Mechanical and Civil Engineering Seminar
Amongst many data-driven modal decompositions of utility in fluid mechanics, the frequency-domain version of the proper orthogonal decomposition, which we call spectral POD (SPOD), plays a special role in the analysis of stationary turbulence. SPOD modes are optimal in expressing structures that evolve coherently in both space and time, and they can be regarded as optimally-averaged DMD modes, and approximations of eigenfunctions of the Koopman operator. The SPOD spectrum is also related to the resolvent spectrum of the linearized dynamics (the linearized Navier-Stokes equations in this case) and examination of the relationship between the SPOD and resolvent modes yields information about how coherent structures are forced by nonlinear interactions amongst coherent and incoherent fluctuations. We discuss the application of these tools to analyze turbulence in high-speed jets. The analysis identifies both classical (e.g. Kelvin Helmholtz) and novel amplification mechanisms in jets. For example, the lift-up mechanism, known to be important in wall bounded flows, also leads to coherent streaky structures in jets. Finally, we highlight recent analysis that confirms an important role for eddy viscosity models in resolvent analysis.