Horizontal convection is non-turbulent

F. Paparella, W. R. Young

Research output: Contribution to journalArticlepeer-review


Consider the problem of horizontal convection: a Boussinesq fluid, forced by applying a non-uniform temperature at its top surface, with all other boundaries insulating. We prove that if the viscosity, v, and thermal diffusivity, K, are lowered to zero, with σ Ξ v/k fixed, then the energy dissipation per unit mass, ε, also vanishes in this limit. Numerical solutions of the two-dimensional case show that despite this anti-turbulence theorem, horizontal convection exhibits a transition to eddying flow, provided that the Rayleigh number is sufficiently high, or the Prandtl number σ sufficiently small. We speculate that horizontal convection is an example of a flow with a large number of active modes which is nonetheless not 'truly turbulent' because ε → 0 in the inviscid limit.

Original languageEnglish (US)
Pages (from-to)205-214
Number of pages10
JournalJournal of Fluid Mechanics
StatePublished - Sep 10 2002

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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