Hilbert statistics of vorticity scaling in two-dimensional turbulence

  title={Hilbert statistics of vorticity scaling in two-dimensional turbulence},
  author={H. S. Tan and Y. X. Huang and Jianping Meng},
  journal={Physics of Fluids},
In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed ω(x, y) in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang transform, to a vorticity field obtained from a 81922 grid-points direct numerical simulation of the 2D turbulence with a forcing scale k f = 100 and an Ekman friction. The measured joint probability density function p(C, k) of mode C i (x) of… 

Two-scale correlation and energy cascade in three-dimensional turbulent flows

In this paper, we propose a high-order harmonic-free methodology, namely arbitrary-order Hilbert spectral analysis, to estimate the two-scale correlation (TSC). When applied to fully developed

Intermittency measurement in two-dimensional bacterial turbulence.

An experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system by performing a Hilbert-based methodology analysis.

Cascade and intermittency of the sea surface temperature in the oceanic system

In this paper, we analyze the sea surface temperature obtained from the global drifter program. The experimental Fourier power spectrum shows a two-decade power-law behavior as Eθ(f) ∝ f−7/3 in the

Detrended structure-function in fully developed turbulence

The classical structure-function (SF) method in fully developed turbulence or for scaling processes in general is influenced by large-scale energetic structures, known as the infrared effect.

Wind turbine wake intermittency dependence on turbulence intensity and pitch motion

Turbulence intermittency characteristics of the flow behind pitching and fixed wind turbines are assessed via hot-wire anemometry in a wind tunnel experiment. The pitching wind turbine model is free

Multi-level segment analysis: definition and application in turbulent systems

For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale

Stochastic Analysis of Scaling Time Series: From Turbulence Theory to Applications

This book presents the mathematical theory behind the stochastic analysis of scaling time series, including a general historical introduction to the problem of intermittency in turbulence, as well as how to implement this analysis for a range of different applications.



Intermittency in two-dimensional turbulence with drag.

This work considers the enstrophy cascade in forced two-dimensional turbulence with a linear drag force, and obtains and compares theoretically and numerically derived results for the dependence on separation r of the probability distribution of delta(r)omega, the difference between the vorticity at two points separated by a distance r.

Vorticity statistics in the direct cascade of two-dimensional turbulence.

For the direct cascade of steady two-dimensional Navier-Stokes turbulence, the probability of strong vorticity fluctuations is derived analytically and is presented as a function of a single argument, ϖ/ϖ(rms), in distinction from other known direct cascades.

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

It is shown that high-order moment scaling exponents of the Lagrangian structure function exponents have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process.

Inertial Ranges in Two‐Dimensional Turbulence

Two‐dimensional turbulence has both kinetic energy and mean‐square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k)∼e2/3k−5/3 and E(k)∼η2/3k−3, where

Identifying turbulent energy distributions in real, rather than fourier, space.

This Letter determines the form of the signature function, which plays the role of an energy density, somewhat analogous to E(k), and finds that dissipation-range phenomena, such as the so-called bottleneck effect, are evident in the Signature function, while absent in the structure function.

Physical mechanism of the two-dimensional enstrophy cascade.

This work investigates the basic mechanism by numerical simulation of the forced Navier-Stokes equation and obtains the probability distributions of the local enstrophy flux and of the alignment angle between vorticity gradient and transport vector, which are surprisingly symmetric.

Universal direct cascade in two-dimensional turbulence.

  • FalkovichLebedev
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
The form of those correlation functions is universal, i.e., independent of the pumping, and a set of integrodifferential equations is established which gives a logarithmic renormalization of the vorticity correlation functions in the inertial interval.

Vorticity Statistics in the Two-Dimensional Enstrophy Cascade

We report the first extensive experimental observation of the two-dimensional enstrophy cascade, along with the determination of the high order vorticity statistics. The energy spectra we obtain are

Second-order structure function in fully developed turbulence.

An analysis of passive scalar (temperature) turbulence time series is presented to show the influence of large-scale structures in real turbulence and the efficiency of the Hilbert-based methodology, and corresponding scaling exponents ζ(θ)(q) provided by the Hilbert -based approach indicate that the Passive scalar turbulence field may be less intermittent than what was previously believed.