On three-dimensional synthetic turbulence

Carlos Rosales
PhD Thesis, The Johns Hopkins University
March 2007, Baltimore MD

ABSTRACT:

Methods currently available to generate synthetic vector fields as surrogates for turbulent velocity fields are not able to reproduce the non-Gaussian statistics of turbulence nor to produce phase coherency. In this work, a method (called MMLM) to generate non-Gaussian synthetic vector fields is introduced. The method is based on a minimal Lagrangian map, by which an initial Gaussian field generated using random-phase Fourier modes is deformed by moving fluid particles of a sequence of low-pass filtered fields at their fixed velocity for some scale-dependent time-interval, interpolating onto regular grids, and imposing the divergence-free condition. The analysis shows that the resultant fields display many statistical and structural properties commonly observed in turbulence, which cannot be reproduced by Gaussian fields with random phases. The MMLM fields are used as initial conditions in DNS and LES of decaying isotropic turbulence, and results are compared with initializations using Gaussian fields. The MMLM fields yield more realistic results with significantly shortened initial adjustment periods. Then, a second variant of the method is developed that includes additionally the capability to generate inertial-range anomalous scaling. The energy dissipation field is analyzed by means of the multifractal formalism. The pressure field induced by the method is also examined. For all these properties the results are consistent with observations in real turbulence. Only statistics specifically associated with high vorticity are not realistic, due to the absence of vorticity filaments in the synthetic fields.

The last part of the work studies a forcing scheme (linear forcing) that can be applied in physical space. It is shown that the linearly-forced system converges to a stationary state that depends on domain size and Reynolds number, but not on the spectral shape of the initial condition. Also, the extent of Kolmogorov -5/3 range is similar to that achieved using the standard band-limited forcing, but the integral length scale is smaller. It is concluded that linear forcing is a useful alternative method that does not require transformation to Fourier space and is easily integrated into physical-space numerical codes.