Physics of Fluids, Volume 33, Issue 3, March 2021. Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter a = 1), in which all the strain in the plane of the layer goes toward vorticity stretching, as well as Migdal's recent steady asymmetric solution for axisymmetric strain (a = 1/2), in which half of the strain goes into vorticity stretching. In addition to considering asymmetric, symmetric, and antisymmetric steady solutions [math], it is shown that for a < 1, i.e., anything less than the Townsend case, the vorticity inherently decays in time: only boundary conditions that maintain a supply of vorticity at one or both ends lead to a non-zero steady state. For the super-Townsend case a > 1, steady states have a sheath of opposite sign vorticity. Comparison is made with homogeneous-isotropic turbulence, in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend. Only zero-integral perturbations of the a > 1 steady solutions are stable; otherwise, the solution grows. Finally, the appendix shows that the average flow in the strain eigenframe is (apart from an extra term) the Reynolds-averaged Navier–Stokes equation.

## Authors

## Departments

## Libraries

## Recent Articles

- Extraction of negative hydrogen ions produced with aluminum plasma grid
- Shell mass effect on the hot-spot pressure in inertial confinement fusion implosion
- Metasurface-tuning: A camouflaging technique for dielectric obstacles
- A two-sensor 3ω-2ω method for thermal boundary resistance measurement
- Effect of reduction produced defects on the dielectric relaxation and electrical conduction of Na0.5Bi0.5TiO3-based ceramics
- TiO2 nanoparticle deposition on cotton fabric through pulsed electrical current in water/TiO2 solution
- Thermal- and photo-induced spin crossover in the 1D coordination polymer [Fe(4-tBupy)3][Au(CN)2]2 (4-tBupy = 4-tert-butylpyridine)
- InGaN-based nanowires development for energy harvesting and conversion applications
- Controlling surface/interface states in GaN-based transistors: Surface model, insulated gate, and surface passivation
- A deep learning-based concept for high throughput image flow cytometry
- Ultrasound differential phase contrast using backscattering and the memory effect
- Controlling relaxation dynamics of excitonic states in monolayer transition metal dichalcogenides WS2 through interface engineering
- Viscous vortex layers subject to more general strain and comparison to isotropic turbulence
- Lagrangian models of particle-laden flows with stochastic forcing: Monte Carlo, moment equations, and method of distributions analyses
- The dynamics of flow-induced flutter of a thin flexible sheet
- Overstable rotating convection in the presence of a vertical magnetic field
- Poisson structures of near-symplectic manifolds and their cohomology
- Reaction pathways in the solid state and the Hubbard U correction
- KS-pies: Kohn–Sham inversion toolkit
- Electric-field-driven coexistence of positive and negative electrocaloric effects near room temperature for high-efficiency two-stage cooling