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This research explores shallow and deep surface waves, the effects of bottom topology, and methods of measuring them.
We first verify an existing method of measuring the global topology of the free-surface of a liquid, the Free-Surface Synthetic Schlieren method.
This method utilizes the image refraction of a random dot pattern, which is placed parallel to and below a volume of fluid.
We then extend this method to a case in which the dot pattern may take any three-dimensional shape, which is not necessarily flat or parallel to the fluid surface.
This is shown to be theoretically valid under a small pattern slope approximation and verified against the previously mentioned, flat-pattern, free-surface synthetic Schlieren technique.
This new method may increase the resolution in low-amplitude regions by increasing the surface-pattern distance below these regions and correspondingly reduces the sensitivity in high-strain regions by decreasing the surface-pattern distance, resolving both regions simultaneously.
This shows promise in resolving multi-scale surface waves in highly viscous liquids or waves travelling over barriers, which may include very high amplitude regions quickly followed by very low amplitude regions.
We then perform a study on Faraday waves by producing them in a rectangular channel and measuring their free-surface using the above mentioned free-surface synthetic schlieren technique.
Although the original measurement technique is not typically applied to Faraday waves, which involve an oscillating bath of fluid, we demonstrate its validity in this case without altering the original method, simplifying their measurement significantly.
Finally, we explore free-surface waves travelling over shelf-like barriers, revisiting a long wave approximation method proposed by Lamb, offering a simple matrix method for solving systems of waves passing over multiple barriers.
Although our method predicts transmission coefficients significantly higher than experiments show, it does approximate the general shape of the transmission coefficient curve, with respect to frequency.
This discrepancy may be accounted for by viscous losses and losses caused by imaginary modes, which are both neglected in our analysis.
The work is towards M.Sc. degree under the supervision of Assistant Professor, Yuval Dagan, Faculty of Aerospace Engineering, Technion – Israel Institute of Technology
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