Vassilios Dallas

Strong polymer-turbulence interactions in viscoelastic turbulent channel flow.

This paper is focused on the fundamental mechanism(s) of viscoelastic turbulence that leads to polymer-induced turbulent drag reduction phenomenon. A great challenge in this problem is the computation of viscoelastic turbulent flows, since the understanding of polymer physics is restricted to mechanical models. An effective state-of-the-art numerical method to solve the governing equation for polymers modeled as nonlinear springs, without using any artificial assumptions as usual, was implemented here on a three-dimensional channel flow geometry. The capability of this algorithm to capture the strong polymer-turbulence dynamical interactions is depicted on the results, which are much closer qualitatively to experimental observations. This allowed a more detailed study of the polymer-turbulence interactions, which yields an enhanced picture on a mechanism resulting from the polymer-turbulence energy transfers.

Rapid growth of cloud droplets by turbulence

Assuming perfect collision efficiency, we demonstrate that turbulence can initiate and sustain the rapid growth of very small water droplets in air even when these droplets are too small to cluster, and even without having to take gravity and small-scale intermittency into account. This is because the range of local Stokes numbers of identical droplets in the turbulent flow field is broad enough even when small-scale intermittency is neglected. This demonstration is given for turbulence which is one order of magnitude less intense than is typical in warm clouds but with a volume fraction which, even though small, is nevertheless large enough for an estimated a priori frequency of collisions to be ten times larger than in warm clouds. However, the time of growth in these conditions turns out to be one order of magnitude smaller than in warm clouds.

Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence

The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlated with regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j. Viscous dissipation (∝S2) as well as Ohmic dissipati...

Stagnation point von Kármán coefficient.

On the basis of various direct numerical simulations (DNS) of turbulent channel flows the following picture is proposed. (i) At a distance y from either wall, the Taylor microscale lambda is proportional to the average distance l(s) between stagnation points of the fluctuating velocity field, i.e., lambda(y)=B(1)l(s)(y) with B(1) constant, for delta(nu) << y < or approximately equal to delta, where the wall unit delta(nu) is defined as the ratio of kinematic viscosity nu to skin friction velocity u(tau) and delta is the channels half-width. (ii) The number density n(s) of stagnation points varies with height according to n(s)=(C(s)/delta(nu)(3))y(+)(-1) where y(+) identical with y/delta(nu) and C(s) is constant in the range delta(nu) << y < or approximately equal to delta. (iii) In that same range, the kinetic energy dissipation rate per unit mass, equals 2/3(E(+)((u(tau)(3)/kappa(s)y) where E(+) is the total kinetic energy per unit mass normalized by u(tau)(2) and kappa(s)=B(1)(2)/C(s) is the stagnation point von Kármán coefficient. (iv) In the limit of exceedingly large Reynolds numbers Re(tau) identical with delta/delta(nu), large enough for the Reynolds stress -(uv) to equal u(tau)(2) in the range delta(nu) << y << delta, and assuming that production of turbulent kinetic energy balances dissipation locally in that range and limit, the mean velocity U(+), normalized by u(tau), obeys (d/dy)U(+) approximately equal to 2/3(E(+)/kappa(s)y) in that same range. (v) It follows that the von Kármán coefficient kappa is a meaningful and well-defined coefficient and the log law holds in turbulent channel/pipe flows only if E(+) is independent of y(+) and Re(tau) in that range, in which case kappa approximately kappa(s). (vi) In support of (d/dy)U(+) approximately equal to 2/3(E(+)/kappa(s)y), DNS data of turbulent channel flows which include the highest currently available values of Re(tau) are best fitted by E(+) approximately equal to 2/3(B(4)y(+)(-2/15)) and (d/dy(+))U(+) approximately equal to (B(4)/kappa(s))y(+)(-1-2/15) with B4 independent of y in delta(nu) << y << delta if the significant departure from -(uv) approximately equal to u(tau)(2) at these Re(tau) values is taken into account.

Forcing-dependent dynamics and emergence of helicity in rotating turbulence

The effects of large scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of numerical simulations, varying systematically the nature of the mechanical force in time. We demonstrate that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relatively to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We find that the nature of the mechanical force in time and the emergence of helicity have direct implications on the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak-wave turbulent conditions.

Statistical Equilibria of Large Scales in Dissipative Hydrodynamic Turbulence.

We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.

Triad interactions and the bidirectional turbulent cascade of magnetic helicity

Using direct numerical simulations we demonstrate that magnetic helicity exhibits a bidirectional turbulent cascade at high but finite magnetic Reynolds numbers. Despite the injection of positive magnetic helicity in the flow, we observe that magnetic helicity of opposite signs is generated between large and small scales. We explain these observations by carrying out an analysis of the magnetohydrodynamic equations reduced to triad interactions using the Fourier helical decomposition. Within this framework, the direct cascade of positive magnetic helicity arises through triad interactions that are associated with small scale dynamo action, while the occurrence of negative magnetic helicity at large scales is explained through triad interactions that are related to stretch-twist-fold dynamics and small scale dynamo action, which compete with the inverse cascade of positive magnetic helicity. Our analytical and numerical results suggest that the direct cascade of magnetic helicity is a finite magnetic Reynolds number

The onset of turbulent rotating dynamos at the low magnetic Prandtl number limit

Rm

Large-scale dynamics of magnetic helicity

effect that will vanish in the limit

Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows

Rm \to \infty