Publications de Tobias Schneider

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 ...

Cambridge2023

Constructing 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 ...

2022

Variational 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 PRESS2022

Invariant 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 Publishing2022

Periodic 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 SOC2021

Invariant 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 PRESS2020

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 PRESS2020

Invariant 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 PRESS2020

Nondestructive 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

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Tobias Schneider

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Invariant tori in dissipative hyperchaos

Modified snaking in plane Couette flow with wall-normal suction

Periodic orbits exhibit oblique stripe patterns in plane Couette flow

Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states

Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states

Nondestructive Prediction of the Buckling Load of Imperfect Shells

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Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Invariant tori in dissipative hyperchaos

Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states

Periodic orbits exhibit oblique stripe patterns in plane Couette flow

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Modified snaking in plane Couette flow with wall-normal suction

Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states

Nondestructive Prediction of the Buckling Load of Imperfect Shells