Person
Tobias Schneider
Related publications (50)
Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques
Tobias Schneider, Omid Ashtari
Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational challenge, rendering many ...
Cambridge2023Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method
Tobias Schneider, Sajjad Azimi, Omid Ashtari
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...
2022Variational methods for finding periodic orbits in the incompressible Navier Stokes equations
Tobias Schneider, Jeremy Peter Parker
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...
CAMBRIDGE UNIV PRESS2022Invariant tori in dissipative hyperchaos
Tobias Schneider, Jeremy Peter Parker
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points ...
AIP Publishing2022Modified snaking in plane Couette flow with wall-normal suction
Tobias Schneider, Sajjad Azimi
A specific family of spanwise-localised invariant solutions of plane Couette flow exhibits homoclinic snaking, a process by which spatially localised invariant solutions of a nonlinear partial differential equation smoothly grow additional structure at the ...
2021Periodic orbits exhibit oblique stripe patterns in plane Couette flow
Tobias Schneider, Florian Reetz
Spatiotemporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A recent dynamical syst ...
AMER PHYSICAL SOC2021Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states
Tobias Schneider, Florian Reetz
Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number . Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of ...
CAMBRIDGE UNIV PRESS2020Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers
Tobias Schneider, Sajjad Azimi
At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistica ...
CAMBRIDGE UNIV PRESS2020Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states
Tobias Schneider, Florian Reetz
Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flows. As a function of the strength of thermal driving and the angle of inclination, a mul ...
CAMBRIDGE UNIV PRESS2020Nondestructive Prediction of the Buckling Load of Imperfect Shells
Tobias Schneider, Emmanuel Georges Albert Virot, Emilio José Lozano Vazquez
From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to imperceptible defects ...
AMER PHYSICAL SOC2020