| dc.description.abstract | Velocity gradients embody the small-scale behavior of turbulence and hold the key to understanding important phenomena such as small-scale intermittency, local-streamline geometry, scalar-mixing, and material-element-deformation. The goal of this dissertation is to investigate velocity-gradient dynamics using direct numerical simulation (DNS) data of turbulent flows to (i) develop deeper understanding of the small-scale dynamics and turbulence processes and (ii) derive a model for the Lagrangian velocity-gradient dynamics in incompressible turbulent flows.
We begin with the proposal that improved insight can be obtained by investigating the internal-structure and the magnitude of the velocity-gradient tensor, individually. This is done by factorizing the velocity-gradient tensor into a bounded normalized velocity-gradient tensor, that represents local-streamline geometry and an intermittent magnitude, that represents the scale of the streamlines. Analysis of the DNS datasets of isotropic turbulence and turbulent channel flow demonstrates
that the normalized velocity-gradient geometry exhibits a distinct universality across different Reynolds numbers, while the magnitude grows with Reynolds number.
The dynamics of the velocity-gradient geometry and magnitude in turbulence are investigated within the state-space of the normalized velocity-gradient tensor. The effects of different turbulence processes – inertial, pressure, viscous, and large-scale forcing – on velocity-gradient dynamics are clearly identified and explicated. The key findings are that pressure along with inertia drive all flow geometries toward pure-shear, while viscosity not only reduces the velocity-gradient magnitudes but also drives the local-flow towards strain-dominated geometries.
The turbulence small-scale dynamics is revisited using a novel velocity-gradient triple decomposition. In this decomposition, the effects of normal-strain and pure-rotation are clearly demarcated from that of shear. The analysis of DNS data reveals that shear constitutes the most dominating contribution toward velocity gradients in a turbulent flow field and may be the most responsible for its intermittent nature.
A new Lagrangian velocity-gradient model is derived by modeling the bounded dynamics of the normalized velocity-gradient tensor and the dynamics of intermittent magnitude separately. The nonlocal flow-physics are captured by a data-driven closure in the bounded four-dimensional state-space of normalized velocity gradients, while the magnitude is modeled as a near-lognormal diffusion process. The resulting velocity-gradient model shows improved agreement with the small-scale statistics of DNS. | |
