Open AccessEnergy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling
Author(s) -
Magnus Hieronymus,
Jeffrey R. Carpenter
Publication year - 2016
Publication title -
journal of physical oceanography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.706
H-Index - 143
eISSN - 1520-0485
pISSN - 0022-3670
DOI - 10.1175/jpo-d-15-0155.1
Subject(s) - heat flux , scaling , mechanics , convection , dissipation , thermodynamics , turbulence , buoyancy , rayleigh number , energy budget , physics , energy balance , flux (metallurgy) , statistical physics , heat transfer , natural convection , mathematics , materials science , geometry , metallurgy
The steady-state energy and thermal variance budgets form the basis for most current methods for evaluating turbulent fluxes of buoyancy, heat, and salinity. This study derives these budgets for a double-diffusive staircase and quantifies them using direct numerical simulations; 10 runs with different Rayleigh numbers are considered. The energy budget is found to be well approximated by a simple three-term balance, while the thermal variance budget consists of only two terms. The two budgets are also combined to give an expression for the ratio of the heat and salt fluxes. The heat flux scaling is also studied and found to agree well with earlier estimates based on laboratory experiments and numerical simulations at high Rayleigh numbers. At low Rayleigh numbers, however, the authors find large deviations from earlier scaling laws. Last, the scaling theory of Grossman and Lohse, which was developed for Rayleigh–Bénard convection and is based on the partitioning of the kinetic energy and tracer variance dissipation, is adapted to the diffusive regime of double-diffusive convection. The predicted heat flux scalings are compared to the results from the numerical simulations and earlier estimates.