Vortex Motion State of the Dry Atmosphere with Nonzero Velocity Divergence

Robert Zakinyan,Roman Ryzhkov,Arthur Zakinyan,Julia Semenova

doi:10.3390/atmos9020061

Abstract

In the present work, an analytical model of the vortex motion basic state of the dry atmosphere with nonzero air velocity divergence is constructed. It is shown that the air parcel moves along the open curve trajectory of spiral geometry. It is found that for the case of nonzero velocity divergence, the atmospheric basic state presents an unlimited sequence of vortex cells transiting from one to another. On the other hand, at zero divergence, the basic state presents a pair of connected vortices, and the trajectory is a closed curve. If in some cells the air parcel moves upward, then in the adjacent cells, it will move downward, and vice versa. Upon reaching the cell’s middle height, the parcel reverses the direction of rotation. When the parcel moves upward, the motion is of anticyclonic type in the lower part of the vortex cell and of cyclonic type in the upper part. When the parcel moves downward, the motion is of anticyclonic type in the upper part of the vortex cell and of cyclonic type in the lower part.

Highlights

It is well known that the geostrophic state is a two-dimensional basic state for large-scale atmospheric motion [1,2,3]
Exact solutions of the Navier–Stokes equations for a three-dimensional vortex have been discovered [7,8,9,10,11]; of particular interest is Sullivan’s two-cell vortex solution, because the flow spirals in toward the axis and out along it, but it has a region of reverse flow near the axis
We further develop the theoretical model of the vortex motion state of the atmosphere

Summary

Introduction

It is well known that the geostrophic state is a two-dimensional basic state for large-scale atmospheric motion [1,2,3]. It should be noted that there are a large number of works dedicated to the theoretical study of atmospheric vortices. Most of these are concerned with the numerical solution of the atmospheric motion equations. In [14,15,16], three-dimensional atmospheric vortex motion is analyzed by considering the primitive dynamic and thermodynamic equations, including the Coriolis, pressure gradient and viscous forces. We further develop the theoretical model of the vortex motion state of the atmosphere.

Main Equations

Solution of the Main Equations

Conclusions

Introduction totoDynamic