Coronavirus Information for the UC San Diego Community

Our leaders are working closely with federal and state officials to ensure your ongoing safety at the university. Stay up to date with the latest developments. Learn more.

Improved bounds on horizontal convection

TitleImproved bounds on horizontal convection
Publication TypeJournal Article
Year of Publication2020
AuthorsRocha C.B, Bossy T., Smith SGL, Young W.R
Volume883
Date Published2020/01
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000508121500041
Keywordsenergy; mechanics; Ocean circulation; physics; variational methods
Abstract

For the problem of horizontal convection the Nusselt number based on entropy production is bounded from above by C Ra-1/3 as the horizontal convective Rayleigh number Ra -> infinity for some constant C (Siggers et al., J. Fluid Mech., vol. 517, 2004, pp. 55-70). We re-examine the variational arguments leading to this `ultimate regime' by using the Wentzel-Kramers-Brillouin method to solve the variational problem in the Ra -> infinity limit and exhibiting solutions that achieve the ultimate Ra(1/)3 scaling. As expected, the optimizing flows have a boundary layer of thickness similar to Ra-1/3 pressed against the non-uniformly heated surface; but the variational solutions also have rapid oscillatory variation with wavelength similar to Ra-1/3 along the wall. As a result of the exact solution of the variational problem, the constant C is smaller than the previous estimate by a factor of 2.5 for no-slip and 1.6 for no-stress boundary conditions. This modest reduction in C indicates that the inequalities used by Siggers et al. (J. Fluid Mech., vol. 517, 2004, pp. 55-70) are surprisingly accurate.

DOI10.1017/jfm.2019.850
Student Publication: 
No
sharknado