Abstract
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≤Re≤3000 and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with (Re,Sc)=(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.
Highlights
WakeGravity currents are primarily horizontal flows arising from a density difference between the current and surrounding ambient fluids
For Reynolds numbers O(100) the presence of lobes-and-clefts in the current head is dependent on the Schmidt number
As over-running of ambient fluid is observed in the (ReI, Sc) = (3000, 1) case (Figure 8), providing the Reynolds number of the flow is sufficiently high this flow feature may be captured without increasing Schmidt number above 1
Summary
Gravity currents are primarily horizontal flows arising from a density difference between the current and surrounding ambient fluids. For the lower Reynolds number flows, they observe that increasing Sc changes head shape, with a depression separating head from body appearing as Sc increases, and that the effect of Sc on front velocity in these flows is highly dependent on the density contour chosen to define the front They claim that while the pattern of lobe-and-cleft structures is not strongly dependent on the Schmidt number, the formation of vortices along the body is. A scatter plot based on a table from Bonometti and Balachandar 33 is presented, showing the distribution of stable/unstable interfaces between the current and ambient fluids based on a bulk Richardson number for their work and a few other investigations This suggests that the interface stability is only weakly dependent on Schmidt number, with the interface becoming slightly more stable with increased Sc. This suggests that the interface stability is only weakly dependent on Schmidt number, with the interface becoming slightly more stable with increased Sc This data is based almost entirely on two-dimensional direct numerical simulation (DNS) data sets.
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