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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. [ABSTRACT FROM AUTHOR]

In this paper, we perform direct statistical simulations of a model of two-dimensional flow that exhibits a transition from jets to vortices. The model employs two-scale Kolmogorov forcing, with energy injected directly into the zonal mean of the flow. We compare these results with those from direct numerical simulations. For square domains, the solution takes the form of jets, but as the aspect ratio is increased, a transition to isolated coherent vortices is found. We find that a truncation at second order in the equal-time but nonlocal cumulants that employ zonal averaging (zonal CE2) is capable of capturing the form of the jets for a range of Reynolds numbers as well as the transition to the vortex state but, unsurprisingly, is unable to reproduce the correlations found for the fully nonlinear (non-zonally symmetric) vortex state. This result continues the program of promising advances in statistical theories of turbulence championed by Kraichnan. [ABSTRACT FROM AUTHOR]

In an earlier paper [P. W. Livermore, D. W. Hughes, and S. M. Tobias, “The role of helicity and stretching in forced kinematic dynamos in a spherical shell,” Phys. Fluids 19, 057101 (2007)], we considered the kinematic dynamo action resulting from a forced helical flow in a spherical shell. Although mean field electrodynamics suggests that the resulting magnetic field should have a significant mean (axisymmetric) component, we found no evidence for this; the dynamo action was distinctly small scale. Here we extend our investigation into the nonlinear regime in which the magnetic field reacts back on the velocity via the Lorentz force. Our main result is somewhat surprising, namely, that nonlinear effects lead to a considerable change in the structure of the magnetic field, its final state having a significant mean component. By investigating the dominant flow-field interactions, we isolate the dynamo mechanism and show schematically how the generation process differs between the kinematic and nonlinear regimes. In addition, we are able to calculate some components of the transport coefficient α and thus discuss our results within the context of mean field electrodynamics. [ABSTRACT FROM AUTHOR]

Considerations of mean-field theory suggest that small-scale helical flows are an effective means of generating large-scale (mean) magnetic fields, whereas fast dynamo considerations reveal the importance of Lagrangian chaos in the flow for generating small-scale magnetic fields in the limit of high magnetic Reynolds number. We explore these ideas further by considering the kinematic magnetic fields generated by three forced steady flows in a spherical shell that differ both in their helicity and in their stretching properties. The full magnetic induction equation is solved numerically, with no a priori assumptions about the nature of the generated magnetic field. There are two surprising aspects to our results. One is that the most significant mean field is generated by a flow with zero net helicity; the other is that the flow with the “best” stretching properties turns out to be the most inefficient dynamo. Our results, therefore, suggest that it may not be possible to determine the nature of a kinematic-dynamo generated magnetic field simply from the knowledge of certain flow properties. [ABSTRACT FROM AUTHOR]