be of the order of the integral vertical length scale of turbulence. The forced oscillations are analysed by the method of Rauscher (1938) [1] to predict the amplitude of the oscillations, possible resonances and discontinuities in the amplitude-frequency space. If the forcing term has multiple harmonics, in some cases a blow up of the oscillator is forecast. Some tests including a small damping, in order to evaluate the effects of viscosity, show that a jump is expected in the amplitude-frequency diagram and a range of unstable frequency. The presence of a small damping should also prevent the blow up for multiple harmonics in the forcing term.