Fabian Bleitner

Heat transport properties for buoyancy driven fluids

The dynamics of buoyancy driven fluids, such as Rayleigh-Bénard convection, are apparent in a vast variety of physical phenomena, ranging from astrophysical over geophysical range scales, as in atmospheric or earth mantle convection to every day applications such as cooking in a pot. In this project our primary objective is to study the evolution of such systems and in particular providing rigorous mathematical bounds for the apparent physically relevant quantities. In the context of Rayleigh-Bénard convection we aim to prove scaling laws on the average upward heat transport, described by the Nusselt number, with respect to the system parameters at hand, while in a thermally non-diffusive setting we are investigating in the large time behavior and the stability of the hydrostatic equilibrium, where the buoyancy force is balanced by the pressure. This research focuses in refining previous results and extending them to more realistic settings such as allowing roughness or slip on the boundaries.

Advisor: Prof. Dr. Camilla Nobili

Co-Advisor: Prof. Dr. Ingenuin Gasser

14.-16.08.2023

Workshop on Stability, Mixing and Fluid Dynamics, Münster (GER): “Navier-Slip Boundary Conditions for Buoyancy Driven Two Dimensional Flows”
https://www.uni-muenster.de/MathematicsMuenster/events/2023/fluids23.shtml

 

14.-18.05.2023

SIAM Applications of Dynamical Systems, Portland (USA): “Bounds on Heat Transport for Rayleigh-Bénard Convection with Rough Navier-Slip Boundaries”
https://www.siam.org/conferences/cm/conference/ds23

 

20.-22.03.2023

Workshop on Modeling, Simulation & Optimization of Fluid Dynamic Applications 2023, Groß Schwansee (GER): “Navier slip boundary conditions for two dimensional Boussinesq equations”
https://user.math.uni-kiel.de/~malte-braack/cse2023/index.html

 

04.-06.01.2023

Firedrake User and Developer Workshop, Totnes (UK): “Two-dimensional Rayleigh-Bénard convection with Navier-slip boundary conditions on curved boundaries” https://www.firedrakeproject.org/firedrake_22.html

 26.-30.09.2022

Horizons in Nonlinear PDEs, Ulm (GER): “Heat Transfer Properties for Rayleigh-Bénard Convection with Navier-Slip Boundary Conditions”
https://www.uni-ulm.de/mawi/iaa/forschung/horizons-in-non-linear-pdes-summer-school-2022/

 

04.-08.04.2022

Mathematical Advances in Geophysical Flows, Marseille (FRA): “Bounds on the Heat Transfer for Rayleigh-Bénard Convection between Rough Navier-Slip Boundaries”
https://www.chairejeanmorlet.com/2575.html

 

21.-24.03.2022

Workshop on Modeling, Simulation & Optimization of Fluid Dynamic Applications 2022, Groß Schwansee (GER): “Lower Bounds for the Advection-Hyperdiffusion Equation”
https://www.c3s.uni-hamburg.de/rtg2583/teaching/workshops/workshop-maerz-2022.html

 

22.-25.03.2021

Workshop on Modeling, Simulation & Optimization of Fluid Dynamic Applications 2021 (Online): “The Background Flow Method for the Kuramoto-Sivashinsky Equation”
https://www.c3s.uni-hamburg.de/rtg2583/teaching/workshops/workshop-maerz-2021

 

 

1. Bleitner, F., Carlson, E., Nobili, C.: “Large time behaviour of the 2D thermally non-diffusive Boussinesq equations with Navier-slip boundary conditions”, submitted,  preprint arXiv:2309.05400, 2023

2. Bleitner, F., Nobili, C.: “Lower Bounds for the Advection-Hyperdiffusion Equation”, to appear in “Modeling, Simulation and Optimization of Fluid Dynamic Applications”, Springer, preprint arXiv:2302.13078, 2023

3. Bleitner, F., Nobili, C.: “Bounds on heat transport for two-dimensional buoyancy driven flows between rough boundaries”, Nonlinearity 37 ( https://arxiv.org/abs/2301.00226) , 2024