Asymmetry in the spin-up of a stratified fluid in a sliced, square cylinder

Abstract Previously, we have reported theory and experiments on the spin-up of a linearly stratified fluid contained in sealed square cylinder with bottom sloped at angle $$\alpha$$ α (Munro & Foster, Phys. Fluids , 26 026603, 2014). The motion is characterized by small Rossby number, $$\epsilon$$ ϵ fractional change rotation rate, Ekman E Burger S ratio buoyancy frequency (or Brunt-Väisälä frequency) to base rate. This paper, supplementing what has gone before, focused horizontal vertical structure propagating vorticity waves (Rossby waves), alternating anti-cyclonic cyclonic cells, which move across tank from east west, thereby accomplishing least early stages spin-up. We find strong dependence modal these waves, their speed, number. However, particularly noteworthy observed north-south asymmetry wave field. that not consistent typical Rossby-wave theories (Pedlosky Greenspan, J. Fluid Mech. 27 p. 291, 1967), but attributable second-order effects asymptotic expansion streamfuntion powers .