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Direct Numerical Simulation (DNS) of spatially-developing turbulent boundary layers (SDTBL) is performed over isothermal/adiabatic flat plates for incompressible and compressible-subsonic (M∞ = 0.5 and 0.8) flow regimes. Similar low Reynolds numbers are considered in all cases with the purpose of assessing modest flow compressibility on low/high order flow statistics of Zero Pressure Gradient (ZPG) flows. The considered molecular Prandtl number is 0.72. Additionally, temperature is regarded as a passive scalar in the incompressible SDTBL with the purpose to examine differences in the thermal transport phenomena of subsonic flows, i.e., passive vs. active scalar. It was found that the Van Driest transform and Morkovin scaling are able to collapse incompressible and subsonic quantities very well.
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On mathematical analysis of complex fluids in active hydrodynamics
This is a survey article for this special issue providing a review of the recent results in the mathematical analysis of active hydrodynamics. Both the incompressible and compressible models are discussed for the active liquid crystals in the Landau-de Gennes Q-tensor framework. The mathematical results on the weak solutions, regularity, and weak-strong uniqueness are presented for the incompressible flows. The global existence of weak solution to the compressible flows is recalled. Other related results on the inhomogeneous flows, incompressible limits, and stochastic analysis are also reviewed.
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- Award ID(s):
- 1907519
- PAR ID:
- 10330693
- Date Published:
- Journal Name:
- Electronic Research Archive
- Volume:
- 29
- Issue:
- 6
- ISSN:
- 2688-1594
- Page Range / eLocation ID:
- 3817
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/era.2021063
