The flow generated in a continuously stratified rotating fluid by the differential rotation of a plane horizontal disc

Abstract

Results are presented from a modelling investigation into the response of a rotating, linearly stratified fluid to local forcing induced by a differentially rotating smooth, horizontal disc. Attention was directed at cases in which the disc forcing is relatively strong, with Rossby number ε = ω / 2 Ω of order 1 or greater; here ω and Ω are the disc and background rotation frequencies, respectively. The principal flow dynamics resulting in the mixing and deformation of the initially stable density distribution were identified as (i) shear-induced mixing due to the local increase in fluid vorticity above the disc and (ii) meridional circulations produced by Ekman processes and the constraint of the container sidewall. Laboratory experiments revealed the growth of a mixed layer adjacent to the disc and the subsequent development of layers within the mixed region. Furthermore, the experiments showed that, even at relatively large ε , Ekman processes associated with background rotation constituted the dominant mechanism controlling development and evolution of the primary interface between mixed and unmixed fluid regions. Theoretical, energy-based scalings are derived to describe the growth rate of the interfacial region for ε ≳ O ( 1 ) which are consistent with the ε → ∞ limit corresponding to the Ω = 0 case. These scalings are shown to describe well the development of the density field within the forced flow.