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Tobias Schneider

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Related publications (43)

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Exact invariant solution reveals the origin of self-organized oblique turbulent-laminar stripes

Tobias Schneider, Tobias Klaus Kreilos, Florian Reetz

Wall-bounded shear flows transitioning to turbulence may self-organize into alternating turbulent and laminar regions forming a stripe pattern with non-trivial oblique orientation. Different experiments and flow simulations identify oblique stripe patterns ...

Nature Research2019

Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions

Tobias Schneider, Alessia Ferraro

We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields ...

2025

Predicting chaotic statistics with unstable invariant tori

Tobias Schneider, Omid Ashtari, Jeremy Peter Parker

It has recently been speculated that long-time average quantities of hyperchaotic dissipative systems may be approximated by weighted sums over unstable invariant tori embedded in the attractor, analogous to equivalent sums over periodic orbits, which are ...

American Institute of Physics2023

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 ...

American Institute of Physics2022

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 University Press2022

Spatio-temporal patterns in inclined layer convection

Tobias Schneider

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle gamma and the Rayleigh number R. The present numerical i ...

Cambridge University Press2016

Natural convection in a vertical channel. Part 2. Oblique solutions and global bifurcations in a spanwise-extended domain

Tobias Schneider, Zheng Zheng

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-d ...

Cambridge University Press2024

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 ...

Cambridge University Press2023

Ghost States Underlying Spatial and Temporal Patterns: How Nonexistent Invariant Solutions Control Nonlinear Dynamics

Tobias Schneider, Omid Ashtari, Jeremy Peter Parker, Zheng Zheng, Pierre Beck

Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in low-d ...

AMER PHYSICAL SOC2025

Modified 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 ...

Cambridge University Press2021

Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids

Tobias Schneider

Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of dra ...

2018

Secondary instability and tertiary states in rotating plane Couette flow

Tobias Schneider

Recent experimental studies have shown rich transition behaviour in rotating plane Couette flow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of equilibrium and periodic orbit tertiary states via Floquet ...

Cambridge University Press2014

Search for Unstable Relative Periodic Orbits in Channel Flow Using Symmetry-reduced Dynamic Mode Decomposition

Tobias Schneider, Omid Ashtari

In the dynamical systems approach to turbulence, unstable periodic orbits (UPOs) provide valuable insights into system dynamics. Such UPOs are usually found by shooting-based Newton searches, where constructing sufficiently accurate initial guesses is diff ...

CAMBRIDGE UNIV PRESS2025

Infinite geometric frustration in a cubic dipole cluster

Tobias Schneider

The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry, and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium orientation of eig ...

American Physical Society2015

Edge states control droplet breakup in subcritical extensional flows

François Gallaire, Tobias Schneider, Giacomo Gallino

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the nonbreaking base state is linearly stable, implying th ...

2018

Oscillating Turing Rolls as Periodic Orbits of the Lugiato-Lefever Equation

Savyaraj Ravindra Deshmukh, Andrey Shusharin, Tobias Kippenberg, Tobias Schneider, Andrey Gelash

The Lugiato-Lefever equation (LLE) is a fundamental nonlinear model of pattern formation in damped-driven optical Kerr cavities with applications ranging from fiber to chip-integrated optical resonators. In standard dimensionless form the LLE describes dyn ...

IEEE2025

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 ...

2020

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 University Press2020

Homoclinic snaking in plane Couette flow: bending, skewing and finite-size effects

Tobias Schneider

Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow exhibits homoclinic s ...

Cambridge University Press2016

Localized travelling waves in the asymptotic suction boundary layer

Tobias Schneider, Tobias Klaus Kreilos

We present two spanwise-localized travelling-wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwi ...

Cambridge University Press2016