### Abstract

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra = 1.5 × 101 ^{11}. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.

Original language | English (US) |
---|---|

Article number | 035302 |

Journal | Physical Review E |

Volume | 71 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2005 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E*,

*71*(3), [035302]. https://doi.org/10.1103/PhysRevE.71.035302

**Fluctuations of temperature gradients in turbulent thermal convection.** / Sreenivasan, K. R.; Bershadskii, A.; Niemela, J. J.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 71, no. 3, 035302. https://doi.org/10.1103/PhysRevE.71.035302

}

TY - JOUR

T1 - Fluctuations of temperature gradients in turbulent thermal convection

AU - Sreenivasan, K. R.

AU - Bershadskii, A.

AU - Niemela, J. J.

PY - 2005/3

Y1 - 2005/3

N2 - Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra = 1.5 × 101 11. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.

AB - Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra = 1.5 × 101 11. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.

UR - http://www.scopus.com/inward/record.url?scp=37649028919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37649028919&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.035302

DO - 10.1103/PhysRevE.71.035302

M3 - Article

AN - SCOPUS:37649028919

VL - 71

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

M1 - 035302

ER -