Spectral condensation of turbulence in plasmas and fluids and its role in low-to-high phase transitions in toroidal plasma

Geometric frustration induces the transition between rotation and counterrotation in swirled granular media

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: At low densities, the particle cluster rotates in the same direction as the swirling motion of the container, while at high densities it rotates in the opposite direction. We investigate this phenomenon experimentally and numerically using a corotating reference frame in which the system reaches a statistical steady state. In this steady state, the particles form a cluster whose translational degrees of freedom are stationary, while the individual particles constantly circulate around the cluster's center of mass, similar to a ball rolling along the wall within a rotating drum. We show that the transition to counterrotation is friction dependent. At high particle densities, frictional effects result in geometric frustration, which prevents particles from cooperatively rolling and spinning. Consequently, the particle cluster rolls like a rigid body with no-slip conditions on the container wall, which necessarily counterrotates around its own axis. Numerical simulations verify that both wall-disk friction and disk-disk friction are critical for inducing counterrotation.

Inverse cascade of the vortical structures near the contact line of evaporating sessile droplets

Microscopic imaging as well as the particle image velocimetry (PIV) are carried out to evaluate the concentration, velocity and vorticity fields near the contact line of the nano-particles-laden evaporating sessile droplets. After the onset of the linear thermocapillary instabilities due to the Marangoni perturbations, the non-linear state sets in and the micro-scale jet-like vortex structures are ejected from the contact line towards the center of the droplet. Afterwards, the jet-like vortical structures expand in the spanwise directions and start to interact with the neighbouring structures. Two types of the inverse cascade mechanisms are found to occur. In the first kind, the vortices of the similar length scale merge and continuously produce larger vortices and corresponding wavelength growth. The second inverse cascade mechanism takes place due to the entrainment of the smaller vortices into the larger structures. Both inverse cascade processes are identified as the continuous feeding of the kinetic energy from the smaller scales to the larger scales. For individual micro-jets the velocity field characterizes the jet-like vortex structures ejected from the contact line towards the droplet center opposing the bulk flow from the center towards the contact line. In addition, the vorticity field overlaid by the velocity streamlines identify the sense of rotation of the low pressure zones on either side of the micro-jet as well as the high pressure stagnation point at the tip.

Dynamics of reversals and condensates in two-dimensional Kolmogorov flows

We present numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large-scale drag with a dimensionless damping rate 1/Rh. The linear response to the forcing is a 6×6 square array of counterrotating vortices, which is stable when the Reynolds number Re or Rh are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when Re and Rh are increased, we study the transitions between the different turbulent regimes observed for large Re by varying Rh. A large-scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large-scale drag (Rh large). When Rh is decreased, the condensate becomes unstable and a regime with random reversals between two large-scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large-scale velocity that continuously bifurcates to a Gaussian distribution when Rh is decreased further.

Characteristics of two-dimensional quantum turbulence in a compressible superfluid

Fluids subjected to suitable forcing will exhibit turbulence, with characteristics strongly affected by the fluid's physical properties and dimensionality. In this work, we explore two-dimensional (2D) quantum turbulence in an oblate Bose-Einstein condensate confined to an annular trapping potential. Experimentally, we find conditions for which small-scale stirring of the condensate generates disordered 2D vortex distributions that dissipatively evolve toward persistent currents, indicating energy transport from small to large length scales. Simulations of the experiment reveal spontaneous clustering of same-circulation vortices and an incompressible energy spectrum with k(-5/3) dependence for low wave numbers k. This work links experimentally observed vortex dynamics with signatures of 2D turbulence in a compressible superfluid.

Inverse energy cascade and turbulent transport in a quasi-two-dimensional magnetized electrolyte system: an experimental study

We present an experimental study of the inverse energy cascade, spectral condensation, and turbulent particle transport in an electromagnetically driven thin layer of NaCl electrolyte. The presence of the bottom friction provides an energy sink at large scales for the turbulent flow. This energy sink crucially contributes to the balance of the forcing and dissipation which makes the inverse cascade steady. The present work provides an estimation of the linear dissipation rate on an experimental basis. We also show how the dissipation rate affects the characteristic features of the velocity spectrum and the dynamics of the spectral condensation. A quantitative study of the turbulent diffusion shows a significant decrease of the radial transport during the spectral condensation process.

