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Full-Text Articles in Applied Mathematics
The Steady Boundary Layer Due To A Fast Vortex, Andrew J. Bernoff, Harald J. H. M. Van Dongen, Seth Lichter
The Steady Boundary Layer Due To A Fast Vortex, Andrew J. Bernoff, Harald J. H. M. Van Dongen, Seth Lichter
All HMC Faculty Publications and Research
A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex cv is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically …
Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell
Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell
All HMC Faculty Publications and Research
The dynamics of two‐dimensional Rayleigh–Bénard convection rolls are studied in a finite layer with no‐slip, fixed temperature upper and lower boundaries and no‐slip insulating side walls. The dominant mechanism controlling the number of rolls seen in the layer is an instability concentrated near the side walls. This mechanism significantly narrows the band of stable wavenumbers although it can take a time comparable to the long (horizontal) diffusion time scale to operate.