Analyzing emission, reflection and diffraction of internal waves using the Hilbert transform

Hilbert Transform applied to two-dimensional internal waves allows a greater understanding of fundamental experiments such as diffraction and reflection. Robustness of this technique based on time and spatial filtering is tested through different types of internal waves generated using a recently developed wavemaker. The analysis of wavefields radiated by a slit and due to an incoming internal plane wave (whose wavelength is comparable to the width of the slit) reveals a diffraction-like pattern. Althouhg differences from the optical phenomenon due to the atypical nature of internal waves are evident, they can be explained with the same principle than ``classical'' diffraction. The study of reflection of internal plane waves using the Hilbert transform focuses on the search for a possible back-reflected beam. In the case of internal plane waves reflecting on a plane slope, no back-reflected beam is observed as predicted by theory. But the case of concave/convex surfaces remains opened.