Abstract
We present a series of three-dimensional visualizations of numerically simulated turbulent wakes in a stably stratified fluid with a focus on the effects of the wake Reynolds number, Re, on the wake flow. The visualization of stratified wakes is complicated by the coexistence of regions of distinct dynamics in the flow, including large-scale ‘pancake vortices,’ small-scale shear instabilities within layers of concentrated vertical shear, and internal waves emitted by the wake flow to the ambient fluid. We apply various techniques to identify dynamically distinct regions within the wake flow and visualize them separately. The volume fractions occupied by each of these regions are also quantified. Through the visualizations, we observe three significant effects on the wake’s evolution associated with increasing wake Reynolds number: (1) nontrivial modifications to the structure of the pancake vortices, (2) prolongation of the period of internal wave emission from the wake, and (3) greater longevity of small-scale shear instabilities within the anisotropic flow structures. These observations reveal a trend in Re that can potentially be extrapolated to stratified wakes at even larger Reynolds numbers that are typical of geophysical wakes and currently not accessible to laboratory experiments or numerical simulations.
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Notes
It is perhaps worth noting that the calculation of PV requires the gradients of all velocity components and density simultaneously which is typically difficult to achieve in experiments. In stratified wake experiments [e.g., Spedding (1997)], the vertical component of vorticity, \(\omega _z\), is typically calculated to visualize vortical motions.
Here and in Watanabe et al. (2016), \(\langle . \rangle \) indicates an average along the centerline of the R100 wake at \(Nt=21\).
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Acknowledgements
Support by the Natural Sciences and Engineering Research Council of Canada (NSERC), through a Discover Grant (RGPIN-2018-04329) awarded to Q.Z. and an Undergraduate Student Research Award (USRA) awarded to S.M., is gratefully acknowledged. C.T. is supported by the Program for Undergraduate Research Experience (PURE) at the University of Calgary (UofC). We thank Dr. Doug Phillips of the High Performance Computing group at UofC for technical support. This research was enabled in part by support provided by the Advanced Research Computing (ARC) cluster at UofC and by Compute Canada (www.computecanada.ca). Additional support for Q.Z. was provided by the Marine Environmental Observation, Prediction and Response (MEOPAR) network of Canada through an early career faculty grant. We thank an anonymous referee whose constructive comments helped to improve the paper.
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Halawa, B., Merhi, S., Tang, C. et al. Three-dimensional visualization of stratified turbulent wakes at varying Reynolds number. J Vis 23, 437–447 (2020). https://doi.org/10.1007/s12650-020-00638-x
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DOI: https://doi.org/10.1007/s12650-020-00638-x