Generalized scaling laws for the irrotational motions bordering a turbulent region

Zecchetto, M., Xavier, R. P., Teixeira, M. A. C. ORCID: https://orcid.org/0000-0003-1205-3233 and da Silva, C. B. (2024) Generalized scaling laws for the irrotational motions bordering a turbulent region. Physical Review E, 109 (6). 065107. ISSN 1539-3755 doi: 10.1103/PhysRevE.109.065107

Abstract/Summary

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI x_2 much bigger than the integral scale L in the nearby turbulent region (x_2 >> L), the variance of the velocity fluctuations <u_i^2> (i = 1,2,3) depends on the shape of the kinetic energy spectrum in the infrared region E(k) ∼ k^n [O.M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955); Xavier et al., J. FluidMech. 918, A3 (2021)]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of n. While the cases n = 4 (Batchelor turbulence) and n = 2 (Saffman turbulence) have been previously derived, with <u_i^2> ~ x_2^(−4) and <u_i^2> ~ x_2^(−3), for n = 4 and n = 2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955); Xavier et al., J. FluidMech. 918, A3 (2021).], we extend these results by including any other value of n. In particular, we obtain <u_i^2> ~ x_2^(-2) and <u_i^2> ~x_2^(-4) for n = 2 and n > 4, respectively, while n = 3 yields <u_i^2> ~ x_2^(-4) ln(x_2). These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

Item Type	Article
URI	https://reading-pure-test.eprints-hosting.org/id/eprint/116849
Identification Number/DOI	10.1103/PhysRevE.109.065107
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
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