188 citations · 1.4k across the 48 of their papers we have counts for
33 papers · 1 filter
Long-time behavior of optimal mixing in an advection-diffusion shell model
Jiajia Guo, Baole Wen, Christian Seis +1
We investigate the long-time behavior of optimal mixing in an advection-diffusion equation using a shell model framework. Our focus is on quantifying the decay of the scalar varian…
Heat transport in a hierarchy of reduced-order convection models
Matthew L. Olson, Charles R. Doering
Reduced-order models (ROMs) are systems of ordinary differential equations (ODEs) designed to approximate the dynamics of partial differential equations (PDEs). In this work, a dis…
Steady Rayleigh--Bénard convection between no-slip boundaries
Baole Wen, David Goluskin, Charles R. Doering
The central open question about Rayleigh--Bénard convection -- buoyancy-driven flow in a fluid layer heated from below and cooled from above -- is how vertical heat flux depends on…
Steady Rayleigh--Bénard convection between stress-free boundaries
Baole Wen, David Goluskin, Matthew LeDuc +2
Steady two-dimensional Rayleigh--Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls…
Exact relations between Rayleigh-Bénard and rotating plane Couette flow in 2D
Bruno Eckhardt, Charles R. Doering, Jared P. Whitehead
Rayleigh-Bénard convection (RBC) and Taylor-Couette Flow (TCF) are two paradigmatic fluid dynamical systems frequently discussed together because of their many similarities despite…
Heat transport bounds for a truncated model of Rayleigh-Bénard convection via polynomial optimization
Matthew L. Olson, David Goluskin, William W. Schultz +1
Upper bounds on time-averaged heat transport are obtained for an eight-mode Galerkin truncation of Rayleigh's 1916 model of natural thermal convection. Bounds for the ODE model---a…
Wall-to-wall optimal transport in two dimensions
Andre N. Souza, Ian Tobasco, Charles R. Doering
Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of ve…
Thermal Convection over Fractal Surfaces
Srikanth Toppaladoddi, Andrew J. Wells, Charles R. Doering +1
We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-Bénard convection in cells with a fractal boundary in two dimensions for and…
Diffusion-limited mixing by incompressible flows
Christopher J. Miles, Charles R. Doering
Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived…
Optimal heat transfer and optimal exit times
Florence Marcotte, Charles R. Doering, Jean-Luc Thiffeault +1
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, wit…
Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations
Diego A. Ayala, Charles R. Doering, Thilo M. Simon
We derive and assess the sharpness of analytic upper bounds for the instantaneous growth rate and finite-time amplification of palinstrophy in solutions of the two-dimensional inco…
Optimal wall-to-wall transport by incompressible flows
Ian Tobasco, Charles R. Doering
We consider wall-to-wall transport of a passive tracer by divergence-free velocity vector fields . Given an enstrophy budget $\langle |\nabla \mathbf{u}|^{2} \rangle \l…
Bounds for convection between rough boundaries
David Goluskin, Charles R. Doering
We consider Rayleigh-Bénard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates wi…
Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field
Basile Gallet, Charles R. Doering
We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: fo…
Wall to Wall Optimal Transport
Pedram Hassanzadeh, Gregory P. Chini, Charles R. Doering
The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for…
Bounds on Surface Stress Driven Shear Flow
George I. Hagstrom, Charles R. Doering
The background method is adapted to derive rigorous limits on surface speeds and bulk energy dissipation for shear stress driven flow in two and three dimensional channels. By-prod…
Internal heating driven convection at infinite Prandtl number
Jared P. Whitehead, Charles R. Doering
We derive an improved rigorous bound on the space and time averaged temperature of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries…
"Ultimate state" of two-dimensional Rayleigh-Benard convection between free-slip fixed temperature boundaries
Jared P. Whitehead, Charles R. Doering
Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard convection between stress-free isothermal boundaries are derived from the Boussinesq approxi…
Models and measures of mixing and effective diffusion
Zhi Lin, Katarína Bodová, Charles R. Doering
Mixing a passive scalar field by stirring can be measured in a variety of ways including tracer particle dispersion, via the flux-gradient relationship, or by suppression of scalar…
Optimal stirring strategies for passive scalar mixing
Zhi Lin, Jean-Luc Thiffeault, Charles R. Doering
We address the challenge of optimal incompressible stirring to mix an initially inhomogeneous distribution of passive tracers. As a quantitative measure of mixing we adopt the $H^{…
The Mixing efficiency of open flows
Jean-Luc Thiffeault, Charles R. Doering
Mixing in open incompressible flows is studied in a model problem with inhomogeneous passive scalar injection on an inlet boundary. As a measure of the efficiency of stirring, the…
Extreme vorticity growth in Navier-Stokes turbulence
Joerg Schumacher, Bruno Eckhardt, Charles R. Doering
According to statistical turbulence theory, the ensemble averaged squared vorticity rho_E is expected to grow not faster than drho_E/dt ~ rho_E^{3/2}. Solving a variational problem…
Destabilizing Taylor-Couette flow with suction
Basile Gallet, Charles R. Doering, Edward A. Spiegel
We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linear…
Variation on the Kolmogorov Forcing: Asymptotic Dissipation Rate Driven by Harmonic Forcing
B. Rollin, Y. Dubief, C. R. Doering
The relation between the shape of the force driving a turbulent flow and the upper bound on the dimensionless dissipation factor is presented. We are interested in non-trivial…