Non-reflecting cylindrical wave propagation in the ocean of changing depth

Non-reflecting wave propagation is important for different applications of wave theory, where it is required that waves propagate over large distances without loss of energy. It has been found, that such waves exist not only in homogeneous or quasi-homogeneous media, but also in strongly inhomogeneous ones. For one-dimensional and quasi one-dimensional planar wave propagation in the ocean the corresponding solutions were found for convex bottom profiles and for a set of U- and V-shaped narrow bays and channels (Didenkulova et al. 2009, Didenkulova and Pelinovsky, 2009, 2011). However, this type of problem may also arise in the framework of cylindrical or radially symmetric waves. In geophysical applications, this corresponds to tsunami wave propagation from the meteorite fallen into the sea, or from underwater volcanic eruptions. In this work we find strongly varied sea bottom geometries, which allow for traveling wave solutions in the framework of cylindrical wave equation. Here we find two classes of non-reflecting geometries, which correspond to a bottom profiles next to (i) a radially symmetric deep sea trench and next to (ii) a volcanic island. Wave dynamics along these bottom geometries is also discussed.

The work was carried out with support from the RSF grant no. 23-77-01074.

 

Didenkulova, I., Pelinovsky, E., Soomere, T. Long surface wave dynamics along a convex bottom, J. Geophysical Research – Oceans, 114, C07006 (2009).

Didenkulova, I., Pelinovsky, E. Non-dispersive traveling waves in strongly inhomogeneous water channels, Physics Letters A, 373 (42), 3883-3887 (2009).

Didenkulova, I., Pelinovsky, E. Runup of tsunami waves in U-shaped bays, Pure and Applied Geophysics, 168 (6-7), 1239-1249 (2011).