On the energy spectrum of the 3D velocity field, generated by an ensemble of vortex loops

Abstract Energy spectrum of turbulent fluids exhibit a bump at an intermediate wavenumber, between the inertial and the dissipation range. This bump is called bottleneck. Such bottlenecks are also seen in the energy spectrum of the solutions of hyperviscous Burgers equation. Previous work have shown that this bump corresponds to oscillations in real space velocity field. In this paper, we present numerical and analytical results of how the bottleneck and its real space signature, the oscillations, grow as we tune the order of hyperviscosity. We look at a parameter regime α ∈ [1, 2] where α = 1 corresponds to normal viscosity and α = 2 corresponds to hyperviscosity of order 2. We show that even for the slightest fractional increment in the order of hyperviscosity (α) bottlenecks show up in the energy spectrum. Graphical abstract

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OBSERVATION OF NEARSHORE CURRENT AND EDGE WAVES

Coastal Engineering Proceedings ◽

10.9753/icce.v16.45 ◽

1978 ◽

Vol 1 (16) ◽

pp. 45 ◽

Cited By ~ 2

Author(s):

Tamio O. Sasaki ◽

Kiyoshi Horikawa

Keyword(s):

Energy Spectrum ◽

Velocity Field ◽

Conceptual Models ◽

Edge Waves ◽

Nearshore Zone ◽

Nodal Lines ◽

Spatial Velocity ◽

Sloping Beach

Nodal lines normal to the shoreline of infragravity low mode edge waves in the nearshore zone were observed with eleven wave staffs simultaneously with the nearshore current spatial velocity field on a gently sloping beach. About five peaks were found in the energy spectrum and their frequencies agreed well with cut-off mode edge waves [Huntley(1976)]. Based on the above observation, conceptual models of nearshore current patterns for the infragravity domain are proposed and general current patterns for the three domains are discussed by combining the horizontal patterns of Harris(1969) and the vertical patterns of Sasaki et al.(1976).

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Energy Spectrum of the 3D Velocity Field, Induced by Vortex Tangle

Journal of Low Temperature Physics ◽

10.1007/s10909-012-0791-4 ◽

2012 ◽

Vol 171 (5-6) ◽

pp. 504-510 ◽

Cited By ~ 16

Author(s):

Sergey K. Nemirovskii

Keyword(s):

Energy Spectrum ◽

Velocity Field ◽

Vortex Tangle

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Wavelet-spectral analysis of droplet-laden isotropic turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.515 ◽

2019 ◽

Vol 875 ◽

pp. 914-928 ◽

Cited By ~ 2

Author(s):

Andreas Freund ◽

Antonino Ferrante

Keyword(s):

Fourier Transform ◽

Energy Spectrum ◽

Velocity Field ◽

Turbulent Flows ◽

Carrier Phase ◽

Single Phase ◽

Spatial Information ◽

Isotropic Turbulence ◽

Wavelet Energy ◽

High Wavenumbers

The spectrum of turbulence kinetic energy for homogeneous turbulence is generally computed using the Fourier transform of the velocity field from physical three-dimensional space to wavenumber $k$. This analysis works well for single-phase homogeneous turbulent flows. In the case of multiphase turbulent flows, instead, the velocity field is non-smooth at the interface between the carrier fluid and the dispersed phase; thus, the energy spectra computed via Fourier transform exhibit spurious oscillations at high wavenumbers. An alternative definition of the spectrum uses the wavelet transform, which can handle discontinuities locally without affecting the entire spectrum while additionally preserving spatial information about the field. In this work, we propose using the wavelet energy spectrum to study multiphase turbulent flows. Also, we propose a new decomposition of the wavelet energy spectrum into three contributions corresponding to the carrier phase, droplets and interaction between the two. Lastly, we apply the new wavelet-decomposition tools in analysing the direct numerical simulation data of droplet-laden decaying isotropic turbulence (in absence of gravity) of Dodd & Ferrante (J. Fluid Mech., vol. 806, 2016, pp. 356–412). Our results show that, in comparison to the spectrum of the single-phase case, the droplets (i) do not affect the carrier-phase energy spectrum at high wavenumbers ($k_{m}/k_{min}\geqslant 128$), (ii) increase the energy spectrum at high wavenumbers ($k_{m}/k_{min}\geqslant 256$) by increasing the interaction energy spectrum at these wavenumbers and (iii) decrease the energy at low wavenumbers ($k_{m}/k_{min}\leqslant 16$) by increasing the dissipation rate at these wavenumbers.

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The Cameron—Martin—Wiener method in turbulence and in Burgers’ model: general formulae, and application to late decay

Journal of Fluid Mechanics ◽

10.1017/s0022112070000770 ◽

1970 ◽

Vol 41 (3) ◽

pp. 593-618 ◽

Cited By ~ 10

Author(s):

W-H. Kahng ◽

A. Siegel

Keyword(s):

Energy Spectrum ◽

Velocity Field ◽

Equations Of Motion ◽

Navier Stokes Equation ◽

Hermite Expansion ◽

Burgers Model ◽

Non Linear ◽

Gaussian Case ◽

Non Gaussian ◽

Flatness Factor

We apply the Cameron—Martin—Wiener (formerly ‘Wiener—Hermite’) expansion of a random velocity field to the analytical study of turbulence. The kernels of this expansion contain all statistical information about the ensemble. Complete expressions are derived for constructing statistical quantities in terms of the kernels, and for the equations of motion of the kernels. We rigorously prove the Gaussian trend of the velocity field of the Navier—Stokes equation in the very late stage when the non-linear term is neglected. Then-dependence (nis the order of derivative) of the flatness factor, minus three for derivatives of the velocity field, shows a rapid increase withnin this stage.The late decay problem of the Burgers model of turbulence is studied analytically with a view to obtaining suggestive guidelines for fitting the non-linear aspects of the model turbulence. We can divide the energy spectrum density into two parts, the larger of which is a kind of steady solution, which we call the ‘equilibrium state’, which remains self-similar in time in terms of an appropriate variable. The deviation from this ‘equilibrium solution’ satisfies the Kármán—Howarth equation. As initial velocity field, we take two particular cases: (a) a pure Gaussian, and (b) a non-Gaussian velocity field. With these two cases a detailed spectral analysis has been obtained. The energy spectrum deviation from ‘equilibrium’ declines exponentially to zero for all wave-numbers. The Gaussian case shows that the flatness factor minus three increases rapidly withn, while the non-Gaussian case does not show any marked dependence onn.

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Anomalous behaviour of a passive tracer in wave turbulence

Journal of Fluid Mechanics ◽

10.1017/s0022112002001337 ◽

2002 ◽

Vol 467 ◽

pp. 163-203 ◽

Cited By ~ 17

Author(s):

ALEXANDER M. BALK

Keyword(s):

Energy Spectrum ◽

Velocity Field ◽

Numerical Simulations ◽

Power Law ◽

Anomalous Diffusion ◽

Wave Turbulence ◽

Passive Tracer ◽

Random Waves ◽

Tracer Particles ◽

Separation Of Scales

We consider the behaviour of a passive tracer in multiscale velocity field, when there is no separation of scales; the energy spectrum of the velocity field extends into the region of long waves and even can be singular there. We suppose that the velocity field is a superposition of random waves. The turbulence of various ocean or atmospheric waves provides examples. We find anomalous diffusion (sub- and super-diffusion), anomalous drift (super-drift), and anomalous spreading of a passive tracer cloud. For the latter we find the existence of two regimes: (i) ‘close’ passive tracer particles diverge sub- or supper-exponentially in time, and (ii) a ‘large’ passive tracer cloud spreads as a power-law in time. The exponents, as well as the corresponding pre-factors, are found. The theory is confirmed by numerical simulations.

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The energy spectrum of reconnected vortex loops in He II

Low Temperature Physics ◽

10.1063/10.0001907 ◽

2020 ◽

Vol 46 (10) ◽

pp. 977-981

Author(s):

V. A. Andryushchenko ◽

L. P. Kondaurova

Keyword(s):

Energy Spectrum ◽

Vortex Loops

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Coherent structures, uniform momentum zones and the streamwise energy spectrum in wall-bounded turbulent flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.493 ◽

2017 ◽

Vol 826 ◽

Cited By ~ 15

Author(s):

Theresa Saxton-Fox ◽

Beverley J. McKeon

Keyword(s):

Energy Spectrum ◽

Velocity Field ◽

Turbulent Flows ◽

Coherent Structures ◽

Large Scale ◽

Stokes Equations ◽

Structural Features ◽

Travelling Wave ◽

Spectral Signature ◽

Representative Model

Large-scale motions (LSMs) in wall-bounded turbulent flows have well-characterised instantaneous structural features (Kovasznay et al., J. Fluid Mech., vol. 41 (2), 1970, pp. 283–325; Meinhart & Adrian, Phys. Fluids, vol. 7 (4), 1995, pp. 694–696) and a known spectral signature (Monty et al., J. Fluid Mech., vol. 632, 2009, pp. 431–442). This work aims to connect these previous observations through the development and analysis of a representative model for LSMs. The model is constructed to be consistent with the streamwise energy spectrum (Monty et al. 2009) and amplification characteristics of the Navier–Stokes equations (McKeon & Sharma, J. Fluid Mech., vol. 658, 2010, pp. 336–382), and is found to naturally recreate characteristics of instantaneous turbulent structures, including a bulge shape (Kovasznay et al. 1970) and the presence of uniform momentum zones (Meinhart & Adrian 1995) in the streamwise velocity field. The observed structural similarity between the LSM representative model and instantaneous experimental data supports the use of travelling wave models to connect statistical and instantaneous descriptions of coherent structures, and clarifies a simple general equivalency between symmetry in a Reynolds-decomposed velocity field and asymmetry in the laboratory frame.

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