Phenomenology of buoyancy-driven turbulence: recent results

Verma, Mahendra K.; Kumar, Abhishek; Pandey, Ambrish

doi:10.1088/1367-2630/aa5d63

Cited by 125 publications

(123 citation statements)

References 117 publications

(379 reference statements)

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“…[36,37], the authors show that a Kolmogorov like spectrum (k enstrophy) spectra tend to follow a k −11/5 (respectively, k −1/5 ) scaling corresponding to the Bolgiano regime [36][37][38][39]. Our results are consistent with Verma et al [36] and Kumar et al [37] confirming the two-dimensional nature of our experiment with a strong kinetic energy inverse cascade which will be discussed below when we consider energy fluxes in Fig.…”

Section: Energy and Enstrophy Spectrasupporting

confidence: 91%

“…We give here the first few values for k = 0...7: [36,41]. This slope can be observed in particular in Fig.…”

Section: Appendix D: Entropy Spectrummentioning

confidence: 59%

“…10 of Ref. [36]. They obtained this value for the even wave-numbers with a rigorous calculation of the Fourier coefficients.…”

Section: Appendix D: Entropy Spectrummentioning

confidence: 85%

“…They obtained a scaling of k −5/3 in their temperature spectrum. Mishra et al [36,[41][42][43] also observed this kind of oscillations (called dual branches in their articles) and they also proposed a theoretical explanation for this behavior. They predicted different scalings for the upper (k −2 ) and the lower (k −5/3 or k…”

Section: Entropy Spectramentioning

confidence: 85%

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Numerical simulations of thermal convection on a hemisphere

et al. 2018

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In this paper we present numerical simulations of two-dimensional turbulent convection on a hemisphere. Recent experiments on a half soap bubble located on a heated plate have shown that such a configuration is ideal for studying thermal convection on a curved surface. Thermal convection and fluid flows on curved surfaces are relevant to a variety of situations, notably for simulating atmospheric and geophysical flows. As in experiments, our simulations show that the gradient of temperature between the base and the top of the hemisphere generates thermal plumes at the base that move up from near the equator to the pole. The movement of these plumes gives rise to a two-dimensional turbulent thermal convective flow. Our simulations turn out to be in qualitative and quantitative agreement with experiments and show strong similarities with Rayleigh-Bénard convection in classical cells where a fluid is heated from below and cooled from above. To compare to results obtained in classical Rayleigh-Bénard convection in standard three-dimensional cells (rectangular or cylindrical), a Nusselt number adapted to our geometry and a Reynolds number are calculated as a function of the Rayleigh number. We find that the Nusselt and Reynolds numbers verify scaling laws consistent with turbulent Rayleigh-Bénard convection: Nu ∝ Ra 0.31 and Re ∝ Ra 1/2 . Further, a Bolgiano regime is found with the Bolgiano scale scaling as Ra −1/4 . All these elements show that despite the significant differences in geometry between our simulations and classical 3D cells, the scaling laws of thermal convection are robust.

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Section: Energy and Enstrophy Spectrasupporting

confidence: 91%

“…We give here the first few values for k = 0...7: [36,41]. This slope can be observed in particular in Fig.…”

Section: Appendix D: Entropy Spectrummentioning

confidence: 59%

“…10 of Ref. [36]. They obtained this value for the even wave-numbers with a rigorous calculation of the Fourier coefficients.…”

Section: Appendix D: Entropy Spectrummentioning

confidence: 85%

Section: Entropy Spectramentioning

confidence: 85%

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Numerical simulations of thermal convection on a hemisphere

et al. 2018

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“…This has been observed in the numerical studies of Refs. [18,19,26]. The K41 scaling theory rests on the assumption of local isotropy, which is not maintained in stratified flows with sufficiently strong stratification [20].…”

Section: Introductionmentioning

confidence: 99%

Kolmogorov or Bolgiano-Obukhov scaling: Universal energy spectra in stably stratified turbulent fluids

Basu

Bhattacharjee²

2019

Phys. Rev. E

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We set up the scaling theory for stably stratified turbulent fluids. For a system having infinite extent in the horizontal directions, but with a finite width in the vertical direction, this theory predicts that the inertial range can display three possible scaling behaviour, which are essentially parametrised by the buoyancy frequency N , or dimensionless horizontal Froude number F h , and the vertical length scale lv that sets the scale of variation of the velocity field in the vertical direction, for a fixed Reynolds number. For very low N or very high Re b or F h , and with lv being of the same order as l h , the typical horizontal length scale, buoyancy forces are irrelevant and hence, unsurprisingly, the kinetic energy spectra shows the well-known K41 scaling in the inertial range. In this regime, the local temperature behaves as a passively advected scalar, without any effect on the flow fields. For intermediate ranges of values of N, F h ∼ O(1), corresponding to moderate stratification, buoyancy forces are important enough to affect the scaling. This leads to the Bolgiano-Obukhov scaling which is isotropic, when lv ∼ l h . Finally, for very large N or equivalently for vanishingly small F h , Lo, corresponding to strong stratification, together with a very small lv, the system effectively twodimensionalise; the kinetic energy spectrum is predicted to be anisotropic with only the horizontal part of the kinetic energy spectra follows the K41 scaling, suggesting an intriguing re-entrant K41 scaling, as a function of stratification, for v ⊥ in this regime. The scaling theory further predicts the scaling of the thermal energy in each of these three scaling regimes. Our theory can be tested in large scale simulations and appropriate laboratory-based experiments.

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3D Rayleigh‐Bénard‐type natural convection in MWCNT‐nanofluid‐filled L‐shaped enclosures with consideration of aggregation effect

Almeshaal

Maatki

Kolsi

et al. 2020

Math Methods in App Sciences

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Rayleigh‐Bénard type convective heat transfer in a 3D L‐shaped enclosure filled with multiwalled carbon nanotube (MWCNT)‐water nanofluids has been studied. The governing equations have been written using the vorticity‐vector potential formalism and solved based on the finite volume method (FVM). The simulations were performed for various values of Rayleigh number, aspect ratio, and MWCNT volume fraction. The aggregation effect was considered, and the viscosity and thermal cavity were evaluated accordingly to fit with the experimental properties. The heat transfer is enhanced by increasing MWCNT volume fraction. The aspect ratio is found to be an optimization parameter of heat transfer especially for low Ra values. The aspect ratio equal to 0.4 provides the highest heat transfer for fraction nanofluid less than 3% and Ra number less than 105. Increasing the aspect ratio and fraction nanofluid enhances of the 3D character.

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Phenomenology of buoyancy-driven turbulence: recent results

Cited by 125 publications

References 117 publications

Numerical simulations of thermal convection on a hemisphere

Numerical simulations of thermal convection on a hemisphere

Kolmogorov or Bolgiano-Obukhov scaling: Universal energy spectra in stably stratified turbulent fluids

3D Rayleigh‐Bénard‐type natural convection in MWCNT‐nanofluid‐filled L‐shaped enclosures with consideration of aggregation effect

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