The effect of Schmidt number on gravity current flows: The formation of large-scale three-dimensional structures

• Published in: Physics of fluids (1994) Vol. 33; no. 10
• Main Authors: Marshall, C. R., Dorrell, R. M., Dutta, S., Keevil, G. M., Peakall, J., Tobias, S. M.
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.10.2021
• Subjects: Density distribution; Diffusivity; Direct numerical simulation; Fluid dynamics; Fluid flow; Interface stability; Physics; Reynolds number; Schmidt number; Three dimensional flow
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0064386

The Schmidt number, defined as the ratio of scalar to momentum diffusivity, varies by multiple orders of magnitude in real-world flows, with large differences in scalar diffusivity between temperature, solute, and sediment driven flows. This is especially crucial in gravity currents, where the flow dynamics may be driven by differences in temperature, solute, or sediment, and yet the effect of Schmidt number on the structure and dynamics of gravity currents is poorly understood. Existing numerical work has typically assumed a Schmidt number near unity, despite the impact of Schmidt number on the development of fine-scale flow structure. The few numerical investigations considering high Schmidt number gravity currents have relied heavily on two-dimensional simulations when discussing Schmidt number effects, leaving the effect of high Schmidt number on three-dimensional flow features unknown. In this paper, three-dimensional direct numerical simulations of constant-influx solute-based gravity currents with Reynolds numbers 100 ≤ R e ≤ 3000 and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with ( R e , S c ) = ( 100 , 10 ) ,   ( 100 , 100 ) , and (500, 10). These data are used to establish the effect of Schmidt number on different properties of gravity currents, such as density distribution and interface stability. It is shown that increasing Schmidt number from 1 leads to substantial structural changes not seen with increased Reynolds number in the range considered here. Recommendations are made regarding lower Schmidt number assumptions, usually made to reduce computational cost.