Nonlinear saturation of thermal instabilities

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Abstract

Recent low-frequency simulations of a one-layer model with lateral buoyancy inhomogeneity have revealed circulatory motions resembling quite closely submesoscale features on the ocean surface often visible in satellite observations. This model is known to lack a high-wavenumber instability cutoff and, thus, to possibly undergo ultraviolet catastrophe. However, the numerically observed instabilities, referred to as "thermal"due the ability of the above inhomogeneous-layer model to incorporate thermodynamic processes, are not seen to grow indefinitely. In this note, I show that the presence of a convex pseudo-energy-momentum integral of motion for the inviscid, unforced dynamics can arrest their nonlinear grow in the zonally symmetric case. Our result is an application of Arnold and Shepherd's methods.

Original languageEnglish (US)
Article number036608
JournalPhysics of Fluids
Volume33
Issue number3
DOIs
StatePublished - Mar 1 2021

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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