Aspects of reduced-order modeling of turbulent channel flows: From linear mechanisms to data-driven approaches
In most engineering applications that involve flow of a fluid past a surface, that flow will be turbulent. Because wall-bounded turbulence is typically accompanied by substantial friction drag, a more complete understanding of it that could be exploited to reduce drag has the potential to effect enormous economic and environmental savings. However, our current ability to make predictions that are useful for engineering purposes is limited by the high costs associated with reproducing these flows in a laboratory or simulation. Accordingly, reduced-order models that balance tractability and physical fidelity are extremely valuable tools for advancing our understanding of wall-bounded turbulence. This talk concerns two key aspects of such reduced-order models: linear mechanisms, and nonlinear interactions. Both aspects are explored by way of example through analysis of a problem 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 admits 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.
Contact: Benedikt Barthel firstname.lastname@example.org