Search Results

You are looking at 1 - 2 of 2 items for

  • Author or Editor: Mark T. DiBattista x
  • Refine by Access: All Content x
Clear All Modify Search
Mark T. DiBattista and Andrew J. Majda

Abstract

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a rim current and localized temperature anomaly. Furthermore, rigorous explicit nonlinear stability analysis guarantees the stability of these steady states for a suitable range of parameters. Both random heton distributions in a basin with quiescent flow as well as heton addition to an ambient barotropic flow in the basin are studied here. Also, systematic results are presented on the influence of the Rossby deformation radius compared to the basin scale on the structure of the predictions of the statistical theory.

Full access
Mark T. DiBattista, Andrew J. Majda, and John Marshall

Abstract

Within basins that exhibit open-ocean convection, convectively mixed fluid is often observed in regions of upward-doming isopycnal surfaces, preconditioned by either cyclonic circulation and/or bottom topography. Here, an equilibrium statistical theory for open-ocean convection, developed in the context of two-layer heton models, is adapted to study the outcome of basinwide cooling events over preexisting large-scale ambient flow. A range of prototype ambient flows is studied—including cyclonic and anticyclonic gyres, purely barotropic circulations, and topographically induced flow about a localized seamount and within a broad bowl-like depression. The critical element of these elementary ambient flows is the position of the fluid interface separating the upper and lower layers; it is displaced upward within the cyclonic gyre and the upwelling seamount, downward within the anticyclonic gyre and the bowl-like depression, and is flat for purely barotropic flow. The authors then consider the effect of applying cooling by introducing cold hetons over the preconditioned flow. The most probable postconvection state is found by maximizing the entropy contained in the coarse-grained vorticity field subject to key large-scale constraints. Consistent with observations, the most probable distribution of the cold-temperature anomalies, introduced by the convective overturning that follows a basin-scale surface cold-air outbreak, is indeed concentrated about the peaks of upwelling isopycnals. In contrast, ambient flows with isopycnal surfaces that slope downward fail to confine the cold-temperature anomalies as hetons tend to cluster along the edges and corners of the basin with much weaker displacements.

Full access