Schlieren measurements of internal waves in non-Boussinesq fluids

Abstract

Previous experiments that have examined the generation of internal gravity waves by a monochromatic source have been restricted to small amplitude forcing in Boussinesq stratified fluids. Here we present measurements of internal waves generated by a circular cylinder oscillating at large amplitude in a non-Boussinesq fluid. The ‘synthetic schlieren’ optical measurement technique (Sutherland et al. in J Fluid Mech 390:93–126, 1999) is extended to stratifications in which the index of refraction of the fluid may vary nonlinearly with density. The method is applied to examine disturbances in approximately uniformly stratified ambient fluids consisting either of sodium chloride (NaCl) or sodium iodide (NaI) solutions whose concentrations increase to near-saturation at the bottom of the tank. In particular, we report upon the first extensive measurements of the optical properties of NaI solutions as they depend upon concentration and density. Applying the results to experiments, we find that large amplitude forcing generates a patch of oscillatory turbulence surrounding the cylinder, thereby increasing the effective cylinder size and decreasing the amplitude of the waves in comparison with the predictions of linear theory. We parameterize the influence of the turbulent boundary layer in terms of an effective cylinder radius and forcing amplitude.