**Author details**

(**Figure 7**). Circulation of substance in different parts of modon occurs in opposite

*The isodense picture of the galaxy Markaryan 266 with two nuclei, rotating in the opposite direction [36].*

Now it is difficult to judge about a way of evolution of these structures, for example, whether monopole vortices lead to the formation of planets in circumstellar disks, or the formation of stars or clouds in the galactic gas disk? Or, if it could transformed the dipole vortices to well-known double objects, such as double stars, double nuclei in galaxies (as Mrk 266 [36], **Figure 10**), as well as in giant molecular clouds, or a planet with a companion in circumstellar disk, or not? As for dusty protoplanetary disks, long-lived anticyclonic vortical structures can capture the �10 cm to meter-sized particles and grow up them into planetesimals. Let's estimate an order of magnitudes of time (86), and mass (87) for planetesimal formation by Burgers vortex for a model of a disk of radius 30 AU and mass 0*:*5 M<sup>⊙</sup> round a star of solar mass: M ≈ M⊙. Taking R0 ¼ 20 AU we will obtain estimations Ω<sup>0</sup> ≈ 8 � <sup>10</sup>�9s�<sup>1</sup> and <sup>Σ</sup> � 1600 g*=*cm2. For a typical protoplanetary disk at considering distance the vertical scale height is of order H ≈ 108km and sound speed cs ≈ HΩ<sup>0</sup> ≈ 0*:*8 km*=*s. Let the maximum rotation speed of a vortex be �10 m/s at distance r0 <sup>≈</sup> <sup>10</sup>10m from its center, and converging speed of a stream be vr ¼ A � r0 ≈ 5 m*=*s. Then we

ω ≈ 10�<sup>9</sup>

s �1 , A <sup>≈</sup> <sup>5</sup> � <sup>10</sup>�10s

Ω0. The dimensionless parameter α is constant value of an order α �

The condition (85) is carried out with a large supply for protoplanetary disks. The molecular viscosity of gas, estimated by the formula *ν* � λ*cs*, in which λ is the mean free path of molecules, *cs* is the speed of a sound, does not play an appreciable role in processes of a protoplanetary disk. For this reason, the "α-disk" model [29] is used, in which turbulent viscosity is represented by the expression

. The scale of viscous length thus makes L<sup>ν</sup> ≈ 106km, so Burgers vortex of big

sizes cannot be destroyed by viscosity. Keplerian shear length makes Lshear ≈ 6 � 109km. Hence, vortices with the sizes reff < Lshear can have circular form.

Taking ρ ∗ *=*ρ ≈ 10<sup>10</sup> in a midplane of a disk, using in (87) and (86) also the average value for viscosity from stability condition (85), we will receive the

Mp <sup>≈</sup> <sup>10</sup>28g; <sup>τ</sup> � <sup>3</sup> � <sup>10</sup><sup>6</sup>ð Þ <sup>m</sup>*=*<sup>D</sup> yrs*:*

�1 *:*

direction (**Figure 4**)!

*Vortex Dynamics Theories and Applications*

**Figure 10.**

will have

<sup>ν</sup> � <sup>α</sup>csH <sup>≈</sup> <sup>α</sup>H2

estimations:

10�<sup>2</sup>

**38**

Martin G. Abrahamyan Yerevan Haybusak University, Armenia

\*Address all correspondence to: haybusaksci@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
