Generalised Quasilinear Approximation of the Interaction of Convection and Mean Flows in a Thermal Annulus

In this paper, we examine the interaction of convection, rotation and mean flows in a thermal annulus. In this system, mean flows are driven by correlations induced by rotation leading to non-trivial Reynolds stresses. The mean flows act back on the convective turbulence acting as a barrier to transport. For this system, we demonstrate that the generalized quasilinear approximation (Marston et al. 2016 Phys. Rev. Lett.116, 214501. (doi:10.1103/PhysRevLett.116.214501)) may provide a much better approximation to the complicated full nonlinear dynamics than the widely used quasilinear approximation. This result will enable the construction of more accurate statistical theories for the description of geophysical and astrophysical flows

Conformal invariance in two-dimensional turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl

Efficient Mixing at low Reynolds numbers using polymer additives

Mixing in fluids is a rapidly developing field of fluid mechanics \cite{Sreen,Shr,War}, being an important industrial and environmental problem. The mixing of liquids at low Reynolds numbers is usually quite weak in simple flows, and it requires special devices to be efficient. Recently, the problem of mixing was solved analytically for a simple case of random flow, known as the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Here we demonstrate experimentally that very viscous liquids at low Reynolds number, $Re$. Here we show that very viscous liquids containing a small amount of high molecular weight polymers can be mixed quite efficiently at very low Reynolds numbers, for a simple flow in a curved channel. A polymer concentration of only 0.001% suffices. The presence of the polymers leads to an elastic instability \cite{LMS} and to irregular flow \cite{Ours}, with velocity spectra corresponding to the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Our detailed observations of the mixing in this regime enable us to confirm sevearl important theoretical predictions: the probability distributions of the concentration exhibit exponential tails \cite{Fal,Fouxon}, moments of the distribution decay exponentially along the flow \cite{Fouxon}, and the spatial correlation function of concentration decays logarithmically.Comment: 11 pages, 5 figure

Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence

The Rayleigh--Taylor (RT) turbulence is investigated by means of high resolution numerical simulations. The main question addressed here is on whether RT phenomenology can be considered as a manifestation of universality of Navier--Stokes equations with respect to forcing mechanisms. At a theoretical level the situation is far from being firmly established and, indeed, contrasting predictions have been formulated. Our first aim here is to clarify the above controversy through a deep analysis of scaling behavior of relevant statistical observables. The effects of intermittency on the mean field scaling predictions is also discussed.Comment: 4 pages, 5 figure

Macroscopic effects of the spectral structure in turbulent flows

Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure

Energy Transfer and Spectra in Simulations of Two-dimensional Compressible Turbulence

We present results of high-resolution numerical simulations of compressible 2D turbulence forced at intermediate spatial scales with a solenoidal white-in-time external acceleration. A case with an isothermal equation of state, low energy injection rate, and turbulent Mach number $M\approx0.34$ without energy condensate is studied in detail. Analysis of energy spectra and fluxes shows that the classical dual-cascade picture familiar from the incompressible case is substantially modified by compressibility effects. While the small-scale direct enstrophy cascade remains largely intact, a large-scale energy flux loop forms with the direct acoustic energy cascade compensating for the inverse transfer of solenoidal kinetic energy. At small scales, the direct enstrophy and acoustic energy cascades are fully decoupled at small Mach numbers and hence the corresponding spectral energy slopes comply with theoretical predictions, as expected. At large scales, dispersion of acoustic waves on vortices softens the dilatational velocity spectrum, while the pseudo-sound component of the potential energy associated with coherent vortices steepens the potential energy spectrum.Comment: 10 pages, 6 figures. To appear in: Turbulence in Complex Conditions, Proc. Euromech/Ercoftac Colloquium 589, ed. M. Gorokhovski, Springer, 201

Vortices in (2+1)d Conformal Fluids

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational velocities and the temperature. They have a rich space of solutions characterized by the radial energy and angular momentum fluxes. We do a detailed study of the phases in the one-parameter family of solutions with no energy flux. This parameter is the product of the asymptotic vorticity and temperature. When it is large, the radial fluid velocity reaches the speed of light at a finite inner radius. When it is below a critical value, the velocity is everywhere bounded, but at the origin there is a discontinuity. We comment on turbulence, potential gravity duals, non-viscous limits and non-relativistic limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe

Towards DNS of the Ultimate Regime of Rayleigh--B\'enard Convection

In this contribution we have briefly introduced the problem of turbulent thermal convection with a particular look at its transition to the ultimate regime and the resolution requirements needed for the direct numerical simulation of this flow.Comment: 10 pages, 6 figure

Wall roughness induces asymptotic ultimate turbulence

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains a challenge, especially for rotating and thermally driven turbulence. By combining extensive experiments and numerical simulations, here, taking as example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents. If only one of the walls is rough, we reveal that the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is thoroughly eliminated in the boundary layers and we thus achieve asymptotic ultimate turbulence, i.e. the upper limit of transport, whose existence had been predicted by Robert Kraichnan in 1962 (Phys. Fluids {\bf 5}, 1374 (1962)) and in which the scalings laws can be extrapolated to arbitrarily large Reynolds numbers