Related papers: Identifying recurrent flows in high-dimensional di…
Turbulent flow control has numerous applications and building reduced-order models (ROMs) of the flow and the associated feedback control laws is extremely challenging. Despite the complexity of building data-driven ROMs for turbulence, the…
The dynamics and statistical properties of two-dimensional (2D) turbulence are often investigated through numerical simulations of incompressible, viscous fluids in doubly periodic domains. A key challenge in 2D turbulence research is…
We propose, analyze, and test a penalty projection-based efficient and accurate algorithm for the Uncertainty Quantification (UQ) of the time-dependent Magnetohydrodynamic (MHD) flow problems in convection-dominated regimes. The algorithm…
Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…
The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align…
Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent…
Hydraulic valves, for the purpose of targeted pressure relief and damping, are a ubiquitous part of modern suspension systems. This paper deals with the analytical computation of fixed points of the dynamical system of a single-stage shock…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information…
It is demonstrated that improved entrainment control of chaotic systems can maintain periodic goal dynamics near unstable periodic orbits without feedback. The method is based on the optimization of goal trajectories and leads to small…
Modelling fluid turbulence using a `skeleton' of coherent structures has traditionally progressed by focusing on a few canonical laboratory experiments such as pipe flow and Taylor-Couette flow. We here consider the stratified inclined…
The understanding of non-linear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity the beam lifetime optimisation. A detailed analysis of the multidimensional phase space…
We consider long simulations of 2D Kolmogorov turbulence body-forced by $\sin4y \ex$ on the torus $(x,y) \in [0,2\pi]^2$ with the purpose of extracting simple invariant sets or `exact recurrent flows' embedded in this turbulence. Each…
Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…
Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of…
Wakes of upswept afterbodies are often characterized by a counter-rotating streamwise vortex pair. The unsteady dynamics of these vortices are examined with a spatio-temporally resolved Large-Eddy Simulation dataset on a representative…
When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global…