A reason has been given for the inverse energy cascade in the two-dimensionalised rapidly rotating 3D incompressible turbulence. For such system, literature shows a possibility of the exponent of wavenumber in the energy spectrum's relation to lie between -2 and -3. We argue the existence of a more strict range of -2 to -7/3 for the exponent in the case of rapidly rotating turbulence which is in accordance with the recent experiments. Also, a rigorous derivation for the two point third order structure function has been provided helping one to argue that even with slow rotation one gets, though dominated, a spectrum with the exponent -2.87, thereby hinting at the initiation of the two-dimensionalisation effect with rotation.
We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in two-dimensional (2D) isotropic homogeneous unforced turbulence. We adopt the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) and show that how the 2D turbulence's results, obtainable using other methods, may be established in a simpler way. Same method is used to calculate some third-order structure functions for quasi-geostrophic (QG) turbulence for the forward cascade of pseudo-potential enstrophy and the inverse energy c…
We analyse the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterised by universal scaling exponents in the inertial range. To elucidate the scaling regimes, we set up a scaling analysis of the 3D Navier-Stokes equation for a rotating fluid that is driven by large-scale external forces. We use scaling arguments to extract the scaling exponents, which characterise the different scaling regimes of the energy spectra. We speculate on the intriguing possibility of two-dimensio…
A form for the two-point third order structure function has been calculated for three dimensional homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalisation of the 3D incompressible turbulence owing to rotation.
We present Direct Numerical Simulations of decaying Magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number. The domain considered is bounded by periodic boundary conditions in the two directions perpendicular to the magnetic field and by two plane Hartmann walls in the third direction. High magnetic fields (Hartmann number of up to 896) are considered thanks to a numerical method based on a spectral code using the eigenvectors of the dissipation operator. It is found that the decay proceeds through two phases: first, energy and integral lengthscales vary rapidly during a two-dime…
We investigate coarsening dynamics in the two-dimensional, incompressible Toner-Tu equation. We show that coarsening proceeds via vortex merger events, and the dynamics crucially depend on the Reynolds number Re. For low Re, the coarsening process has similarities to Ginzburg-Landau dynamics. On the other hand, for high Re, coarsening shows signatures of turbulence. In particular, we show the presence of an enstrophy cascade from the intervortex separation scale to the dissipation scale.
Turbulence in superfluid helium~II is a tangle of quantized vortex lines which interact via the classical Biot-Savart law. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonlocal contributions, we find that in Vinen tangles the motion of vortex lines depends mainly on the local curvature, wherea…
We quantify the scaling of magnetic energy density in the inertial range of solar wind turbulence seen in-situ at 1AU with respect to solar activity. At solar maximum, when the coronal magnetic field is dynamic and topologically complex, we find self-similar scaling in the solar wind, whereas at solar mimimum, when the coronal fields are more ordered, we find multifractality. This quantifies the solar wind signature that is of direct coronal origin, and distinguishes it from that of local MHD turbulence, with quantitative implications for our understanding of coronal heating of the solar wind.
We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that there exists a connection between the patterns in laminar instability and the birth of turbulent spots is strengthened. We examine why the relationship between instability and transition to turbulence is manifest in some cases and appears to be totally absent in others. Novel cellular automaton type simulations of the transition zone are conducted, and the …
We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We choose parameters, e.g., the surface tension, such that we have a droplet of the minority phase moving inside a turbulent background of the majority phase. We characterize the deformation of the droplet and show that it displays multifractal dynamics. The probability distribution functions of the components of the acceleration of the center of mass of the dro…
The title of this paper echoes the title of a paragraph in the famous book by Frisch on classical turbulence. In the relevant chapter, the author discusses the role of the statistical dynamics of vortex filaments in the fascinating problem of turbulence and the possibility of a breakthrough in constructing an advanced theory. This aspect arose due to the large amount of evidence, both experimental and numerical, that the vorticity field in turbulent flows has a pronounced filamentary structure. In fact, there is unquestionably a strong relationship between the dynamics of chaotic vortex filame…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The dynamical evolution of the tracer particles is strongly dominated by the emergence and evolution of coherent structures. For a statistical analysis we focus on the Lagrangian acceleration as a central quantity. For more geometrical aspects we investigate the curvature along the trajectories. We find strong signatures for self-similar universal behavior.
We demonstrate that special correlations in the initial conditions of freely evolving, homogeneous magnetohydrodynamic (MHD) turbulence can lead to the formation of enormous current sheets. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all the non-linear interactions during the formation of turbulence. Even though the largest scale separation has been achieved at this point, these structures are coherent with a size that spans our computational domain dominating the scaling of the energy spectrum, which…
We present a spatio-temporal analysis of a statistically stationary rotating turbulence experiment, aiming to extract a signature of inertial waves, and to determine the scales and frequencies at which they can be detected. The analysis uses two-point spatial correlations of the temporal Fourier transform of velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale. We show that this space-time-dependent anisotropy is well described by th…
As a reduced representation of the nonlinear spectral fluxes of ideal invariants in incompressible magnetohydrodynamics, we construct a gradient-diffusion network model that combines phenomenological considerations and geometrical analysis of the exact nonlinear energy transfer function. The reduced-order representation of the conservative spectral transport of energy and cross-helicity is of port-Hamiltonian form, which highlights the flexibility and modularity of this approach. Numerical experiments with Reynolds numbers up to $~10^6$ yield clear power-law signatures of inertial-range energy…
An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.
Scalings of the streamwise velocity energy spectra in turbulent boundary layers were considered in Part 1. A spectral decomposition analysis provided a means to separate out attached and non-attached eddy contributions and was used to generate three spectral sub-components, one of which is a close representation of the spectral signature induced by self-similar, wall-attached turbulence. Since sub-components of the streamwise turbulence intensity $\overline{u^2}$ follow from an integration of the velocity energy spectra, we here focus on the scaling of the former. Wall-normal profiles and Reyn…
Geophysical flows are often turbulent and subject to rotation. This rotation modifies the structure of turbulence and is thereby expected to sensibly affect its Lagrangian properties. Here, we investigate the relative dispersion and geometry of pairs, triads and tetrads in homogeneous rotating turbulence, by using direct numerical simulations at different rotation rates. Pair dispersion is shown to be faster in the vertical direction (along the rotation axis) than in the horizontal one. At long times, in Taylor's regime, this is due to the slower decorrelation of the vertical velocity componen…
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-simi…
We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model, and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to $2048^2$ points. In all simulations, the Froude number varies between $0.015$ and $0.05$, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, non-l…
Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by self-similar instantonic structures traveling coherently through the inertial range. These solutions might influence the energy transfer and the anomalous scaling properties empirically observed for the forced and viscous models. In this paper we present a study of the instantonic solutions for a set of four shell models of turbulence based on the exact decomposition of the Navier-Stokes equations …
We describe results from particle-in-cell simulations of driven turbulence in collisionless, magnetized, relativistic pair plasma. This physical regime provides a simple setting for investigating the basic properties of kinetic turbulence and is relevant for high-energy astrophysical systems such as pulsar wind nebulae and astrophysical jets. In this paper, we investigate the statistics of turbulent fluctuations in simulations on lattices of up to $1024^3$ cells and containing up to $2 \times 10^{11}$ particles. Due to the absence of a cooling mechanism in our simulations, turbulent energy dis…
A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied to examine how the energy cascade is established and how this event could serve as a new test of LES turbulence models. This vorticity surge event is tied to the formation of the energy cascade in a direct numerical simulation by the traditional signatures of a turbulent energy cascade such as spectra approaching -5/3 and strongly Beltramized vortex tubes. A coherent mechanism is suggested by the nearly simultaneous development of a maximum of the peak vorticity $\|ω\|_\infty$, growth …
