Skip to content
Research Article Open access CC BY 4.0

Analytic Solutions of the Rotating and Stratified Hydrodynamical Equations

Imre F. Barna, L. Mátyás

Asian Journal of Research and Reviews in Physics · pp. 14–26 · Published 22 Jan 2021

10.9734/ajr2p/2021/v4i130133

Abstract

In this article we investigate the two-dimensional incompressible rotating and stratified, just rotating,  just stratified Euler equations, comparing with each other and with the normal Euler equations with  the self-similar Ansatz. The motivation of our study is the following the presented rotating stratified  fluid equations can be interpreted as a well-established starting point of various more complex and  more realistic meteorologic, oceanographic or geographic models. We present analytic solutions  for all four models for density, pressure and velocity fields, most of them are some kind of power-law  type of functions. In general the presented solutions have a rich mathematical structure. Some  solutions show nonphysical explosive properties others, however are physically acceptable and  have finite numerical values with power law decays. For a better transparency we present some figs  for the most complicated velocity and pressure fields. To our knowledge there are no such analytic  results available in the literature till today. Our results may attract attention in various scientific fields.   

Mathematical formulation conservation laws and constitutive relations stratified flows.

References (26)

  1. 1 Geophysical Fluid Dynamics [DOI]
  2. 2 Similarity and Dimensional Methods in Mechanics [DOI]
  3. 3 Atmospheric and Oceanic Fluid Dynamics [DOI]
  4. 4 Atmospheric and Oceanic Fluid Dynamics [DOI]
  5. 5 Seismic Wave Propagation in Stratified Media [DOI]
  6. 6 Similarity and Dimensional Methods in Mechanics [DOI]
  7. 7 Seismic wave propagation in stratified media [DOI]
  8. 8 Similarity and Dimensional Methods in Mechanics [DOI]
  9. 9 Turbulence in Rotating, Stratified and Electrically Conducting Fluids [DOI]
  10. 10 Mathematical Geophysics [DOI]
  11. 11 Sound Propagation in Stratified Fluids [DOI]
  12. 12 Geophysical Fluid Dynamics [DOI]
  13. 13 Environmental Stratified Flows [DOI]
  14. 14 SIMILARITY, SELF-SIMILARITY AND INTERMEDIATE ASYMPTOTICS [DOI]
  15. 15 Convection in Rotating Fluids [DOI]
  16. 16 Theory and Modeling of Rotating Fluids [DOI]
  17. 17 Fluid Flow and Heat Transfer in Rotating Porous Media [DOI]
  18. 18 Fundamentals of Geophysical Hydrodynamics [DOI]
  19. 19 Physics of Rotating Fluids [DOI]
  20. 20 Rotating Fluids in Engineering and Science [DOI]
  21. 21 Dynamics of a vortex ring in a rotating fluid [DOI]
  22. 22 Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer [DOI]
  23. 23 Environmental Hydraulics: Stratified Flows [DOI]
  24. 24 Environmental Stratified Flows [DOI]
  25. 25 Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids
  26. 26 Rotating fluids in engineering and science [DOI]

Cited by 3

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

Imre Ferenc Barna, Mihály András Pocsai, László Mátyás · Mathematics · 2022

The Formulation of Scaling Expansion in an Euler-Poisson Dark-Fluid Model

Balázs Endre Szigeti, Imre Ferenc Barna, Gergely Gábor Barnaföldi · Universe · 2023

Showing 2 of 3 known citations — external sources report more than can currently be individually listed.

Article metrics

Real usage data collected on this platform.

14

Page views

0

PDF downloads

1

Outbound clicks

3

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.