A new, exact Floquet theory is presented for linear waves in two-layer fluidsover a periodic bottom of arbitrary shape and amplitude. A method of conformaltransformation is adapted. The solutions are given, in essentially analytical form, forthe dispersion relation between wave frequency and generalized wavenumber (Floquetexponent), and for the waveforms of free wave modes. These are the analogues of theclassical Lamb’s solutions for two-layer fluids over a flat bottom. For internal modesthe interfacial wave shows rapid modulation at the scale of its own wavelength that iscomparable to the bottom wavelength, whereas for surface modes it becomes a longwave carrier for modulating short waves of the bottom wavelength. The approximationusing a rigid lid is given. Sample calculations are shown, including the solutions thatare inside the forbidden bands (i.e. Bragg resonated).
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