TY - JOUR

T1 - Waves in a Heavy Stratified Gas: Splitting Into Acoustic and Gravity Waves Subproblems

AU - Кшевецкий, Сергей Петрович

AU - Курдяева, Юлия Андреевна

AU - Гаврилов, Николай Михайлович

PY - 2024/12

Y1 - 2024/12

N2 - Abstract—Two-dimensional linearized hydrodynamic equations describing wave propagation in a stratified heavy gas are considered. The hydrodynamic equation system is reformulated as a single Schrödinger type operator equation. Waves with are considered, where and are the characteristic vertical and horizontal scales, respectively, and study the asymptotic behavior of solutions as . It is shown that the set of solutions depending on form two disjoint classes. For solutions from each of the selected classes, its own, asymptotic as , approximate equation system is proposed. The selected classes of solutions are acoustic and internal gravity waves. It is shown that the hydrodynamic variables of acoustic and gravity wavesare related by certain stationary relationships, different for each class. This makes it possible to formulate the problem of separating the contributions of acoustic and gravity waves in the initial condition. The existence of a solution to this wave separation problem is shown. Examples of solving the problem of dividing the general problem into subproblems on the propagation of acoustic and gravity

AB - Abstract—Two-dimensional linearized hydrodynamic equations describing wave propagation in a stratified heavy gas are considered. The hydrodynamic equation system is reformulated as a single Schrödinger type operator equation. Waves with are considered, where and are the characteristic vertical and horizontal scales, respectively, and study the asymptotic behavior of solutions as . It is shown that the set of solutions depending on form two disjoint classes. For solutions from each of the selected classes, its own, asymptotic as , approximate equation system is proposed. The selected classes of solutions are acoustic and internal gravity waves. It is shown that the hydrodynamic variables of acoustic and gravity wavesare related by certain stationary relationships, different for each class. This makes it possible to formulate the problem of separating the contributions of acoustic and gravity waves in the initial condition. The existence of a solution to this wave separation problem is shown. Examples of solving the problem of dividing the general problem into subproblems on the propagation of acoustic and gravity

KW - fluid dynamic equations, long waves, asymptotic solutions, operator equation, Hilbert space, acoustic waves, internal gravity waves, dispersion relation

U2 - 10.1134/S1063771024601833

DO - 10.1134/S1063771024601833

M3 - Article

VL - 70

SP - 1012

EP - 1026

JO - Acoustical Physics

JF - Acoustical Physics

SN - 1063-7710

IS - 6

ER -