Traveling internal waves in a two-layer shallow medium with variable bathymetry and current

Article Mechanics

Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2

Semyon M. Churilov et al.

Summary: In this study, three classes of reflectionless wave propagation in a channel with spatially varying depth, width, and current speed have been identified. The analysis shows that these three classes exhaust all possible cases of exact solutions for the problem considered. The study also reveals the existence of global and limited interval reflectionless flows.

JOURNAL OF FLUID MECHANICS (2022)

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Article Meteorology & Atmospheric Sciences

Reflectionless Internal-Wave Propagation in a Channel with Variable Cross Section and Current

S. M. Churilov

Summary: This study investigates the propagation of linear long internal waves in a two-layer fluid with a variable cross section under a rigid cover. Two types of flow that allow for wave propagation without reflection are identified and analyzed. The results are compared with those obtained for channels without current, showing that the presence of a steady flow limits the existence of self-consistent channels without wave reflection over unlimited distances. This limitation is due to the difference in velocity change between the fluid flow and wave propagation, leading to a point where they become equal.

IZVESTIYA ATMOSPHERIC AND OCEANIC PHYSICS (2022)

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Article Multidisciplinary Sciences

Traveling Waves in Shallow Seas of Variable Depths

Efim Pelinovsky et al.

Summary: This paper discusses the problem of the existence of traveling waves in inhomogeneous fluid and proposes new solutions. The study finds that under certain bottom profile conditions, traveling waves can propagate over long distances in strongly inhomogeneous water medium, and the temporal shape of the waves changes with distance.

SYMMETRY-BASEL (2022)

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Article Mechanics

Reflectionless wave propagation on shallow water with variable bathymetry and current

Semyon M. Churilov et al.

Summary: In the linear approximation, the one-dimensional problem of reflectionless wave propagation on the surface of a shallow duct with spatially varying water depth, duct width, and current is studied. It is shown that both global and bounded exact solutions exist for the reflectionless propagation of long waves in opposite directions for specific variations of these parameters. The general analysis of the problem is illustrated by constructing solutions for specific cases of spatial profiles of flow and wave propagation velocities.

JOURNAL OF FLUID MECHANICS (2021)

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Article Mathematics, Applied