We present the results of photometric observations of three TeV blazars, 3C 66A, S5 0954+658 and BL Lacertae, during the period 2013-2017. Our extensive observations were performed in a total of 360 nights which produced ∼6820 image frames in BVRI bands. We study flux and spectral variability of these blazars on these lengthy timescales. We also examine the optical Spectral Energy Distributions of these blazars, which are crucial in understanding the emission mechanism of long-term variability in blazars. All three TeV blazars exhibited strong flux variability during our observations. The colour variations are mildly chromatic on long timescales for two of them. The nature of the long-term variability of 3C 66A and S5 0954+658 is consistent with a model of a non-thermal variable component that has a continuous injection of relativistic electrons with power law distributions around 4.3 and 4.6, respectively. However, the long-term flux and colour variability of BL Lac suggests that these can arise from modest changes in velocities or viewing angle toward the emission region, leading to variations in the Doppler boosting of the radiation by a factor ∼ 1.2 over the period of these observations.

The present investigation is devoted to the revealing of the physical essence of the action of the rigid boundary on the linear dynamics of perturbations in plane shear flows. \emph{A new mathematical approach is proposed which accurately and completely replaces the horizontal rigid boundary by the actions of certain localized sources placed on the plane of the boundary ($z = 0$) in the original/canonical shear flow dynamical equations for wave and vortex mode perturbations}, i.e., for perturbations with zero and nonzero potential vorticity (PV). The approach is elaborated on the example of the well-known problem of geophysical hydrodynamics -- the linear dynamics of perturbations in semi-infinite ($z \geq 0$) flow of stratified rotating fluid with a vertical shear of velocity, ${\textbf{U}}_0(Az,0,0)$, zero beta, $\beta=0$, and horizontal rigid boundary at $z = 0$ -- which analytical wave and vortex mode solutions are well-known and serve as the reference solutions of our model equations. From the beginning, we have replaced the rigid boundary with localized sources for vortices and wave modes separately. The sources are the sum of the delta function and its first derivative the coefficients in front of which were unknown at this stage. In what follows, we accurately calculated these coefficients and thus determined the exact expressions for localized sources. Subsequent mathematical analysis showed that the localized sources give rise to new perturbations which can be labeled as secondary. The revealed physical essence of the action of the rigid boundary is as follows: being the external (localized) source of the analyzed open complex flow system, the rigid boundary puts an additional energy into perturbation harmonics that becomes an important power supplier supporting the linear dynamics of the system under study.

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ABSTRACT.The simplest case of the nonlinear turbulent dynamo mechanism is proposed. It is shown that under certain conditions the generated mean magnetic field can become stronger than the small-scale one. Some manifestations (the model of Cyg X-l bimodal behaviour, asymmetric accretion onto the magnetized rotating compact star) of this mean field are discussed.It can be considered that the existence of mean magnetic fields in the majority of astrophysical objects is determined by the turbulent dynamo action where the field generation sources are the differential rotation of the medium and the gyrotropic character of the turbulence (Moffatt, 1978;Weinstein et al., 1980). In the accretion disks the convective turbulence is small-scaled (£ z « 0.1 Z 0 ) (Chagelishvili and Lominadze, 1984), and this fact, at the Kepler rotation, leads to the anomalous large values of dynamo number (D), the only parameter determining the mean field growth rate in the turbulent dynamo linear theory in αω approximation. The accretion time is long (Shakura and Sunyaev, 1973), anyway it is much longer than the mean field growth time. That is why the generated mean magnetic fields are capable to grow up to the maximum possible values. The determination of these values and the magnetic field structure requires the help of the strongly nonlinear theory where, in the simplest case, two more parameters -I and Ê 0 -appear (É 0 = (Β θΓ ,Β 0 φ,Β ΟΖ ) determines the value and structure of seed average magnetic field, and ξ the order of mean field influence on the average turbulent helicity). The three parameters D, £ and B 0 are of equal importance.Considering the convectively active geometrically thin disk (z 0 « r where z 0 is the disk half-width and r the distance from the considered region up to the disk centre), we can write down the turbulent dynamo nonlinear equations in αω approximation (in the one-dimensional case)