Stably stratified flow around a horizontal rectangular cylinder in a channel of finite depth

Abstract

This paper describes a numerical study of the two-dimensional flow of a linearly stably-stratified Boussinesq fluid around a rectangular cylinder in a channel of finite depth. To attain highly stratified flow, a difference scheme combining two grids was applied. Attention was focused upon the interaction between the vortex shedding and the internal gravity waves. A parameter K is used, which is the ratio of the fastest linear internal-wave speed to the mean flow speed. As K increases, the symmetric configuration with the cylinder placed at the mid-depth first stimulates the symmetric vertical dominant mode of the columnar disturbance at K ∼ 2, but the non-symmetric configuration with the cylinder displaced stimulates the non-symmetric mode at K ∼ 1. Once a columnar disturbance of a certain mode is created, accompanied by the lee waves, the wave speed of the columnar disturbance is not characterized by cylinder conditions, but by linear theory. A critical change in the Strouhal number is observed, shortly after appearance of the lee wave, which probably influences the dynamics of vortex formation. The likely flow alteration is thought to occur when the lee waves grow in amplitude and the wavelength becomes sufficiently short so that the wake cavity is suppressed/biased by the first troughs of the lee waves.