Classical and symmetrical horizontal convection: detaching plumes and oscillations

Philipp Reiter,Olga Shishkina

doi:10.1017/jfm.2020.211

Philipp Reiter, Olga Shishkina

Open Access

https://doi.org/10.1017/jfm.2020.211

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Abstract

Classical and symmetrical horizontal convection is studied by means of direct numerical simulations for Rayleigh numbers up to 3 × 1012 and Prandtl numbers , 1 and 10. For both set-ups, a very good agreement in global quantities with respect to heat and momentum transport is attained. Similar to Shishkina & Wagner (Phys. Rev. Lett., vol. 116, 2016, 024302), we find Nusselt number versus scaling transitions in a region . Above a critical , the flow undergoes either a steady–oscillatory transition (small ) or a transition from steady state to a transient state with detaching plumes (large ). The onset of the oscillations takes place at and the onset of detaching plumes at . These onsets coincide with the onsets of scaling transitions.

Highlights

In a horizontal convection (HC) system, heating and cooling take place over a single horizontal surface of a fluid layer. Sandstrom (1908) argued that, due to the absence of a pressure gradient, a closed circulation cannot be maintained in such systems
First we observe that Nu and Re in classical horizontal convection (CHC) and symmetrical horizontal convection (SHC) match remarkably well, with nearly equal absolute values over the whole parameter range
Both set-ups can be used for the investigation of the global heat and momentum transport in HC

Summary

Introduction

In a horizontal convection (HC) system, heating and cooling take place over a single horizontal surface of a fluid layer. Sandstrom (1908) argued that, due to the absence of a pressure gradient, a closed circulation cannot be maintained in such systems. Six decades later, Rossby (1965) demonstrated in his experiments that HC alone, independent of any other sources, is able to create a circulation of a fluid and a net convective buoyancy flux. By considering the dynamics to be driven by a turbulent endwall plume, Hughes et al (2007) proposed the scaling Nu ∼ Ra1/5Pr1/5, but, as shown in Shishkina & Wagner (2016), the proposed Pr scaling is too strong and is not supported by direct numerical simulations (DNS). The SGL model suggests Nu ∼ Pr0Ra1/4 for large-Pr and Nu ∼ Pr1/10Ra1/5 for small-Pr laminar flows, which was supported by several numerical studies (Shishkina & Wagner 2016; Ramme & Hansen 2019).

Theoretical background

Results

Dynamics: plumes and oscillations

Dissipation rates

Conclusions