Studies of the structure of turbulence by high-resolution simulation and theory

Abstract

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project was a study of structures of fluid turbulence using high-resolution direct numerical simulation and the theory development based on observations and measurements on the numerical simulations. Significant advances have been made in the study of fundamental fluid turbulence through numerical and theoretical work. The research has been focussed on the following areas: (1) The dynamics of advected passive scalar: Using the equations of motion, we analytically predict the anomalous scaling exponents for a passive scalar advected by fluid turbulence. The exponents are verified through large-scale simulation with 8192{sup 2} mesh points. This is the first case in which anomalous scaling exponents for a turbulence problem have been deduced from the equations of motion. (2) The inertial range scaling in three-dimensional (3D) turbulence: High-resolution direct numerical simulations of 3D Navier-Stokes turbulence with normal viscosity and hyperviscosity are carried out to study the inertial-range statistics. It is found that both the scalings and the probability distribution functions are independent of the dissipation mechanism, but the near-dissipation-range fluctuations show significant structural differences; (3) Statistics and structures of pressure field, vorticity, and dissipation in three-dimensional incompressible isotropic turbulence have been studied. The statistical relations among pressure, vorticity, dissipation, and kinetic energy are investigated using a conditional averaging process; and (4) The refined similarity hypothesis: We studied the conditionally averaged velocity increments as a function of the locally averaged dissipation. Our results provide direct evidence in support of the refined similarity hypotheses.