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Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. Turbulent flows promote efficient transport and mixing by their inherent randomness. Laminar flows lack such a natural mixing mechanism and…
One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are…
The Sun is a magnetic star, and the only spatio-temporally resolved astrophysical system displaying turbulent MHD thermal convection. This makes it a privileged object of study to understand fluid turbulence in extreme regimes and its…
In this paper we develop a method for the estimation of {\bf T}ransport {\bf I}nduced by the {\bf M}ean-{\bf E}ddy interaction (TIME) in two-dimensional unsteady flows. The method is built on the dynamical systems approach and can be viewed…
Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured,…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic…
In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three-dimensional, their detection remains challenging in the most common situation, when…
The evolution of organismal populations is not typically thought of in terms of classical mechanics. However, many of the conceptual models used to approximate evolutionary trajectories have implicit parallels to dynamic physical systems.…
Context. The one-dimensional treatment of turbulent convection had large successes until the early 2000s. However, the recent abundance and precision of observational data shows that this problem is far from solved. A modern approach should…
Mesoscale eddies are critical in ocean circulation and the global climate system. Standard eddy identification methods are usually based on deterministic optimal point estimates of the ocean flow field. However, uncertainty exists in…
The particle trajectories in irrotational, incompressible and inviscid deep-water surface gravity waves are open, leading to a net drift in the direction of wave propagation commonly referred to as the Stokes Drift, which is responsible for…
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier--Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms.…
Computational Fluid Dynamics (CFD) is an indispensable method of fluid modelling in engineering applications, reducing the need for physical prototypes and testing for tasks such as design optimisation and performance analysis. Depending on…
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of…
We document the long-term evolution of an Agulhas ring detected from satellite altimetry using a technique from nonlinear dynamical systems that enables objective (i.e., observer-independent) eddy framing. Such objectively detected eddies…
We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a…