E. Levich

On the helical nature of three-dimensional coherent structures in turbulent flows

Abstract Available experimental data on three-dimensional coherent structures in various turbulent flows are used to demonstrate the helical nature of these structures.

On the role of helical structures in three-dimensional turbulent flow

Abstract Arguments are presented for the existence of helical structures and fluctuations in three-dimensional turbulent flow that may account for the phenomena of intermittency and coherent structures.

Drag reduction in turbulent channel flow by phase randomization

Results of numerical simulations of plane turbulent channel flow are presented in which a forcing is introduced which derives from the randomization of selected Fourier modes. In all cases, the randomization is introduced uniformly throughout the channel. The properties of the resulting turbulence are strongly dependent on both the wave numbers whose phases are randomized and the forcing frequency. Two principal wave‐number bands have been selected. The first includes a selected subset of the largest length scales of the turbulence. Forcing in this band results in a fully sustained maximum mass flux increase above that of normal turbulence of 30%, which translates into a drag reduction of 58%. Many of the statistical properties of the simulated drag‐reduced turbulence generated in this manner are in good qualitative agreement with the statistical properties of turbulence observed in experiments in which drag reduction is achieved through the introduction of small concentrations of long‐chained polymers into the flow. In a second set of simulations, the phases of the intermediate and smallest wavelengths were randomized. Forcing at these scales of motion results in a drag increase. Speculations on the mechanism of the drag reduction by phase randomization are offered.

An experimental study of helicity related properties of a turbulent flow past a grid

Results of direct measurements of helicity density and other velocity derivative related flow properties are reported for a turbulent flow past a grid at Reλ=75. The velocity and vorticity vectors exhibit a tendency to be aligned. The flow is found to lack reflectional symmetry, which is manifested by a nonzero correlation between the velocity and vorticity vector fluctuations and considerable asymmetry in the probability density function of the cosine of the angle between the velocity and vorticity vector fluctuations. This asymmetry, as well as the tendency for alignment, increases for larger values of ‖v‖ ‖ω‖.

On the role of helicity in complex fluid flows

Abstract Results of direct numerical simulations of the Taylor-Green vortex are analysed by conditional sampling. In regions of small energy dissipation, there are tendencies for (1) velocity, u , and vorticity, ω , to be aligned and (2) vorticity and curl of vorticity, ▿ × ω, to be nearly orthogonal. The fields of dissipation, enstrophy, turbulence production, and vortex stretching exhibit a striking similarity in their spatial structure.

Long‐wave instability of periodic flows at large Reynolds numbers

It is shown that simple unidirectional and helical periodic flows are unstable to long‐wave perturbations at large Reynolds numbers. Consideration is given to the cases of periodic flow sustained by an applied force and periodic flow freely decaying owing to viscosity.

Hamiltonian description of ideal MHD revealing new invariants of motion

Abstract A new hamiltonian formulation for the ideal magnetohydrodynamics equations is suggested. The equations yield an infinite set of dynamical invariants. Important applications of these invariants for the theory of turbulence and numerical computations are conjectured.

Helical structures, fractal dimensions and renormalization-group approach in homogeneous turbulence☆

Abstract The concept of helicity-fluctuation hierarchy as generating the fractal structure of turbulence in conjunction with the renormalization-group theory are utilized to renormalize the iterative solution of the Navier-Stokes equation in all orders of perturbation theory. This solution produces the value of the intermittency exponent μ = 0.4 for both the lognormal and the β model of homogeneous turbulence.

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.

Coherence and large fluctuations of helicity in homogeneous turbulence

Abstract The build up of coherent large amplitude helicity fluctuations is detected in numerical experiments on 3-D homogeneous turbulence.