arXiv subjects
Publications and source records attributed to O. G. Chkhetiani.
Both dissipation of helicity and it spectrum we are study on the basis of asymptotic model. Introduction into model dependence of angle between turbulent components vorticity and velocity on the governing parameters leads to the spectra of helicity observed experimentally and obtained by DNS model computations by various authors. At the same time, it settles the problem of helicity dissipation divergence with growing Reynolds number.
The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator product expansion within two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents $ε-η$, where $ε$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2ε}$, and $η$ is related to the correlation time at the wave number $k$ which is scaled as $k^{-2+η}$. The restrictions given by nonzero helicity on the regions with stable fixed points which correspond to the scaling regimes are analyzed in detail. The dependence of the effective diffusivity on the helicity parameter is discussed. The anomalous exponents of the structure functions of the passive scalar field which define their anomalous scaling are calculated and it is shown that although the separate composite operators which define them strongly depend on the helicity parameter the resulting two-loop contributions to the critical dimensions of the structure functions are independent of helicity. Details of calculations are shown.
We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow in the frame of extended Kraichnan model. Turbulent fluctuations of velocity field are assumed to have the Gaussian statistics with zero mean and defined noise with finite time-correlation. Actual calculations have been done up to two-loop approximation in the frame of field-theoretic renormalization group approach. It turned out that space parity violation (helicity) of turbulent environment does not affect anomalous scaling which is peculiar attribute of corresponding model without helicity. However, stability of asymptotic regimes, where anomalous scaling takes place, strongly depends on the amount of helicity. Moreover, helicity gives rise to the turbulent diffusivity, which has been calculated in one-loop approximation.
We analyze the stability of a cylindrical Couette flow under the imposition of a weak axial flow in case of a very short cylinder with a narrow annulus gap. We consider an incompressible viscous fluid which is contained in the narrow gap between two concentric short cylinders, where the inner cylinder rotates with constant angular velocity. The caps of the cylinders have narrow tubes conically tapering to super narrow slits which allow for an axial flow along the surface of the inner cylinder. The approximated solution for the Couette flow for short cylinders was found and used for the stability analysis instead of the exact but bulky solution. The sensitivity of the Couette flow to general small perturbations and to the weak axial flow was studied. We demonstrate that perturbations coming from the axial flow cause the propagation of dispersive waves in the Taylor-Couette flow. The coexistence of a rotation and of an axial flow requires to study in addition to the energy and the angular momentum also the helicity of the flow. The approximated form for the helicity formula in case of short cylinders was derived. We found that the axial flow stabilizes the Taylor - Couette flow. The supercritical flow includes a rich variety of vortical structures including a symmetric pair of Taylor vortices, an anomalous single vortex and quasi periodic oscillating vortices. Pattern formation was studied at large for rated ranges of azimuthal and axial Reynolds numbers. A region where three branches of different states occur was localized. Numerical simulations in 3D and in axisymmetrical case of the model flow are presented, which illustrate the instabilities analyzed.