### Abstract

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 language | English (US) |
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Pages (from-to) | 205-214 |

Number of pages | 10 |

Journal | Journal of Fluid Mechanics |

Volume | 466 |

DOIs | |

State | Published - Sep 10 2002 |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*466*, 205-214. https://doi.org/10.1017/S0022112002001313

**Horizontal convection is non-turbulent.** / Paparella, Francesco; Young, W. R.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 466, pp. 205-214. https://doi.org/10.1017/S0022112002001313

}

TY - JOUR

T1 - Horizontal convection is non-turbulent

AU - Paparella, Francesco

AU - Young, W. R.

PY - 2002/9/10

Y1 - 2002/9/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037056286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037056286&partnerID=8YFLogxK

U2 - 10.1017/S0022112002001313

DO - 10.1017/S0022112002001313

M3 - Article

AN - SCOPUS:0037056286

VL - 466

SP - 205

EP - 214

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -