Curvature of lagrangian trajectories in turbulence

We report measurements of the curvature of Lagrangian trajectories in an intensely turbulent laboratory water flow measured with a high-speed particle-tracking system. The probability density function (PDF) of the instantaneous curvature is shown to have robust power-law tails. We propose a model for the instantaneous curvature PDF, assuming that the acceleration and velocity are uncorrelated Gaussian random variables, and show that our model reproduces the tails of our measured PDFs. We also predict the scaling of the most probable vorticity magnitude in turbulence, assuming Heisenberg-Yaglom scaling. Finally, we average the curvature along trajectories and show that, by removing the effects of large-scale flow reversals, the filtered curvature reveals the turbulent features.     

Persistence problem in two-dimensional fluid turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Λ to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent θ=2.9±0.2.     

Probability distribution functions of derivatives and increments for decaying burgers turbulence

A Lagrangian method is used to show that the power law with a -7/2 exponent in the negative tail of the probability distribution function (PDF) of the velocity gradient and of velocity increments, predicted by E et al. [Phys. Rev. Lett. 78, 1904 (1997)] for forced Burgers turbulence, is also present in the unforced case. The theory is extended to the second-order space derivative whose PDF has power-law tails with exponent -2 at both large positive and negative values and to the time derivatives. PDF's of space and time derivatives have the same (asymptotic) functional forms. This is interpreted in terms of a random Taylor hypothesis.     

Origin of lagrangian intermittency in drift-wave turbulence

The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This exponential distribution is shown to be a robust feature independent of the Reynolds number. For small adiabaticity, algebraic tails are observed, suggesting the strong influence of point-vortex-like dynamics on the acceleration. A causal connection is found between the shape of the probability density function and the autocorrelation of the norm of the acceleration.     

Decay of homogeneous turbulence in three-range models

New models, with energy spectra which consist of three power-law ranges, are suggested to describe the free evolution of homogeneous and isotropic high-Reynolds-number turbulence. By selecting a single number, a characteristic of the energy spectrum in the model, very good agreement with experiments has been achieved for two independently measured parameters. Also, verifiable dependences of turbulence decay features on characteristics of the turbulence generation process are suggested.     

Origin of non-Gaussian statistics in hydrodynamic turbulence

Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.     

Observation of gravity-capillary wave turbulence

We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.     

Observation of wave turbulence in vibrating plates

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small length scales. Here, wave turbulence is observed in experiments on a vibrating plate. The frequency power spectra of the normal velocity of the plate may be rescaled on a single curve, with power-law behaviors that are incompatible with the weak turbulence theory of Düring et al. [Phys. Rev. Lett. 97, 025503 (2006)10.1103/PhysRevLett.97.025503]. Alternative scenarios are suggested to account for this discrepancy -- in particular the occurrence of wave breaking at high frequencies. Finally, the statistics of velocity increments do not display an intermittent behavior.     

Topology of two-dimensional turbulence

Velocity differences in the direct enstrophy cascade of two-dimensional turbulence are correlated with the underlying flow topology. The statistics of the transverse and longitudinal velocity differences are found to be governed by different structures. The wings of the transverse distribution are dominated by strong vortex centers, whereas the tails of the longitudinal differences are dominated by saddles. Viewed in the framework of earlier theoretical work, this result suggests that the transfer of enstrophy to smaller scales is accomplished in regions of the flow dominated by saddles.     

Fluctuations of energy flux in wave turbulence

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.     

Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence

It is well known that atmospheric turbulence causes significant variations of the arrival angle of laser beams used in free-space communications. Usually, angle-of-arrival fluctuations of an optical wave in the plane of the receiver aperture is calculated by Kolmogorov’s power spectral-density model. Unfortunately, recently increasing experimental evidence has shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in some parts of the troposphere and stratosphere. These experiments have prompted investigations of the optical-wave propagation through atmospheric turbulence described by nonclassical power spectra. In this paper, employing a new approach and considering a non-Kolmogorov power spectrum with a generalized power law instead of the constant standard power-law value 11/3 and a generalized amplitude factor instead of the constant value 0.033, we derive the variances of the angle-of-arrival fluctuations of the plane and spherical waves in a weak turbulence for the horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power-law variations on the angle-of-arrival fluctuations. In addition, the outer scale effect is also analyzed.     

Weak turbulence of short equatorial waves

We derive a normal form of nonlinear equations for short equatorial waves considered in the framework of the rotating shallow water model. We show dynamical splitting of equatorial Rossby and inertia-gravity waves. We derive an effective Hamiltonian for the short inertia-gravity waves and consider their kinetics using the weak turbulence approach. Stationary power-law energy spectra are obtained. They have different slopes for eastward and westward propagating waves due to the fact that resonant triads of inertia-gravity waves exist only in specific regions of the phase-space.     

