Onset of K\"uppers--Lortz-like dynamics in finite
  rotating thermal convection

Speaker: Juan Lopez, Arizona State University

The onset of thermal convection in a finite rotating cylinder is
investigated using direct numerical simulations of the Navier--Stokes
equations with the Boussinesq approximation in a regime where
spatio-temporal complexity is observed directly after onset. The
system is examined in the non-physical limit of zero centrifugal force
as well as with an experimentally realizable centrifugal force,
leading to two different paths to K\"uppers--Lortz like
spatio-temporal chaos.  In the idealized case neglecting centrifugal
force, the onset of convection occurs directly from a conduction state
resulting in square patterns with slow roll-switching, followed by
straight roll patterns with roll switching at higher thermal driving.
The case with a centrifugal force typical of laboratory experiments
exhibits target patterns near the theoretically predicted onset of
convection, followed by a rotating wave that emerges via a Hopf
bifurcation.  A subsequent Hopf bifurcation leads to hexagonal
ratcheting states.  With increasing thermal driving, roll-switching is
observed within the ratcheting hexagonal lattice before
K\"uppers--Lortz like spatio-temporal chaos is observed with the
dissolution of the hexagonal lattice at a slightly stronger thermal
driving.  For both cases, all of these states are observed within a
two percent variation in the thermal driving.