On the strength of the nonlinearity in isotropic turbulence

Turbulence governed by the Navier-Stokes equations shows a tendency to evolve towards a state in which the nonlinearity is diminished. In fully developed turbulence this tendency can be measured by comparing the variance of the nonlinear term to the variance of the same quantity measured in a Gaussian field with the same energy distribution. In order to study this phenomenon at high Reynolds numbers, a version of the Direct Interaction Approximation is used to obtain a closed expression for the statistical average of the mean-square nonlinearity. The wavenumber spectrum of the mean-square nonlinear term is evaluated and its scaling in the inertial range is investigated as a function of the Reynolds number. Its scaling is dominated by the sweeping by the energetic scales, but this sweeping is weaker than predicted by a random sweeping estimate. At inertial range scales, the depletion of nonlinearity as a function of the wavenumber is observed to be constant. At large it is observed that the mean-square nonlinearity is larger than its Gaussian estimate, which is shown to be related to the non-Gaussianity of the Reynolds-stress fluctuations at these scales.Comment: Accepted for publication in J. Fluid Mec

On the scaling of temperature fluctuations induced by frictional heating

The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results. The study shows that previously proposed models underpredict the variance of frictional temperature fluctuations by a factor proportional to the square of the Taylor-scale Reynolds number

Self-organization and symmetry-breaking in two-dimensional plasma turbulence

The spontaneous self-organization of two-dimensional magnetized plasma is investigated within the framework of magnetohydrodynamics with a particular emphasis on the symmetry-breaking induced by the shape of the confining boundaries. This symmetry-breaking is quantified by the angular momentum, which is shown to be generated rapidly and spontaneously from initial conditions free from angular momentum as soon as the geometry lacks axisymmetry. This effect is illustrated by considering circular, square, and elliptical boundaries. It is shown that the generation of angular momentum in nonaxisymmetric geometries can be enhanced by increasing the magnetic pressure. The effect becomes stronger at higher Reynolds numbers. The generation of magnetic angular momentum (or angular field), previously observed at low Reynolds numbers, becomes weaker at larger Reynolds numbers

Turbulence and turbulent pattern formation in a minimal model for active fluids

Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the active turbulence phase calls for a statistical description. Borrowing techniques from turbulence theory, we here establish a quantitative description of correlation functions and spectra of a minimal continuum model for active turbulence. Further exploring the parameter space, we also report on a surprising type of turbulence-driven pattern formation far beyond linear onset: the emergence of a dynamic hexagonal vortex lattice state after an extended turbulent transient, which can only be explained taking into account turbulent energy transfer across scales.Comment: Supplemental videos available at https://youtu.be/gbf6cRho03w https://youtu.be/n0qUUhAUJFQ https://youtu.be/LGmamkM012

Iridium oxide as actuator material for the ISFET-based sensor-actuator system

Acid or base concentrations can be determined by performing an acid-base titration with Coulometrically generated OH- or H+ ions at a noble-metal actuator electrode in close proximity to the pH-sensitive gate of an ISFET. The ISFET is used as the indicator electrode to detect the equivalence point in the titration curve. The potential of the actuator electrode during the generation of the titrant is relatively high for the anodic water electrolysis (or relatively low for the cathodic reaction). Consequently other redox couples which are possibly present in the sample solution can interfere with the water electrolysis. This reduces the efficiency of the current to titrant generation on which this measurement relies. To overcome this problem, iridium oxide has been used as a new electroactive material for the actuator electrode. The reversible redox reaction in this metal oxide occurs at a favourable potential and is attended by the exclusive uptake or release of protons, making a titration possible. It is shown that a Coulometric titration in the presence of Cl¿ ions, formerly not possible with the noble-metal actuator electrode because of the redox interference, can now successfully be carried out with iridium oxide as the actuator material. Calculations show that the ISFET pH-sensor is well suited to determining accurately the equivalence point in the steep part of the titration curve, because of its short response time

Depletion of nonlinearity in two-dimensional turbulence

The strength of the nonlinearity is measured in decaying two-dimensional turbulence, by comparing its value to that found in a Gaussian field. It is shown how the nonlinearity drops following a two-step process. First a fast relaxation is observed on a timescale comparable to the time of for-mation of vortical structures, then at long times the nonlinearity relaxes further during the phase when the eddies merge to form the final dynamic state of decay. Both processes seem roughly independent of the value of the Reynolds number

Extreme Lagrangian acceleration in confined turbulent flow

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer, is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20