| Autor: |
Zecchetto M; IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal., Xavier RP; IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal., Teixeira MAC; Department of Meteorology, University of Reading, Meteorology Building, Whiteknights Road, Earley Gate, Reading RG6 6ET, United Kingdom., da Silva CB; IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal. |
| Jazyk: |
angličtina |
| Zdroj: |
Physical review. E [Phys Rev E] 2024 Jun; Vol. 109 (6-2), pp. 065107. |
| DOI: |
10.1103/PhysRevE.109.065107 |
| Abstrakt: |
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)10.1017/S0305004100030073; Xavier et al., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296]. 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)10.1017/S0305004100030073; Xavier et al., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296.], 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=1 and n≥5, 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. |
| Databáze: |
MEDLINE |
| Externí odkaz: |
|
