The cardinal issues forestalling a better understanding of the turbulence phenomenon are the nonlinearity of the inertial cascade physics and the non-local nature of the action of pressure. In this talk, we focus on analyzing, understanding and modeling the latter, manifested in the pressure strain correlation.
The Reynolds stresses provide an insufficient basis to describe the internal structure of turbulent flows, leading to an inherent degree of uncertainty in predictions using classical turbulence models. We carry out a detailed Dynamical Systems analysis of modal ensembles and individual modes in Fourier space to identify the range of possible behavior and the underlying physics. Based on this insight, Different aspects of the dynamics of pressure are discussed, individually and sequentially, vis-a-vis their amenability to the single point modeling paradigm. Thereon, a set of pragmatic compromises is constituted within the form and the scope of the model to outline a modeling framework. The predictions of an illustrative model are compared to numerical and experimental data while being contrasted against established modeling paradigms.
We conclude by quantifying the uncertainty in the modeling framework. For a set of different states of the mean gradient and the Reynolds stress tensors, we establish the range of this uncertainty for rapid pressure strain closures, identify statistically most likely behavior and their evolution.