Lagrangian evolution of small scales in turbulence: intermittency and large-eddy simulation modeling

Yi Li
PhD Thesis, The Johns Hopkins University
August 2007
Baltimore MD

ABSTRACT: Two directions related to the fundamental dynamics and the modeling of small scales in turbulence are pursued. In the first part of the thesis, in studying the dynamical origin of small-scale intermittency of turbulence, a simple system of equations describing the evolution of small-scale velocity and passive scalar increments is derived by following the Lagrangian evolution of material elements. In this system, the nonlinear self-interaction terms attain simple, closed forms. The system reproduces and thus provides simple dynamical explanations for many observed intermittency trends. The unclosed terms in the system are analyzed using 1024^3 direct numerical simulation (DNS) data made available through a novel turbulence database cluster. The database provides remote access and real-time parallel processing abilities to high resolution DNS data through a series of state-of-the-art information and database technologies. The analysis demonstrates the easy and flexible usage of the database system, and shows that, while overall the unclosed terms tend to counteract the effects of self-interaction terms, they show marked difference in details, which poses challenges to their modeling. A solvable analytic model for material deformation is also obtained, which, compared with DNS data, accurately reproduces the short-time evolution of the shape and orientation of the material volumes. The second part of the thesis is focused on modeling for large-eddy simulation. The mean momentum balance and helicity balance are used to calibrate model coefficients in sheared and helical turbulence, respectively. Surprisingly, the Smagorinsky coefficient adjusted to produce correct mean SGS momentum flux in weakly sheared turbulence is very close to the value obtained from energy balance. On the other hand, the Smagorinsky model with traditional coefficient is shown to underestimate SGS helicity dissipation by 40%. Several helical models are proposed with an additional term to control helicity dissipation. The models, together with the Smagorinsky, dynamic Smagorinsky and dynamic mixed nonlinear models, are tested in isotropic helical turbulence. Results show that the helical term provides some improvements, but the best overall results are obtained with the dynamic models.