Aspects of Reduced-Order Modeling of Turbulent Channel Flows: From Linear Mechanisms to Data-Driven Approaches

Citation

McMullen, Ryan Michael (2020) Aspects of Reduced-Order Modeling of Turbulent Channel Flows: From Linear Mechanisms to Data-Driven Approaches. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/wayx-eh75. https://resolver.caltech.edu/CaltechTHESIS:05282020-161209039

Abstract

This thesis concerns three key aspects of reduced-order modeling for turbulent shear flows. They are linear mechanisms, nonlinear interactions, and data-driven techniques. Each aspect is explored by way of example through analysis of three different problems relevant to the broad area of turbulent channel flow.

First, linear analyses are used to both describe and better understand the dominant flow structures in elastoinertial turbulence of dilute polymer solutions. It is demonstrated that the most-amplified mode predicted by resolvent analysis (McKeon and Sharma, 2010) strongly resembles these features. Then, the origin of these structures is investigated, and it is shown that they are likely linked to the classical Tollmien-Schichting waves.

Second, resolvent analysis is again utilized to investigate nonlinear interactions in Newtonian turbulence. An alternative decomposition of the resolvent operator into Orr-Sommerfeld and Squire families (Rosenberg and McKeon, 2019b) enables a highly accurate low-order representation of the second-order turbulence statistics. The reason for its excellent performance is argued to result from the fact that the decomposition enables a competition mechanism between the Orr-Sommerfeld and Squire vorticity responses. This insight is then leveraged to make predictions about how resolvent mode weights belonging to several special classes scale with increasing Reynolds number.

The final application concerns special solutions of the Navier-Stokes equations known as exact coherent states. Specifically, we detail a proof of concept for a data-driven method centered around a neural network to generate good initial guesses for upper-branch equilibria in Couette flow. It is demonstrated that the neural network is capable of producing upper-branch solution predictions that successfully converge to numerical solutions of the governing equations over a limited range of Reynolds numbers. These converged solutions are then analyzed, with a particular emphasis on symmetries. Interestingly, they do not share any symmetries with the known equilibria used to train the network. The implications of this finding, as well as broader outlook for the scope of the proposed method, are discussed.

Thesis Files