Long-range correlations induced by the self-regulation of zonal flows and drift-wave turbulence

By means of a unique probe array, the interaction between zonal flows and broad-band drift-wave turbulence has been investigated experimentally in a magnetized toroidal plasma. Homogeneous potential fluctuations on a magnetic flux surface, previously reported as long range correlations, could be traced back to a predator-prey-like interaction between the turbulence and the zonal flow. At higher frequency the nonlocal transfer of energy to the zonal flow is dominant and the low-frequency oscillations are shown to result from the reduced turbulence activity due to this energy loss. This self-regulation process turns out to be enhanced with increased background shear flows.

Scaling and asymmetry in an electromagnetically forced dipolar flow structure

A dipolar flow structure is experimentally studied in a layer of salt solution driven by time-independent electromagnetic forcing. In particular, the response of the flow to the forcing is quantified by measuring the Reynolds number Re as a function of the Chandrasekhar number Ch (the ratio of Lorentz forces to viscous forces) and δ (the ratio of vertical to horizontal length scales of the flow domain). In agreement with theoretical predictions, two scaling regimes are found: Re~Ch/π(2) (viscous regime) and Re~Ch(1/2)δ(-1) (advective regime). The transition between the two regimes at Ch(1/2)δ~π(2) is reflected in the flow geometry in the form of an asymmetry of the dipolar flow structure.

Turbulence decay rate as a measure of flow dimensionality

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite-depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes the deviation of damping from the one derived using a quasi-two-dimensional model, can be used as a measure of the flow dimensionality. Experiments in turbulent layers show that when the anomaly coefficient becomes high, the turbulent inverse energy cascade is suppressed. In the opposite limit turbulence can self-organize into a coherent flow.

Universal velocity profile for coherent vortices in two-dimensional turbulence

Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the eta=1/4 scaling in the V is proportional to r(-eta) law of the velocity spatial profile within a vortex, where r is the distance from the vortex center. This scaling, consistent with earlier numerical and laboratory measurements, is universal in its independence of details of the small-scale injection of turbulent fluctuations and details of the shape of the box.

Turbulence-condensate interaction in two dimensions

We present experimental results on turbulence generated in thin fluid layers in the presence of a large-scale coherent flow, or a spectral condensate. It is shown that the condensate modifies the third-order velocity moment in a much wider interval of scales than the second one. The modification may include the change of sign of the third moment in the inverse cascade. This observation may help resolve a controversy on the energy flux in mesoscale atmospheric turbulence (10-500 km): to recover a correct energy flux from the third velocity moment one needs first to subtract the coherent flow. We find that the condensate also increases the velocity flatness.

Suppression of turbulence by self-generated and imposed mean flows

The first direct experimental evidence of the suppression of quasi-two-dimensional turbulence by mean flows is presented. The flow either is induced externally or appears in the process of spectral condensation due to an inverse cascade in bounded turbulence. The observed suppression of large scales is consistent with an expected reduction in the correlation time of turbulent eddies due to shearing. At high flow velocities, sweeping of the forcing-scale vortices reduces the energy input, leading to a reduction in the turbulence level.

Dynamics of energy condensation in two-dimensional turbulence

We report a numerical study, supplemented by phenomenological explanations, of "energy condensation" in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to the emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard k{-5/3} one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to k{-1}. The fluctuations decay slowly as the coherent part grows.

Strong ExB shear flows in the transport-barrier region in H-mode plasma

We report the first experimental observation of stationary zonal flow in the transport-barrier region of the H-mode plasma. Strong peaks in Er shear mark the width of this region. A strong m = n = 0 low-frequency (f < 0.6 kHz) zonal flow is observed in regions of increased Er, suggesting a substantial contribution of zonal flow to the spatial modulation of Er radial profiles. Radial localization of the zonal flow is correlated with a region of zero magnetic shear and low-order (7/5) rational surfaces.

Observation of turbulent-driven shear flow in a cylindrical laboratory plasma device

An azimuthally symmetric radially sheared plasma fluid flow is observed to spontaneously form in a cylindrical magnetized helicon plasma device with no external sources of momentum input. A turbulent momentum conservation analysis shows that this shear flow is sustained by the Reynolds stress generated by collisional drift turbulence in the device. The results provide direct experimental support for the basic theoretical picture of drift-wave-shear-flow interactions.