Critical regimes of internal gravity wave generation

TL;DR

This paper investigates the asymptotic behavior of internal gravity waves generated by a moving source near the maximum group velocity, providing formulas involving Macdonald functions and validating them with numerical calculations.

Contribution

It introduces a new asymptotic representation for internal gravity wave fields in critical regimes using Macdonald functions, enhancing understanding of wave generation near critical velocities.

Findings

Asymptotic formulas expressed via Macdonald functions accurately describe wave fields.

Numerical results confirm the validity of the asymptotic representations.

The study advances theoretical understanding of wave generation in critical regimes.

Abstract

The problem of constructing an asymptotic representation of the solution of the internal gravity wave field exited by a source moving at a velocity close to the maximum group velocity of the individual wave mode is considered. For the critical regimes of individual mode generation the asymptotic representation of the solution obtained is expressed in terms of a zero-order Macdonald function. The results of numerical calculations based on the exact and asymptotic formulas are given.