5 papers
From synthetic turbulence to true solutions: A deep diffusion model for discovering periodic orbits in the Navier-Stokes equations
Jeremy P Parker, Tobias M Schneider
Generative artificial intelligence has shown remarkable success in synthesizing data that mimic complex real-world systems, but its potential role in the discovery of mathematicall…
Local and global bifurcations to large-scale oblique patterns in inclined layer convection
Zheng Zheng, Sajjad Azimi, Florian Reetz +1
In the inclined layer convection system, thermal convection in a Rayleigh--Bénard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varyi…
Natural convection in a vertical channel. Part 3. Bifurcations of many (additional) unstable periodic orbits and their dynamical relevance
Zheng Zheng, Laurette S. Tuckerman, Tobias M. Schneider
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and…
Natural convection in a vertical channel. Part 1. Wavenumber interaction and Eckhaus instability in a narrow domain
Zheng Zheng, Laurette S. Tuckerman, Tobias M. Schneider
In a vertical channel driven by an imposed horizontal temperature gradient, numerical simulations have previously shown steady, time-periodic and chaotic dynamics. We explore the o…
Natural convection in a vertical channel. Part 2. Oblique solutions and global bifurcations in a spanwise-extended domain
Zheng Zheng, Laurette S. Tuckerman, Tobias M. Schneider
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 driv…