On the Parametrically driven surface waves in rectangular containers

Faraday waves are well known in the field of free-surface wave dynamics. Since the day Michael Faraday (1831) discovered a fundamental response (i.e., Faraday wave response) of free-surface to external vibration of the fluid body, researchers such as Lamb, Penny and Price, Taylor, Benjamin and Ursell, Longuet-Higgins, John Miles, Henderson, Schultz, …. have done experiments and developed theories to characterize Faraday wave behavior for low and high-amplitude relative to the wavelength.

For parametrically driven low amplitude wave, research emphasis is on the free-surface stability and resonant frequency regarding the external forcing frequency and threshold amplitude to initiate the wave. A significant consideration in this area has been given to the effect of viscosity as a primary parameter affecting both resonant frequency and corresponding threshold but generally overlooked the effect of the interfacial surface tension. My experimental and theoretical work has shown that the surface tension plays a significant role on the free-surface stability particularly its resonance and according to John Miles theory the effect of surface tension may be opposite to that of the viscosity. Another significant point this study has shown experimentally that Faraday stability holds a property of principle of similarity analogous to the Blasius laminar boundary layer flow. It means that if various stability envelopes corresponding to various wave numbers are plotted in the non-dimensional p-q coordinate system, they all collapse to form a single envelope. This issue has not been addressed in open literature.

Another part of my study is convection driven by large amplitude nonlinear Faraday waves. This subject also has been overlooked by the previous research work. I applied a technique of non-intrusive optical measurement, particle imaging velocimeter (PIV), to measure the bulk fluid convection driven by free surface waves. The waves were parametrically generated by a driving frequency of 24 Hz and a peak-to-peak forcing acceleration of two-time gravitational acceleration. The waves are nonlinear as later confirmed by comparing experimental data with two theories of Penny and Price (1952) and Longuet-Higgins (1997).