Theoretical and computational studies of isotropic homogeneous turbulence

Citation

Huang, Mei-Jiau (1994) Theoretical and computational studies of isotropic homogeneous turbulence. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CQ2T-Z242. https://resolver.caltech.edu/CaltechETD:etd-06222005-133921

Abstract

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Numerical simulations are presented for viscous incompressible homogeneous turbulent flows with periodic boundary conditions. Our numerical method is based on the spectral Fourier method. Rogallo's code is modified and extended to trace fluid particles and simulate the evolution of material line elements.

The first part of the thesis is about modifying and applying the code to simulate a passive vector field convected and stretched by the so-called ABC flows in the presence of viscosity. The correlation of the geometry of the physical structures of the passive vector with the external straining is investigated. It is observed that most amplifications either occur in the neighborhoods of local unstable manifolds of the stagnation points of the ABC flows, if they exist, especially those with only one positive eigenvalue, or they are confined within the chaotic regions of the ABC flows if there is no stagnation point. Tube-like structures in all simulations are observed.

The second part of the thesis is an investigation of the power-law energy decay of turbulence. Two decay exponents, 1.24 and 1.54, are measured from simulations. A new similarity form for the double and triple velocity autocorrelation functions using the Taylor microscale as the scaling, consistent with the Karman-Howarth equation and a power-law, energy decay, is proposed and compared with numerical results. The proposed similarity form seems applicable at small to intermediate Reynolds number. For flows with very large Reynolds number, an expansion form of energy spectrum is proposed instead. Two lengthscales are used to express the energy spectrum in the energy-containing range and in the dissipation range of wave numbers. The uniform expansion is obtained by matching spectra in the inertial subrange to the famous Kolmogorov's [...] spectrum.

The third part of the thesis is a presentation of the Lagrangian data collected by tracking fluid particles in decaying turbulent flows. The mean growth rates of the magnitudes of material line elements, that of the vorticity due to nonlinear forces, and the mean principal rates of strain tensors are found to be proportional to the square root of the mean enstrophy. The proportional coefficients remain constant during the decay. The mean angles between material line elements and the principal directions of the strain tensors corresponding to the most stretching and the intermediate principal rates are about the same which is probably caused by the averaging process and by the possible switch of principal directions. The evolution of these angles under the action of one Burger's vortex is examined and the results support the conjecture. Following fluid particles which suffer substantial stretching in their history, we, through use of flow visualization tools, observe the evolution of nearby vorticity structures. It is observed that vortex sheets are created first by the nonlinear stretching which gradually become tubes at later times by diffusion.

Thesis Files