### Abstract

Original language | English |
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Article number | 023016 |

Number of pages | 9 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 90 |

DOIs | |

Publication status | Published - 25 Aug 2014 |

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*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*90*, [023016 ]. https://doi.org/10.1103/PhysRevE.90.023016

**Energy spectrum of buoyancy-driven turbulence.** / Kumar, Abhishek; Chatterjee, Anando G.; Verma, Mahendra K.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 90, 023016 . https://doi.org/10.1103/PhysRevE.90.023016

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TY - JOUR

T1 - Energy spectrum of buoyancy-driven turbulence

AU - Kumar, Abhishek

AU - Chatterjee, Anando G.

AU - Verma, Mahendra K.

PY - 2014/8/25

Y1 - 2014/8/25

N2 - Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Πu, we demonstrate that, for stably stratified flows, the kinetic energy spectrum Eu(k)∼k-11/5, the potential energy spectrum Eθ(k)∼k-7/5, and Πu(k)∼k-4/5 are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence Eu(k) follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Πu(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Πu(k) and Eu(k)∼k-5/3 for a narrow band of wave numbers. © 2014 American Physical Society.

AB - Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Πu, we demonstrate that, for stably stratified flows, the kinetic energy spectrum Eu(k)∼k-11/5, the potential energy spectrum Eθ(k)∼k-7/5, and Πu(k)∼k-4/5 are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence Eu(k) follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Πu(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Πu(k) and Eu(k)∼k-5/3 for a narrow band of wave numbers. © 2014 American Physical Society.

U2 - 10.1103/PhysRevE.90.023016

DO - 10.1103/PhysRevE.90.023016

M3 - Article

VL - 90

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

M1 - 023016

ER -