×

Direct numerical simulations of bifurcations in an air-filled rotating baroclinic annulus. (English) Zbl 1157.76330

Summary: Three-dimensional direct numerical simulations (DNS) of the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating are presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies, the fluid used is air rather than a liquid as used in all other previous work. This study investigates a bifurcation sequence from the axisymmetric flow to a number of complex flows.
The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady fully developed baroclinic wave to chaotic flow, followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic (MAV). In the context of the baroclinic annulus this sequence is unusual as the vacillation is usually found on decrease of the rotation rate from the steady wave flow.
Further transitions of a steady wave with a higher wavenumber pointed to the possibility that a barotropic instability of the sidewall boundary layers and the subsequent breakdown of these barotropic vortices may play a role in the transition to structural vacillation and, ultimately, geostrophic turbulence.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76-05 Experimental work for problems pertaining to fluid mechanics
76F06 Transition to turbulence
76F65 Direct numerical and large eddy simulation of turbulence
76U05 General theory of rotating fluids
86A10 Meteorology and atmospheric physics
PDFBibTeX XMLCite
Full Text: DOI arXiv