Reduced-order modeling and analysis of fluid flows: from wall-bounded shear flows to convection

The study of problems ranging from wall-bounded shear flows to convection is complicated by the large range of spatiotemporal scales that need to be resolved. Reduced-order models can help explore computationally challenging parameter regimes and facilitate iterative optimization computation. The first part of this talk develops a structured input-output analysis to analyze transitional wall-bounded shear flows. This framework captures the key nonlinear effect that enables the prediction of a wider range of known transitional flow structures within a linear analytical modelling paradigm. The results for plane Couette flow closely match those obtained from extensive direct numerical simulations (DNS) and nonlinear optimal perturbation analysis but are achieved with vastly reduced computational cost. The proposed approach also captures the recently observed oblique turbulent bands that have been linked to transition in experiments and DNS with very large domains. The second part of this talk employs single-mode equations reducing three spatial dimensions into one vertical dimension to analyze well-organized columnar structures. The computational efficiency of this reduced description allows one to reach computationally challenging and oceanographically relevant parameter regimes for salt-finger convection. Single-mode equations were also applied to convection in a porous medium and fixed-flux convection and capture the essential physics in a wide parameter regime.