An investigation of hydrodynamic surface waves with a cylindrical microwave resonator. I. Theory of method

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Abstract
In the first of this series of papers, we show that shifts in the resonant frequencies of a microwave resonator produced by boundary distortions can be used to study surface waves on conducting fluids.Surface waves can easily be studied under conditions where linearity requirements are satisfied. In addition, it is shown that a resonator of rectangular cross section acts as an analogue Fourier analyzer, so that a surface mode of a particular geometry can be observed, even when several modes are present simultaneously on the fluid surface. General results for a cylindrical resonator are first derived for TE and TM electromagnetic modes, and detailed calculations are then presented for resonators of rectangular and circular cross sections, since these are the most important practical examples.
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