Leonid Shtilman

The dynamics of helical decaying turbulence

The dynamics of helical decaying homogeneous turbulence is investigated in direct numerical simulations at moderate Reynolds numbers. A new initialization procedure is presented that allows one to control both the energy and the helicity spectral density of the initial flow field. It is observed that large initial helicity impedes the transfer of energy toward smaller scales, inhibits the buildup of enstrophy, and reduces dissipation for several turnover times. Also, the skewness and flatness of the velocity derivatives reach values typical of turbulence much later than in comparable flows without helicity. However, these effects are significant only if the helicity of the flow is quite high. In simulations with small or vanishing initial helicity it is found that the fluctuations of the average helicity and the helicity spectral density lie within the range suggested by a quasi‐Gaussian approximation. This suggests that at moderate Reynolds number spontaneous fluctuations of helicity are not large enough...

The helical nature of unforced turbulent flows

Results of direct numerical simulations of the decay of nearly isotropic turbulence exhibit clearly that much of the flow evolves in orientation to a state in which the vorticity vector is nearly aligned with the velocity vector.

On the mechanism of the reduction of nonlinearity in the incompressible Navier-Stokes equation

The mechanism of the reduction of nonlinearity recently observed in simulations of decaying isotropic turbulence by Kraichnan and Panda [Phys. Fluids 31, 2395 (1988)] is investigated. It is shown that although the alignment of velocity and vorticity in physical space is not the sole source of the effect, it can enhance the effect significantly. Another source of the reduction seems to be a tendency of the Lamb vector v×ω in Fourier space to align with the wave vector k. The ordering of the energy transfer is suggested to be a dynamically generic effect driving the reduction.

On depression of nonlinearity in turbulence

A comparison is made of the behavior of nonlinearities in regions dominated by enstrophy and strain. It is shown that nonlinear processes like enstrophy production (and many others) are strongly depressed in regions dominated by enstrophy as compared to those dominated by strain.

Nonlinear waves and turbulence in Marangoni convection

In the paper we present a numerical study of a new type of nonlinear waves in Marangoni convection. The waves are caused by nonlinear interaction between long‐scale deformational instability and short‐scale convection. It is shown that, due to a nonlinear coupling with the deformation of the free liquid–gas interface, the primary convection pattern can undergo oscillatory instability generating various kinds of long surface waves which modulate the short‐scale convection. The numerical analysis of the system of nonlinear coupled equations describing these waves confirms the predictions of weakly nonlinear analysis and shows the existence of either standing or travelling waves in the proper parametric regions, at low supercriticality. With increasing supercriticality, the waves undergo various transformations leading to the formation of pulsating travelling waves, aharmonic standing waves as well as irregular wavy behavior resembling ‘‘interfacial turbulence.’’ We map regions in the parameter space where v...

Numerical investigation of helicity in turbulent flow

Abstract Results of direct numerical simulations of decaying, nearly isotropic turbulence are presented. The angular orientation between vorticity and velocity evolves from a state that is initially random to one in which there is a higher probability of vector alignment. Total helicity evolves in a quantitatively different manner than the energy or ensotrophy, reflecting changes of flow topology. From a random, initially zero-helicity field it is seen that viscosity can be a source of spontaneous helicity generation and reflexional symmetry breaking.

Reducing turbulence by phase juggling

The dynamics of decaying turbulence disturbed at small and intermediate scales by energy‐conserving disturbances is investigated in direct numerical simulations at relatively low Reynolds number (Rλ≊20–30). Three types of disturbances are introduced. The reduction of the energy dissipation and related enstrophy growth is achieved by partial destruction of phase coherence ostensibly presented at almost all scales of turbulence. The disturbance preserving both energy and helicity spectrum has been found a most destructive one. Possible implications of the results for anisotropic turbulence is briefly discussed.

A parallel Navier-Stokes solver: the Meiko implementation

A mixed spectral element, pseudospectral, and finite-difference scheme for solving the Navier-Stokes equations is implemented on a Meiko parallel supercomputer. The code for the solution of Navier-Stokes equations for jetlike flows is implemented with a spectral scheme in cross-flow directions, a spectral element scheme in the stream-wise direction, and finite-difference marching in time. Several strategies for distributing the workload onto the processors are discussed. Special attention is paid to using the flexible topology of the Meiko.

On the solenoidality of the Lamb vector

The correlation between reduction of the nonlinearity and other characteristic quantities of turbulent flow is investigated numerically. It is shown in physical space that in the regions exhibiting strong depletion of nonlinearity, the enstrophy and the enstrophy production are large. In the same regions vorticity has a tendency to be perpendicular to the eigenvector of rate of strain corresponding to the smallest eigenvalue. No correlation has been found between reduction of nonlinearity and dissipation.

ON STABILITY OF FLOW IN AN ANNULAR CHANNEL

Linear and nonlinear stability of a flow between the walls of two coaxial cylinders has been investigated. The linear analysis has been carried out within the framework of the temporal linear stability theory. The eigenvalue map has been obtained using the collocation method based on Chebyshev polynomials. The nonlinear analysis is based on a novel parallel code for DNS (direct numerical simulations) of a coaxial pipe flow with periodic boundary conditions in the streamwise direction. It is shown that the major source of finite amplitude instability is associated with the interaction of three-dimensional disturbances and streamwise rolls.