Baroclinic critical levels arise as singularities in the inviscid linear theory of waves
propagating through a stratified, horizontally directed and sheared flow. For a steady
wave forcing, disturbances grow secularly over the criticial layers surrounding these levels,
generating a jet-like defect in the mean flow. We use a matched ...
Baroclinic critical levels arise as singularities in the inviscid linear theory of waves
propagating through a stratified, horizontally directed and sheared flow. For a steady
wave forcing, disturbances grow secularly over the criticial layers surrounding these levels,
generating a jet-like defect in the mean flow. We use a matched asymptotic expansion to
furnish a reduced model of the nonlinear dynamics of such defects. By solving the linear
initial-value problem for small perturbations to the defect, we establish that secondary
instabilities appear at later times. Because the defect is time-dependent, conventional
normal-mode analysis is quantitatively inaccurate, but does successfully predict the
occurrence of the secondary instability. The instability has a singular character in that
disturbances with the shortest horizontal wavelength grow most vigorously at late times,
unless dissipation is included. The instability can be suppressed by weak viscosity; by
itself, thermal dissipation delays, but does not arrest instability. Numerical computations
with the dissipative reduced model demonstrate that the secondary instability saturates
as the defect rolls up into a coherent vortical structure. This structure excites a new wave
propagating at a different phase speed, thereby forcing a new set of baroclinic critical
levels. The implications for self-replication are discussed.