Applicability of Taylor's hypothesis in thermally driven turbulence

Kumar, Abhishek; Verma, Mahendra K.

doi:10.1098/rsos.172152

Cited by 72 publications

(42 citation statements)

References 71 publications

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“…In most convective experiments, the velocity field, u t r, z ( ), and/or the temperature field, T t r, ( ), are probed near the lateral walls of the container. For such experiments, the Taylor's hypothesis [56,94,105] is invoked to relate the frequency power spectrum E( f ) of the time series to the one-dimensional wavenumber spectrum E k ; ( ) this connection is under debate due to the absence of any constant mean velocity field [56,63]. Researchers [57,104,122,123] employ 2D particle image velocimetry for high-resolution visualization and computation of an approximate energy spectrum under the assumption of homogeneity and isotropy, which is not strictly valid in convection [75].…”

Section: Resultsmentioning

confidence: 99%

Phenomenology of buoyancy-driven turbulence: recent results

Kumar²,

2017

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In this paper, we describe the recent developments in the field of buoyancy-driven turbulence with a focus on energy spectrum and flux. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum~-E k k u 11 5OPEN ACCESS RECEIVED on energy spectrum and flux in section 3, and scaling of large-scale quantities in section 4. Section 5 contains a brief description of the dynamics of flow reversal. We conclude in section 6.

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Section: Resultsmentioning

confidence: 99%

Phenomenology of buoyancy-driven turbulence: recent results

Kumar²,

2017

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“…Within an intermediate frequency range (here 10 −1 ω/ω cv ≤ O(1)), denoted below as the anomalous range, the spectrum is characterized by an anomalous 1/ω α power law with exponents α < 1 that vary with Ra and Pr in full spheres (as we will discuss further below). For larger frequencies ω/ω c ≥ O(1) in the turbulent cascade, the spectrum first displays the power law 1/ω 2 expected for Kolmogorov turbulence (Landau & Lifshitz 1987;Kumar & Verma 2018). Finally, the frequencies belong to the dissipation range of the convection when ω/ω c 1, first with the power-law scaling 1/ω 4 in a narrow frequency interval (as found in laboratory experiments, see in Liot et al 2016) and then with a steeper decay.…”

Section: Unperturbed Convectionmentioning

confidence: 91%

“…Finally, the power spectrum of the turbulent cascade is also uncertain. Kolmogorov spectra have been robustly reported for Boussinesq convection (Kumar & Verma 2018), but compressible convection (e.g. Penev et al 2011;Horst et al 2020) may display different non-Kolmogorov spectra (depending on the convection setup).…”

Section: Astrophysical Implicationsmentioning

confidence: 99%

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Vidal

Barker

2020

Monthly Notices of the Royal Astronomical Society

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Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency |ωt| exceeds the turnover frequency ωcv of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity νE acting on the tidal flow when |ωt|/ωcv ≳ 1. We demonstrate that the frequency reduction of νE is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade (|ωt|/ωcv ∼ 1 − 5), the frequency spectrum displays an anomalous 1/ωα power law that is responsible for the frequency-reduction νE∝1/|ωt|α, where α < 1 depends on the model parameters. We then get |νE|∝1/|ωt|δ with δ > 1 for higher frequencies, and δ = 2 is obtained for a Kolmogorov turbulent cascade. A generic |νE|∝1/|ωt|2 suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

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“…Penev et al 2009). Therefore, we evaluate the frequency spectrum, which is a commonly used diagnostic in turbulent convection (e.g Ashkenazi & Steinberg 1999;Kumar et al 2014;Kumar & Verma 2018), by computing…”

Section: Quantities Of Interestmentioning

confidence: 99%

Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

Duguid

Barker

Jones

2020

Monthly Notices of the Royal Astronomical Society

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Turbulent convection is thought to act as an effective viscosity (νE) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency (ω) exceeds the turnover frequency of the dominant convective eddies (ωc). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, and here we explore a wider range of parameters. We obtain several new results: 1) νE is frequency-dependent, scaling as ω−0.5 when ω/ωc ≲ 1, and appears to attain its maximum constant value only for very small frequencies (ω/ωc ≲ 10−2). This frequency-reduction for low frequency tidal forcing has never been observed previously. 2) The frequency-dependence of νE appears to follow the same scaling as the frequency spectrum of the energy (or Reynolds stress) for low and intermediate frequencies. 3) For high frequencies (ω/ωc ≳ 1 − 5), νE∝ω−2. 4) The energetically-dominant convective modes always appear to contribute the most to νE, rather than the resonant eddies in a Kolmogorov cascade. These results have important implications for tidal dissipation in convection zones of stars and planets, and indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited. We briefly touch upon the implications for planetary orbital decay around evolving stars.

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Applicability of Taylor's hypothesis in thermally driven turbulence

Cited by 72 publications

References 71 publications

Phenomenology of buoyancy-driven turbulence: recent results

Phenomenology of buoyancy-driven turbulence: recent results

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

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