A Baroclinic Laminar State for Rotating Stratified Flows

Abstract

A baroclinic laminar model is developed as the late-time equilibrium state in the free decay of rotating stratified turbulence under low-Froude-number scaling. Vertical motions are suppressed by stratification and ambient rotation, and in the laminar end state the flow assumes a quasi-two-dimensional form. Geometric analyses of this nonlinear conservative model reveal an f-plane baroclinic topology characterized by vertical alignment, vanishing nonlinearity, and the complete absence of helicity. Equivalent-barotropic flow is the only nonunique baroclinic solution, and its horizontal topology is restricted to a unidirectional jet and a circular vortex. Such a depleted geometry results from the constraint of basic equations where density is advected as an active scalar. It provides a baroclinic mechanism for the formation of coherent structures in geophysical flows.

Geometric structure of pseudo-plane quadratic flows

“…The geometric properties derived from a steady-state nonviscous Boussinesq-fluid model (named the PIF model) by Sun (2008) are extended to general pseudo-plane flows, revealing a fundamental relation between vertical coherence and streamline topology in ideal fluid. It suggests that for steady pseudo-plane flows, vertical alignment in terms of EB structure only appears in straightline jet and circular vortex.…”

Vertical alignment of stagnation points in pseudo-plane ideal flows

“…While ρ 0 signifies a baroclinic flow, ρ = 0 describes homogeneous fluid in which density equation (5) is redundant. The overdetermination of the PIF model and its symmetry implication have been examined by Sun (2008).…”

“…Helicity measures the knottedness of vortex lines and also measures velocity rotation in a pseudo-plane flow (Sun 2008). Critical point.…”

“…The temperature data from a baroclinic current fluctuate around the basic GEM profile with small rms residues. The low-dimensional structure motivated Sun (2008) to develop a steady pseudo-plane ideal flow (PIF) model based on the notion that geostrophic flows are quasi-horizontal and stratified turbulence tends to collapse into a laminar end state with negligible vertical velocity. Such pseudo-plane flows have vertically varying horizontal velocities but no vertical velocity (Saccomandi 1994).…”

“…As it turns out, the phenomenon stems from the Euler equations and has omnipresence beyond geophysical flows. Sun (2008) derived the PIF model from the stratified-turbulence equations of Riley et al (1981) by taking the limit of vanishing vertical velocity under low Froude number. For a steady pseudo-plane flow u = [u(x, y, z), v(x, y, z), 0], the Euler equations under Boussinesq approximation also reduce to the PIF model…”