Cyclostrophic vortices in polar regions of rotating planets

Abstract

Abstract. Multi-petal, rotating vortices can form in twodimensional flows consisting of an inviscid incompressible fluid under certain conditions. Such vortices are principally nonlinear thermo-hydrodynamical structures. The proper rotation of these structures which leads to time-dependent variations of the associated temperature field can be enregistred by a stationary observer. The problem is analyzed in the framework of the contour dynamics method (CDM). An analytical solution of the reduced equation for a contour curvature is found. We give a classification of the solutions and compare the obtained results with observational data.

Untitled

“…In the case of intense vortices λ ∼ 1, a cyclostrophic rather than geostrophic balance can take place. Solutions for localized cyclostrophic vortices are shown in [32], [75], [66], [68].…”

Hot Spots in Sgr A* Accretion Disk: Hydrodynamic Insights

“…which says that for any specific ξ, ratio κ/ω is uniquely defined. Figure 3 plots Equation (26). For the presented model, the temperature excess τ follows from Equation ( 20) and Equation (23):…”

“…Within this framework-called the contour dynamics method (CDM) (see Refs. [18,[22][23][24][25][26][27])-the distribution of vorticity q for a vortex structure may be written as q = q 0 Θ(x, y). Function Θ(x, y) is a two-dimensional Heaviside step-function equal to one inside the domain in consideration and zero outside.…”

“…In the model, the vorticity clusters are approximated via deltafunctions. As the result, we established the condition of existence of a regular thermo-vorticial structure (Equation (26); see also Figure 2). We also spelled out the relationships that should take place between, on the one hand, the parameters that determine the vortex-structure dynamics-each vortex size (l), its period of proper revolution (2πω −1 ), and temperature excess τ in the vortex-and, on the other hand, the accretion disk characteristics (α and β, i.e., λ θ ) and the angular velocity of the entire accretion disk Ω.…”

“…For quasi-2D flows in thin layers of ideal fluid, another fruitful approach to analysis also exists (for deeper insight, see, Refs. [18,[22][23][24][25][26][27], and applications and references therein). This approach is called the contour dynamics method (CDM).…”