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Articles 1 - 3 of 3
Full-Text Articles in Mechanical Engineering
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 …
Viscous Cross-Waves: An Analytical Treatment, Andrew J. Bernoff, L. P. Kwok, Seth Lichter
Viscous Cross-Waves: An Analytical Treatment, Andrew J. Bernoff, L. P. Kwok, Seth Lichter
All HMC Faculty Publications and Research
Viscous effects on the excitation of cross‐waves in a semi‐infinite box of finite depth and width are considered. A formalism using matched asymptotic expansions and an improved method of computing the solvability condition is used to derive the relative contributions of the free‐surface, sidewall, bottom, and wavemaker viscous boundary layers. This analysis yields an expression for the damping coefficient previously incorporated on heuristic grounds. In addition, three new contributions are found: a viscous detuning of the resonant frequency, a slow spatial variation in the coupling to the progressive wave, and a viscous correction to the wavemaker boundary condition. The wavemaker …
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
All HMC Faculty Publications and Research
A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.