Assessment of large-scale forcing in isotropic turbulence using a closed Kármán–Howarth equation

• Published in: Physics of fluids (1994) 2020-05, Vol.32 (5), p.55104
• Main Authors: Djenidi, L., Antonia, R. A.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computer simulation; Direct numerical simulation; Energy dissipation; Fluid dynamics; Fluid flow; Isotropic turbulence; Kinetic energy; Mathematical models; Physics; Reynolds number; Transport equations
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0006466

We attempt to model the effects of large-scale forcing on the statistical behavior of small scales in isotropic turbulence. More specifically, the effect of large-scale forcing on the second-order velocity structure function, S2, in the region beyond the dissipative range, is analyzed via the transport equation for S2 where a closure model for S3, the third-order velocity structure function, is introduced. The model [L. Djenidi and R. A. Antonia, Fluid Turbulence Applications in Both Industrial and Environmental Topics, Marseille, 9–11 July, 2019, https://fab60.sciencesconf.org/] is based on a gradient type with an eddy-viscosity formulation and has the following expression: S3=−CS3(S2)2ϵ¯∂S2∂r, where ϵ¯ is the mean rate of the turbulent kinetic energy dissipation, r is the spatial increment, and CS3 is a constant. The closed S2-transport equation is further exploited to derive a model for S2 for scales beyond the dissipative range. The model for S2 takes the form S2=CK(ϵ̃rr)23 with ϵ̃r=ϵ¯1−Br/Reλ1/2, where CK is a constant, Reλ is the Taylor microscale Reynolds number, and the function Br accounts for the effect of the large scales. The numerical solutions of the S2 equation and the predictions based on the model for S2 agree very well with direct numerical simulation data for steady-state forced homogeneous and isotropic turbulence. The solutions of the S2-transport equation without large-scale forcing show that S2 behaves like (ϵ¯r)2/3. When forcing is applied, S2 deviates from this behavior. However, increasing the Reynolds number tends to restore this behavior over an increasing range of scales. This is also observed in the predictions of the model for S2.