# Lukianov P.V.

# Inertial Stability as a Result of the Relation Between Transport and Relative Fluid Rotations

The aim of the paper is fluid inertial stability nature determination through the representation of potential (non-rotational) motion as the compensation of two rotations, transport one and relative one. Theoretical methods are used. It is based on well-known description of fluid motion as a sum of three types (Cauchy–Helmholz theorem), but uses theoretical mechanics approach. The motion is considered as a sum of transport and relative ones. Thransport angular velocity corresponds to macroscopic motion, while relative one is caused by fluid parcel deformation.

# Compact Turbulent Vortex Generation: Approximate Model for Relatively Large Time Moments

The aim of research is to develop the analytical model capable o approximate description of compact turbulent vortex generation by finite power circulation source for relatively large time moments. The method is based on turbulence gradient Boussinesk model according to which turbulent viscosity coefficient has a constant value.

# Compact spherical vortex model

Spherical vortex with only radial distribution and also to derive self-similar equation for the vortex’s difusion and it’s solution. The investigations are theoretical ones. The obtained results are the following ones. Any of the vortical flows that has zero radial velocity is always helical one. Meridianal and azimuthal velocity components have the same distributions (are invariant). The vorticity field compensation condition for spherical coordinates does not result into vortex compactness as it is for cylindrical vortexes.

# Sound Generation by Helicopter Blade Swept by Subsonic Flux

The article studies the sound characteristics (rotational noise) of the helicopter blade swept by the subsonic flux. To this end, we analyze the existing theoretical models of the rotational noise and determine their differences as well as the limits of their use. We choose the theory of the small disturbances spreading off the thin wing was chosen as a calculation model. Using this model, we solve the problem of the sound generation by the blade of the helicopter rotor. We also study the generated noise level for different thicknesses of the rotor blade.

# Model of the Quasi-Point Vortex

In this paper, we obtain the nonviscous model of compact vortex close to the classical point vortex. The obtained vortex differs from the classical point vortex flow; its azimuthal velocity field is not potential. In addition to the classical flow solution, there is a term that makes the vortex compensated. The overall vorticity in it equals zero. Unlike the classical point vortex, the obtained one is compact and its velocity field meets the non-slip condition at the outer boundary like the (Taylor-Couette) flow between two coaxial cylinders.

# One-dimensional models of compact vortices

The paper presents a non-viscous model of the compact vortex which consists of two domains that have different signs of vorticity. This vortex is compensated: the overall vorticity equals zero in it. The vortex compensation causes compactness of the velocity field. The study further analyzes self-similar solutions of the vortex turbulent diffusion problem that corresponds to high vorticity moments.