Physics

K-epsilon turbulence model

K-omega turbulence model

Computer network

Mechanics

Statistical physics

Flow control (data)

Artificial intelligence

Turbulence

Control (management)

Turbulence modeling

Flow (mathematics)

Computer science

Control theory (sociology)

Annual Review of Fluid Mechanics

Transient growth and resolvent analyses are routinely used to assess non-asymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input-output techniques enhance resolvent analysis. Specifically, physical insights that may remain hidden in the resolvent analysis are gained by detailed examination of input-output responses between spatially-localized body forces and selected linear combinations of state variables. This differentiating feature plays a key role in quantifying the importance of different mechanisms for bypass transition in wall-bounded shear flows and in explaining how turbulent jets generate noise. We highlight the utility of a stochastic framework, with white or colored inputs, in addressing a variety of open challenges including transition in complex fluids, flow control, and physics-aware data-driven turbulence modeling. Applications with time- or spatially-periodic base flows are discussed and future research directions are outlined.

From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint