The background method: theory and computations

G Fantuzzi, A Arslan, A Wynn - … Transactions of the …, 2022 - royalsocietypublishing.org
The background method is a widely used technique to bound mean properties of turbulent
flows rigorously. This work reviews recent advances in the theoretical formulation and …

The role of boundary conditions in scaling laws for turbulent heat transport

C Nobili - arxiv preprint arxiv:2112.15564, 2021 - arxiv.org
In most results concerning bounds on the heat transport in the Rayleigh-B\'{e} nard
convection problem no-slip boundary conditions for the velocity field are assumed …

Optimal cooling of an internally heated disc

I Tobasco - … Transactions of the Royal Society A, 2022 - royalsocietypublishing.org
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of
optimal heat exchangers, we consider incompressible flows that most efficiently cool an …

Micropolar meets Newtonian. The Rayleigh–Bénard problem

P Kalita, JA Langa, G Łukaszewicz - Physica D: Nonlinear Phenomena, 2019 - Elsevier
We consider the Rayleigh–Bénard problem for the two-dimensional Boussinesq system for
the micropolar fluid. Our main goal is to compare the value of the critical Rayleigh number …

On the optimal design of wall‐to‐wall heat transport

CR Doering, I Tobasco - Communications on Pure and Applied …, 2019 - Wiley Online Library
We consider the problem of optimizing heat transport through an incompressible fluid layer.
Modeling passive scalar transport by advection‐diffusion, we maximize the mean rate of …

Bounds on buoyancy driven flows with Navier-slip conditions on rough boundaries

F Bleitner, C Nobili - Nonlinearity, 2024 - iopscience.iop.org
Bounds on buoyancy driven flows with Navier-slip conditions on rough boundaries Page 1
Nonlinearity PAPER • OPEN ACCESS Bounds on buoyancy driven flows with Navier-slip …

Geometrical dependence of optimal bounds in Taylor–Couette flow

A Kumar - Journal of Fluid Mechanics, 2022 - cambridge.org
This paper is concerned with the optimal upper bound on mean quantities (torque,
dissipation and the Nusselt number) obtained in the framework of the background method …

Exhausting the background approach for bounding the heat transport in Rayleigh–Bénard convection

Z Ding, RR Kerswell - Journal of Fluid Mechanics, 2020 - cambridge.org
Exhausting the background approach for bounding the heat transport in Rayleigh–Bénard
convection Page 1 J. Fluid Mech. (2020), vol. 889, A33. c The Author(s), 2020. Published by …

Relationship between the methods of bounding time averages

S Chernyshenko - arxiv preprint arxiv:1704.02475, 2017 - arxiv.org
The problem of finding bounds of time-averaged characteristics of dynamical systems, such
as the bound on the mean energy dissipation rate in a turbulent flow governed by …

[BOOK][B] Bulk properties and flow structures in turbulent flows

A Kumar - 2023 - search.proquest.com
Turbulence is ever-present: from flows in engineering, such as a wake behind a submarine,
the boundary layer over an aircraft wing, and the swirl in an internal combustion engine, to …