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Full-Text Articles in Mechanical Engineering
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.