Abstract : The transport of momentum and heat by coherent structures in turbulence has long been a central concern in fluid mechanics, especially because of its critical importance in industry, geophysics, and astrophysics. Significant progress has been made in recent years in Navier-Stokes-based variational principles, asymptotic analysis, and dynamical systems theory, finally producing meaningful results for practical applications. This mini-symposium aims to bring together experts with a wide range of related backgrounds, from applied to fundamental, to exchange the latest findings and to set new research directions.
[04104] Analysis of transport by coherent structures; overview
Format : Talk at Waseda University
Author(s) :
Kengo Deguchi (Monash University)
Abstract : A primary ongoing problem in fluid mechanics is the need to comprehend the large-scale average transport features of turbulent flows. For example, the prediction or improvement of heat/momentum transport is critical in a wide range of applications, but currently it relies on trial and error with massive amounts of experiments/simulations. A natural question arises: can we explain the mechanism of the transport logically based on Navier-Stokes equations? The key to the answer seems to lie in the coherent structures in turbulence, and an overview of recent developments will be given in the talk.
[04490] Analysis, modeling, and simulation of slow-fast quasilinear dynamical systems
Format : Online Talk on Zoom
Author(s) :
Greg Chini (University of New Hampshire)
Abstract : We describe a new formalism for quasilinear systems exhibiting slow mean and fast, possibly unstable, linearized fluctuation dynamics. Using ODE and PDE models, we show that a slaving relation for the fluctuation amplitude can be derived by exploiting the tendency for the dynamics to self-organize on a slow marginal-stability manifold. Transient, fully nonlinear bursting events also can be predicted and systematically incorporated into our formalism. We conclude with an application to strongly stratified Kolmogorov flow.
[04122] Steady coherent states in Rayleigh–Bénard convection
Format : Online Talk on Zoom
Author(s) :
Baole Wen (New York Institute of Technology)
David Goluskin (University of Victoria)
Gregory Chini (University of New Hampshire)
Charles Doering (University of Michigan)
Abstract : A central question in Rayleigh--B\'enard convection is how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ as $Ra\to\infty$. Experiments/simulations have yet to rule out either `classical' 1/3 or `ultimate' 1/2 asymptotic scaling. Here we show that certain steady rolls have classical 1/3 scaling and they transport more heat than turbulent experiments/simulations at comparable parameters. If turbulent heat transport continues to be dominated by steady transport asymptotically, it cannot achieve ultimate scaling.
[04022] Optimal heat transport using branching flows
Format : Online Talk on Zoom
Author(s) :
Anuj Kumar (University of California Santa Cruz)
Abstract : We are interested in the design of forcing in the Navier–Stokes equation such that the resultant flow maximizes the transport of a passive temperature between two differentially heated walls for a given power supply budget. Previous work established that the transport cannot scale faster than 1/3-power of the power supply. Recently, Doering & Tobasco (CPAM’19) constructed self-similar two-dimensional steady branching flows, saturating this upper bound up to a logarithmic correction to scaling. We present a construction of three-dimensional “branching pipe flows” that eliminates the possibility of this logarithmic correction and for which the corresponding passive scalar transport scales as a clean 1/3-power law in power supply. Our flows resemble previous numerical studies of the three-dimensional wall-to-wall problem by Motoki, Kawahara & Shimizu (J. Fluid Mech. vol.851, 2018, p.R4}). However, using an unsteady branching flow construction, it appears that the 1/3 scaling is also optimal in two dimensions. After carefully examining these designs, we extract the underlying physical mechanism that makes the branching flows “efficient.”
[04552] Optimisation of horizontal periodicity in steady Rayleigh–Bénard convection
Format : Talk at Waseda University
Author(s) :
Shingo Motoki (Osaka University)
Genta Kawahara (Osaka University)
Masaki Shimizu (Osaka University)
Abstract : Using a Newton–Krylov iteration, we have investigated steady solutions to the Boussinesq equations for Rayleigh–Bénard convection in a square periodic domain between horizontal walls with a constant temperature difference. We have found that a family of three-dimensional steady solutions with an optimal horizontal periodicity achieves higher wall-to-wall heat flux than those of two-dimensional solutions and turbulent states and exhibits the classical scaling commonly observed in convective turbulence.
[04406] Chaos and unstable periodic orbits in subcritical Taylor-Couette flow
Format : Talk at Waseda University
Author(s) :
Baoying Wang (Universitat Politècnica de Catalunya)
Roger Ayats (Institute of Science and Technology Austria (ISTA))
Kengo Deguchi (Monash University)
Alvaro Meseguer (Universitat Politècnica de Catalunya)
Fernando Mellibovsky (Universitat Politècnica de Catalunya)
Abstract : Although spectral approximation of turbulence typically requires a large number of modes, for relatively low Reynolds numbers the turbulent attractor lies on a low-dimensional manifold in phase space. The most extreme case is when the main features of the chaotic attractor can be quantified by a one-dimensional map on Poincaré section. We find this can indeed happen in subcritical Taylor-Couette flow, which should offer an important test case for connecting turbulence and periodic orbit analysis.
[03988] The state-space structure of wall turbulence at high Reynolds numbers: a reduced-order model perspective
Format : Talk at Waseda University
Author(s) :
Matthew McCormack (University of Edinburgh)
André V. G. Cavalieri (Instituto Tecnológico de Aeronáutica)
Yongyun Hwang (Imperial College London)
Abstract : Invariant solutions to the Navier-Stokes equations have been viewed to form the state-space skeleton of turbulence at low Reynolds numbers. However, as Reynolds number is increased, most of these invariant solutions currently computable were recently shown to be able to depict only partial processes of turbulence, and they neither resemble full-scale turbulence statistically nor dynamically. In this talk, I will present our recent efforts to understand the state-space structure of turbulence at moderately high Reynolds numbers in terms of invariant solutions utilising a reliable and robust reduced-order model.
[03140] Coherent structures and the direct cascade in two-dimensional turbulence
Format : Talk at Waseda University
Author(s) :
Roman O Grigoriev (Georgia Institute of Technology)
Mateo Reynoso (Georgia Institute of Technology)
Dmitriy Zhigunov (Georgia Institute of Technology)
Abstract : We describe a mechanism of the direct cascade in 2D turbulence which explains when the predictions of the classical Kraichnan-Leith-Batchelor theory hold, when deviations are found, and what causes these deviations. Coherent structures of two types play a key role in our theory: the first type describes the dynamics of the largest scales accessible to the flow, while the second type describes the dynamics of small-scale filamentary vorticity stretched and folded by the large-scale flow.
