Stability of a stratified viscous shear flow in a tilted tube

The present investigation is concerned with the effects of viscosity on the stability of a bounded stratified shear flow with Prandtl number Pr much g reater than 1. Theoretical results obtained from the solution of the Orr-So mmerfeld equation extended to stratified fluids are compared with experimen ts performed in a tilting tube filled with water and brine. Theoretical ana lysis shows that a complete stabilization of the flow field with respect to infinitesimal disturbances is attained, irrespective of the Richardson num ber J, as the Reynolds number Re decreases below 75. This damping action of viscosity is shown to appreciably reduce the critical Richardson number J( c) with respect to the inviscid limit J(c)=0.25, even at moderately high Re . On the other hand, the destabilizing action enhanced by viscosity through the diffusion of momentum leads to a viscous mode of instability that may develop if J decreases below a threshold value. An extensive series of expe riments has been carried out in a long tilting tube in order to verify theo retical results. The agreement between observations and theory is quite sat isfactory. Kelvin-Helmholtz waves grow whenever theoretical unstable condit ions are attained. The values of measured wavelengths well correspond to ma ximum growth rate wave numbers. The comparison between theoretical and expe rimental results also shows that acceleration plays a stabilizing action. ( C) 1999 American Institute of Physics. [S1070-6631(99)00502-4].