Wave equation and dispersion relations for a compressible rotating fluid
Jose Marin-Antuna, Richard L. Hall, Nasser Saad
TL;DR
This paper derives a fundamental fourth-order PDE for small oscillations in a rotating compressible fluid, analyzing its dispersion relations and velocity regions to deepen understanding of wave behavior in such fluids.
Contribution
It introduces a novel fourth-order PDE specific to rotating compressible fluids and analyzes its dispersion characteristics, advancing theoretical understanding.
Findings
Derived a new fourth-order PDE for oscillations in rotating compressible fluids.
Analyzed dispersion relations and velocity regions for the PDE.
Provided insights into wave behavior in rotating compressible fluids.
Abstract
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of the group and phase velocity are analyzed.
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