# Production of temperature fluctuations in grid turbulence: Wiskind's experiment revisited

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## Abstract

Measurements have been made in nearly-isotropic grid turbulence on which is superimposed a linearly-varying transverse temperature distribution. The mean-square temperature fluctuations,\(\overline {\vartheta ^2 } \), increase indefinitely with streamwise distance, in accordance with theoretical predictions, and consistent with an excess of production over dissipation some 50% greater than values recorded in previous experiments. This high level of\(\overline {\vartheta ^2 } \) production has the effect of reducing the ratio,*r*, of the time scales of the fluctuating velocity and temperature fields. The results have been used to estimate the coefficient,*C*, in Monin's return-to-isotropy model for the slow part of the pressure terms in the temperature-flux equations. An empirical expression by Shih and Lumley is consistent with the results of earlier experiments in which*r* ≈ 1.5, C ≈ 3.0, but not with the present data where r ≈ 0.5, C ≈1.6. Monin's model is improved when it incorporates both time scales.

## Keywords

Temperature Distribution Previous Experiment Temperature Field Theoretical Prediction Early Experiment## List of symbols

*C*coefficient in Monin model, Eq. (5)

*M*grid mesh length

*m*exponent in power law for temperature variance,\(\overline {\vartheta ^2 } \)∝

*x*^{ m }*n*turbulence-energy decay exponent,

*q*^{2}*∝x*^{ -n }*p*_{ϑ}production rate of\(\overline {\vartheta ^2 } /2\)

*p*pressure

*q*^{2}\(\overline {u^2 } + \overline {\upsilon ^2 } + \overline {w^2 } \)

*R*_{λ}microscale Reynolds number

*r*time-scale ratio

*t*/*t*_{ϑ}*T*mean temperature

*U*mean velocity

- \(\overline {u^2 } + \overline {\upsilon ^2 } + \overline {w^2 } \)
mean-square velocity fluctuations (turbulent energy components)

- \(\overline {\upsilon \vartheta } \)
turbulent temperature flux

*x, y, z*spatial coordinates

*β*temperature gradient d

*T*/d*y**γ*thermal diffusivity

*ɛ*dissipation rate of

*q*^{2}/2*β*_{ϑ}dissipation rate of\(\overline {\vartheta ^2 } /2\)

*λ*Taylor microscale (λ

_{2}=5νq_{2}/ε)*λ*_{ϑ}temperature microscale\((\lambda _{\vartheta ^2 } = 6\gamma \overline {\vartheta ^2 } /\varepsilon _\vartheta )\)

- ρ
_{vϑ} temperature-flux correlation coefficient,\(\overline {\upsilon \vartheta } \)/v′ϑ′

*ξ*dimensionless distance from the grid,

*x/M*

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