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Abstract In this work, we consider the problem of learning a reduced-order model of a high-dimensional stochastic nonlinear system with control inputs from noisy data. In particular, we develop a hybrid parametric/nonparametric model that learns the “average” linear dynamics in the data using dynamic mode decomposition with control (DMDc) and the nonlinearities and model uncertainties using Gaussian process (GP) regression and compare it with total least-squares dynamic mode decomposition (tlsDMD), extended here to systems with control inputs (tlsDMDc). The proposed approach is also compared with existing methods, such as DMDc-only and GP-only models, in two tasks: controlling the stochastic nonlinear Stuart–Landau equation and predicting the flowfield induced by a jet-like body force field in a turbulent boundary layer using data from large-scale numerical simulations. 

Turbulent boundary layers are dominated by large-scale motions (LSMs) of streamwise momentum surplus and deficit that contribute significantly to the statistics of the flow. In particular, the high-momentum LSMs residing in the outer region of the boundary layer have the potential to re-energize the flow and delay separation if brought closer to the wall. This work explores the effect of selectively manipulating LSMs in a moderate Reynolds number turbulent boundary layer for separation delay via well-resolved large-eddy simulations. Toward that goal, a model predictive control scheme is developed based on a reduced-order model of the flow that directs LSMs of interest closer to the wall in an optimal way via a body force-induced downwash. The performance improvement achieved by targeting LSMs for separation delay, compared to a naive actuation scheme that does not account for the presence of LSMs, is demonstrated. 

Abstract Since the Voyager mission flybys in 1979, we have known the moon Io to be both volcanically active and the main source of plasma in the vast magnetosphere of Jupiter. Material lost from Io forms neutral clouds, the Io plasma torus and ultimately the extended plasma sheet. This material is supplied from Io’s upper atmosphere and atmospheric loss is likely driven by plasma-interaction effects with possible contributions from thermal escape and photochemistry-driven escape. Direct volcanic escape is negligible. The supply of material to maintain the plasma torus has been estimated from various methods at roughly one ton per second. Most of the time the magnetospheric plasma environment of Io is stable on timescales from days to months. Similarly, Io’s atmosphere was found to have a stable average density on the dayside, although it exhibits lateral (longitudinal and latitudinal) and temporal (both diurnal and seasonal) variations. There is a potential positive feedback in the Io torus supply: collisions of torus plasma with atmospheric neutrals are probably a significant loss process, which increases with torus density. The stability of the torus environment may be maintained by limiting mechanisms of either torus supply from Io or the loss from the torus by centrifugal interchange in the middle magnetosphere. Various observations suggest that occasionally (roughly 1 to 2 detections per decade) the plasma torus undergoes major transient changes over a period of several weeks, apparently overcoming possible stabilizing mechanisms. Such events (as well as more frequent minor changes) are commonly explained by some kind of change in volcanic activity that triggers a chain of reactions which modify the plasma torus state via a net change in supply of new mass. However, it remains unknown what kind of volcanic event (if any) can trigger events in torus and magnetosphere, whether Io’s atmosphere undergoes a general change before or during such events, and what processes could enable such a change in the otherwise stable torus. Alternative explanations, which are not invoking volcanic activity, have not been put forward. We review the current knowledge on Io’s volcanic activity, atmosphere, and the magnetospheric neutral and plasma environment and their roles in mass transfer from Io to the plasma torus and magnetosphere. We provide an overview of the recorded events of transient changes in the torus, address several contradictions and inconsistencies, and point out gaps in our current understanding. Lastly, we provide a list of relevant terms and their definitions. 

Bubble trajectories in the presence of a decaying Lamb–Oseen vortex are calculated using a modified Maxey–Riley equation. Some bubbles are shown to get trapped within the vortex in quasi-equilibrium states. All the trapped bubbles exit the vortex at a time that is only a function of the Galilei number and the vortex Reynolds number. The set of initial bubble locations that lead to entrapment is numerically determined to show the capturing potential of a single vortex. The results provide insight into the likelihood of bubble entrapment within vortical structures in turbulent flows.