Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction

Verma, Mahendra K.

doi:10.1209/0295-5075/98/14003

Cited by 55 publications

(16 citation statements)

References 24 publications

(59 reference statements)

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“…(32)(33)(34) with Π θ (k) ∼ k −0.3 . This is similar to the variable flux arguments presented by Verma [41] and Verma and Reddy [55]. Specifically,…”

Section: Moderate Stratificationsupporting

confidence: 88%

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Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

Kumar

Verma

Sukhatme

2017

Journal of Turbulence

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In this paper we characterize the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence under large-scale random forcing. In the strongly stratified case, a large-scale verically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k −3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k −3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano-Obukhov scaling that transitions from a shallow k −11/5 form at large scales, to a steeper approximate k −3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterized by an approximate k −1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k −2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k −1.6 powerlaw. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale dependent nature of the corresponding flux.

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“…(32)(33)(34) with Π θ (k) ∼ k −0.3 . This is similar to the variable flux arguments presented by Verma [41] and Verma and Reddy [55]. Specifically,…”

Section: Moderate Stratificationsupporting

confidence: 88%

“…5(a,b)], and in is accord with Eq. (41). As mentioned, the PE spectrum does not exhibit dual scaling, and we do not see the k −1 scaling expected from Eq.…”

Section: Very Closelycontrasting

confidence: 40%

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

Kumar

Verma

Sukhatme

2017

Journal of Turbulence

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“…Thus, for k > k f , where k f is the forcing wavenumber, F (k) = 0. In this regime, the flux Π(k) will decrease with k since J (k) is active at all scales [57,58,72,74]. This result is contrary to the constant energy flux observed in fluid turbulence in which ν is effective only at large k's (also see Sec.…”

Section: Qs Mhd Equations In the Fourier Spacementioning

confidence: 84%

Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence

Verma¹

2017

Rep. Prog. Phys.

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In this review we summarise the current status of the quasi-static magnetohydrodynamic turbulence. The energy spectrum is steeper than Kolmogorov's k spectrum due to the decrease of the kinetic energy flux with wavenumber k as a result of Joule dissipation. The spectral index decreases with the increase of interaction parameter. The flow is quasi two-dimensional with strong [Formula: see text] at small k and weak [Formula: see text] at large k, where [Formula: see text] and [Formula: see text] are the perpendicular and parallel components of velocity relative to the external magnetic field. For small k, the energy flux of [Formula: see text] is negative, but for large k, the energy flux of [Formula: see text] is positive. Pressure mediates the energy transfer from [Formula: see text] to [Formula: see text].

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“…Before the onset of the instability, the energy spectrum is best fitted with an exponential dependence. Exponential energy spectra can occur in laminar flows and in flows with strong dissipation [29], [30]. After the onset, the spectrum changes dramatically at small wave numbers: The energy rises, as is expected due to the energy input from the heartbeat.…”

Section: Energy Spectramentioning

confidence: 85%

Turbulence in an Auto-Oscillating Complex Plasma

Schwabe

Zhdanov

Räth

2018

IEEE Trans. Plasma Sci.

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We present an experiment on the development of turbulence in a microparticle cloud in a low temperature plasma laboratory on board the International Space Station. First, the complex plasma cloud was stabilized with an alternating electric field. Once the stabilization was switched off, a so-called heartbeat instability developed in which the microparticles are oscillating radially. We show that the kinetic energy spectra develop a double cascade once the cloud becomes unstable. A double cascade has been predicted by Kraichnan and Leith for forced twodimensional turbulence, but has only seldomly been observed in experiments. We also show that the reduced rates of energy and enstrophy transfer can be used to infer the excitation wave number kexc, in good agreement with kexc obtained from the energy spectrum.

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Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction

Cited by 55 publications

References 24 publications

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence

Turbulence in an Auto-Oscillating Complex Plasma

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