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SCALING EXPONENTS OF VELOCITY SPECTRA AND STRUCTURE FUNCTIONS IN THE MODERATE RANGE OF TAYLOR REYNOLDS NUMBERS IN A TURBULENT JET

Hamed Sadeghi
Institute for Aerospace Studies University of Toronto Toronto, ON, Canada M3H 5T6

Philippe Lavoie
Department of Aerospace Studies University of Toronto 4925 Dufferin Street Toronto, Ontario, Canada M3H 5T6

Andrew Pollard
Department of Mechanical and Materials Engineering, Queen's University, Kingston, Ontario Canada K7L 3N6

Résumé

In this paper, the effect of Reynolds number on the scaling exponents of the velocity spectra and structure functions in a round turbulent jet is considered. Hot-wire measurements were taken over a range of exit Reynolds numbers (10,000 ≤ ReD ≤ 60,000). The energy spectra in the scaling range demonstrate considerable departure from the k−5/3 (Kolmogorov inertial-range scaling) so that the scaling wave number exponent along the jet centreline is in the range -1.56 ≤ m ≤ -1.43. The magnitude of m exhibits a monotonic change with Reynolds number that agrees with earlier findings for grid generated turbulence. In addition, second and third-order structure functions are investigated. A Reynolds number dependence of the second-order structure function scaling exponent is observed. These exponents rise nearly exponentially to 2/3 as the Reynolds number increases. The peak value of the normalized thirdorder structure function asymptotically approaches 4/5 as the Reynolds numbers increases. The present round jet data confirms that a proper inertial range is unlikely to be established unless a very high turbulence Reynolds number (Rλ >>103) can be reached in jet flows.