### Abstract

All three components of the dissipation rate of the fluctuating temperature θ are measured simultaneously in the inner region of a fully developed turbulent boundary layer at a moderate Reynolds number. Measurements are made with a probe of four cold wires consisting of two closely spaced parallel vertical wires mounted a small distance upstream of two closely spaced parallel horizontal wires. In the inner region of the layer, local isotropy is not closely approximated [(∂θ/θz)
^{2}
_{>}(∂ θ/∂y)
^{2}
_{>}(∂θ/∂x)
^{2}]. The spectral density of the sum χ[ = (∂θ/∂x)
^{2} + (∂θ/∂y)
^{2} +(∂θ/∂z)
^{2}] is similar in shape to that of (∂θ/∂y)
^{2} or (∂θ/∂z)
^{2} , but not as rich in high frequency content as that of (∂θ/∂x)
^{2}. The probability density of χ has a lower skewness and flatness factor and is more closely log-normal than those of the individual components. This is true regardless of whether χ and its components are unaveraged or locally averaged over a linear dimension r. When averaging is applied, departures from log-normality are diminished but do not disappear entirely. The variance σ
^{2} of the logarithm of the locally averaged χ is proportional to 1n r over a wide range of r (r
_{max}/r
_{min}≃30), in contrast to the individual components where this ratio may be as small as 2. The value of the Kolmogoroff constant μ
_{θ}determined from the slope of σ
^{2} vs 1n r is about 0.35. This is consistent with the slope of the spectral density of χ and is also in agreement with previous best estimates of μ
_{θ}(and μ) obtained at high Reynolds numbers.

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

Pages (from-to) | 1238-1249 |

Number of pages | 12 |

Journal | Physics of Fluids |

Volume | 20 |

Issue number | 8 |

State | Published - 1977 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Physics and Astronomy(all)
- Mechanics of Materials
- Computational Mechanics
- Fluid Flow and Transfer Processes

### Cite this

*Physics of Fluids*,

*20*(8), 1238-1249.

**Temperature dissipation fluctuations in a turbulent boundary layer.** / Sreenivasan, K. R.; Antonia, R. A.; Danh, H. Q.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 20, no. 8, pp. 1238-1249.

}

TY - JOUR

T1 - Temperature dissipation fluctuations in a turbulent boundary layer

AU - Sreenivasan, K. R.

AU - Antonia, R. A.

AU - Danh, H. Q.

PY - 1977

Y1 - 1977

N2 - All three components of the dissipation rate of the fluctuating temperature θ are measured simultaneously in the inner region of a fully developed turbulent boundary layer at a moderate Reynolds number. Measurements are made with a probe of four cold wires consisting of two closely spaced parallel vertical wires mounted a small distance upstream of two closely spaced parallel horizontal wires. In the inner region of the layer, local isotropy is not closely approximated [(∂θ/θz) 2 >(∂ θ/∂y) 2 >(∂θ/∂x) 2]. The spectral density of the sum χ[ = (∂θ/∂x) 2 + (∂θ/∂y) 2 +(∂θ/∂z) 2] is similar in shape to that of (∂θ/∂y) 2 or (∂θ/∂z) 2 , but not as rich in high frequency content as that of (∂θ/∂x) 2. The probability density of χ has a lower skewness and flatness factor and is more closely log-normal than those of the individual components. This is true regardless of whether χ and its components are unaveraged or locally averaged over a linear dimension r. When averaging is applied, departures from log-normality are diminished but do not disappear entirely. The variance σ 2 of the logarithm of the locally averaged χ is proportional to 1n r over a wide range of r (r max/r min≃30), in contrast to the individual components where this ratio may be as small as 2. The value of the Kolmogoroff constant μ θdetermined from the slope of σ 2 vs 1n r is about 0.35. This is consistent with the slope of the spectral density of χ and is also in agreement with previous best estimates of μ θ(and μ) obtained at high Reynolds numbers.

AB - All three components of the dissipation rate of the fluctuating temperature θ are measured simultaneously in the inner region of a fully developed turbulent boundary layer at a moderate Reynolds number. Measurements are made with a probe of four cold wires consisting of two closely spaced parallel vertical wires mounted a small distance upstream of two closely spaced parallel horizontal wires. In the inner region of the layer, local isotropy is not closely approximated [(∂θ/θz) 2 >(∂ θ/∂y) 2 >(∂θ/∂x) 2]. The spectral density of the sum χ[ = (∂θ/∂x) 2 + (∂θ/∂y) 2 +(∂θ/∂z) 2] is similar in shape to that of (∂θ/∂y) 2 or (∂θ/∂z) 2 , but not as rich in high frequency content as that of (∂θ/∂x) 2. The probability density of χ has a lower skewness and flatness factor and is more closely log-normal than those of the individual components. This is true regardless of whether χ and its components are unaveraged or locally averaged over a linear dimension r. When averaging is applied, departures from log-normality are diminished but do not disappear entirely. The variance σ 2 of the logarithm of the locally averaged χ is proportional to 1n r over a wide range of r (r max/r min≃30), in contrast to the individual components where this ratio may be as small as 2. The value of the Kolmogoroff constant μ θdetermined from the slope of σ 2 vs 1n r is about 0.35. This is consistent with the slope of the spectral density of χ and is also in agreement with previous best estimates of μ θ(and μ) obtained at high Reynolds numbers.

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M3 - Article

VL - 20

SP - 1238

EP - 1249

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 8

ER -