Journal Article

Beta-Effect of Internal Inertia–Gravity Waves in a Stratified Atmosphere in the Incompressible Fluid Approximation

Chernyshov, Andrey V, Zakinyan, Robert G, Zakinyan, Arthur R

2025

Overview

This paper presents a mathematical model that describes the propagation of internal inertia–gravity waves in a stratified atmosphere under the approximations of an incompressible fluid and a traditional β-plane. It demonstrates that, in the incompressible fluid approximation, the temperature field is inconsistent with the heat conduction equation. The system of equations that describes internal inertia–gravity waves is considered in the general case, taking into account the buoyancy force, and reduced to a single equation. The solution is sought in the form of traveling plane waves. A dispersion relation has been obtained in the form of a cubic equation that represents a hypersurface in wave number space, without the assumption of small vertical wavelength. Cross-sections of this surface are plotted, and an extremum study is performed. This shows that a new frequency region appears in the low-frequency spectrum 0<ω

• Publisher: MDPI AG
• Subject: Analysis / Approximation / Atmosphere / beta-plane approximation / Buoyancy / buoyancy frequency / Conduction heating / Conductive heat transfer / Coriolis parameter / Coriolis parameters / Cubic equations / Dispersion / dispersion relation / Earth / Environmental aspects / Fluid flow / Frequency spectra / Frequency spectrum / Gravity waves / Heat / Heat conduction / Hyperspaces / Incompressible flow / incompressible fluid approximation / Incompressible fluids / Inertia / Inertia gravity waves / internal inertia–gravity waves / Mathematical models / Plane waves / Temperature distribution / Temperature fields / Velocity / Wave number / Wavelength