En route to chaos, fluid flows undergo transitions that give rise to large-scale coherent structures, usually associated with increased noise, structural fatigue and drag. Although the exact physics-based modeling framework for transitional, laminar flows is well understood based on hydrodynamic stability analysis, the turbulent regimes still remain a challenging task due to spatiotemporal complexity and high computational cost. This talk will contribute to the efficient characterization and modeling of the underlying intrinsic and extrinsic turbulent dynamics, which is essential for practical control strategies.
For bluff-body wakes exhibiting self-excited intrinsic dynamics, we show that only a small and finite number of spatiotemporal symmetry break instabilities occur before reaching the chaotic regime. The bifurcation thresholds and mode shapes are accurately predicted using global stability analysis and validated against DNS. For turbulent wakes, wind-tunnel measurements reveal the persistence of these instabilities as coherent structures, in a statistical sense. Based on this observation, we propose a stochastic framework for modeling the macroscopic wake behavior. This knowledge was leveraged to design open-loop and closed-loop control algorithms achieving a drag reduction up to 10% in fully turbulent regimes.
On the other hand, wall-bounded flows and mixing layers exhibit extrinsic dynamics and one typically seeks for optimal amplification mechanisms of external perturbations. For the case of a supersonic turbulent jet, the optimal input-output (or resolvent) modes reveal the most important underlying instability mechanisms and compare favorably with LES extracted modes. However, for three-dimensional flows with no homogeneous directions the computational cost of the stability problem is typically intractable. To tackle this, the governing compressible Navier-Stokes equations are accurately parabolized (One-Way) and global solutions are efficiently obtained by reducing the dimensionality of the system by space-marching. We will demonstrate an efficient adjoint-based optimization framework for obtaining optimal inputs that maximize the flow response based on One-Way Navier-Stokes equations.