The soundproof model of an acoustic--internal waves system with low stratification

TL;DR

This paper justifies a soundproof model for a low-stratification compressible fluid system, effectively capturing internal wave dynamics and mean flows while filtering out fast acoustic waves, and analyzes the fast-slow oscillation structure.

Contribution

It introduces and validates a soundproof approximation for low-stratification fluids, capturing key dynamics and oscillation structures not previously addressed.

Findings

Soundproof model accurately captures internal wave and mean flow dynamics.

Fast acoustic waves are effectively filtered out by the model.

Analysis of the fast-slow oscillation structure enhances understanding of wave interactions.

Abstract

This work is devoted to investigating a compressible fluid system with low stratification, which is driven by fast acoustic waves and internal waves. The approximation using a soundproof model is justified. More precisely, the soundproof model captures the dynamics of both the non-oscillating mean flows and the oscillating internal waves, while filters out the fast acoustic waves, of the compressible system with or without initial acoustic waves. Moreover, the fast-slow oscillation structure is investigated.