Lens ghost imaging in a non-Kolmogorov slant turbulence atmosphere

Based on the method of computation reference channel and the extended Huygens–Fresnel integral, the model of lens ghost imaging with fully spatially incoherent linear polarization light through a slant turbulent channel has derived. The model shows that the resolution ratio of ghost imaging decreases as the power-law exponent of non-Kolmogorov turbulence increasing or the object location departing from the source. The zenith angle of channel has little influence to the quality of the ghost imaging. The minimum distinguishable centre-separation of double slit decreases as the power-law exponent of non-Kolmogorov turbulence increasing.     

Capillary turbulence at the surface of liquid hydrogen

The results of studying the nonlinear capillary waves at a charged surface of liquid hydrogen are reported. Spectral density is experimentally determined for the surface elevations excited by spectrally narrow low-frequency pumping. It is shown that the spectral density in the range 100 Hz–5 kHz obeys the power-law dependence constω^m (scaling). The m exponent is close to ?3, indicating that the capillary turbulence regime is established.     

Decaying two-dimensional turbulence in a circular container

We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number 5 x 10(4) in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantities. The no-slip wall produces vortices which are injected into the bulk flow and tend to compensate the enstrophy dissipation. The self-organization of the flow is reflected by the transition of the initially Gaussian vorticity probability density function (PDF) towards a distribution with exponential tails. Because of the presence of coherent vortices the pressure PDF become strongly skewed with exponential tails for negative values.     

Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack Hartmann wave-front sensor

For non-Kolmogorov turbulence we develop a differential angle-of-arrival fluctuation coefficient, which is the ratio between the transverse and longitudinal differential angle-of-arrival variances, and a slope structure-correlation coefficient, which is the ratio between the transverse and longitudinal differences of the slope correlation function and the slope structure function, to measure the power-law exponent of a phase power spectrum with a Shack-Hartmann wave-front sensor: The differential arrival-of-angle fluctuation coefficient and the slope structure-correlation coefficient are both related to power-law exponent beta and are independent of strength parameter rho(0) of the turbulence. We compare the methods developed and use them to evaluate beta in recently completed horizontal atmospheric experiments for 1000-m laser beam propagation.     

Universality of velocity gradients in forced Burgers turbulence

We demonstrate that Burgers turbulence subject to large-scale white-noise-in-time random forcing has a universal power-law tail with exponent -7/2 in the probability density function of negative velocity gradients, as predicted by E, Khanin, Mazel, and Sinai [Phys. Rev. Lett. 78, 1904 (1997)]. A particle and shock tracking numerical method gives about five decades of scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of the unstable manifold associated to the global minimizer.     

Dynamical evolution of coherent structures in intermittenttwo-dimensional MHD turbulence

Recent satellite observations indicate that the Earth's magnetotail is generally in a state of intermittent turbulence. A model of sporadic localized merging of coherent structures has recently been proposed by Chang to describe the dynamics of the Earth's magnetotail. The authors report the results of MHD simulations regarding the development and merging of two dimensional coherent structures. With a magnetic shear, such coherent structures are generated in alignment with the imposed current sheet. The calculated fluctuation spectra suggest long-ranged correlations with power-law characteristics     

Lagrangian dynamics of drift-wave turbulence

The statistical properties of Lagrangian particle transport are investigated in dissipative drift-wave turbulence modelled by the Hasegawa-Wakatani system. By varying the adiabaticity parameter c, the flow regime can be modified from a hydrodynamic limit for c=0 to a geostrophic limit for c→∞. For c of order unity the quasi-adiabatic regime is obtained, which might be relevant to describe the edge turbulence of fusion plasmas in tokamaks. This particularity of the model allows one to study the change in dynamics when varying from one turbulent flow regime to another. By means of direct numerical simulation we consider four values for c and show that the Lagrangian dynamics is most intermittent in the hydrodynamic regime, while the other regimes are not or only weakly intermittent. In both quasi-adiabatic and quasi-geostrophic regimes the PDFs of acceleration exhibit exponential tails. This behaviour is due to the pressure term in the acceleration and not a signature of intermittency.     

Coexistence of self-organized criticality and intermittent turbulence in the solar corona

An extended data set of extreme ultraviolet images of the solar corona provided by the SOHO spacecraft is analyzed using statistical methods common to studies of self-organized criticality (SOC) and intermittent turbulence (IT). The data exhibit simultaneous hallmarks of both regimes: namely, power-law avalanche statistics as well as multiscaling of structure functions for spatial activity. This implies that both SOC and IT may be manifestations of a single complex dynamical process entangling avalanches of magnetic energy dissipation with turbulent particle flows.