Generalized scaling laws for the irrotational motions bordering a turbulent region

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Zecchetto, M (Author) Other; Xavier, RP (Author) Other; Teixeira, MAC (Author) FEUP; da Silva, CB (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: PHYSICAL REVIEW E

Vol. 109

ISSN: 2470-0045

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Other information

Authenticus ID: P-010-JXJ

DOI: 10.1103/physreve.109.065107

Abstract (EN): 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)similar to k(n) [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955); Xavier et al., J. Fluid Mech. 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 x=2 (Saffman turbulence) have been previously derived, with < u(i)(2)>similar to x(2)(-4) and < u(i)(2)>similar to x(2)(-3), for x=4 and x=2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955); Xavier et al., J. Fluid Mech. 918, A3 (2021).], we extend these results by including any other value of n. In particular, we obtain < u(i)(2)>similar to x(2)(-2) and < u(i)(2)>similar to x(2)(-4), for n=1 and n >= 5, respectively, while n=3 yields < u(i)(2)>similar to 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10