Observations of parametric instability and breaking waves in an oscillating tilted tube

Abstract

Experiments are described in which a rectangular tube filled with a stratified fluid and tilted at an angle α (about 12°) is rocked at the critical frequency of waves on a slope, σ = N sin α, where N is the uniform buoyancy frequency of the fluid in the central section of the tube. Localized overturns with axes transverse to the flow are observed with a scale comparable with the tube height, producing convective motions and mixing. The overturns have a periodic structure along the tube and, although occurring on each forcing cycle, they alternate in position, so that they reoccur at a given position only every two cycles, that is at the frequency of the first subharmonic of the forcing frequency. The wavelength and vertical structure of the disturbance are consistent with the presence of an internal wave mode with a frequency half that of the forcing, and this is indicative of a parametric instability. The parameters of the regions where static instability occurs show that, as observed, the fluid is more likely to be unstable to convective motions than in earlier experiments (Thorpe 1994b) on standing waves.