Much faster heat/mass than momentum transport in rotating Couette flows

Geert Brethouwer

doi:10.1017/jfm.2020.1176

Abstract

Highlights

Advective transport of heat and mass by fluid motions is fundamental to planetary and astrophysical processes and many engineering applications (Balbus & Hawley 1998; Kays, Crawford & Weigand 2005)
Optimal transport given minimal power input generates energy savings in applications (Alben 2017; Motoki, Kawahara & Shimizu 2018), but optimization is challenging since flow vortices and eddies generally transport momentum and heat/mass at similar rates. This so-called Reynolds analogy between transport of momentum and heat/mass was postulated by Reynolds (1874), and applies to many shear flows (Kays 1994; Kays et al 2005; Pirozzoli, Bernardini & Orlandi 2016) including astrophysical flows (Guan & Gammie 2009) when Prandtl numbers are close to unity (Ziefuß & Mehdizadeh 2020)
I show through direct numerical simulations (DNSs) that in existing flows, namely incompressible plane Couette flow (PCF) and Taylor–Couette flow (TCF) subject to a Coriolis force, passive tracer transport can be much faster than momentum transport, in violation of the Reynolds analogy

Summary

Introduction

Advective transport of heat and mass by fluid motions is fundamental to planetary and astrophysical processes and many engineering applications (Balbus & Hawley 1998; Kays, Crawford & Weigand 2005). Optimal transport given minimal power input generates energy savings in applications (Alben 2017; Motoki, Kawahara & Shimizu 2018), but optimization is challenging since flow vortices and eddies generally transport momentum and heat/mass at similar rates. This so-called Reynolds analogy between transport of momentum and heat/mass was postulated by Reynolds (1874), and applies to many shear flows (Kays 1994; Kays et al 2005; Pirozzoli, Bernardini & Orlandi 2016) including astrophysical flows (Guan & Gammie 2009) when Prandtl numbers are close to unity (Ziefuß & Mehdizadeh 2020). TCF with heat or mass transport finds applications in, for example, cooling of electrical motors (Fénot et al 2011) and chemical reactors and bioreactors (Nemri, Charton & Climent 2016)

Governing equations and numerical procedure

Results

Concluding remarks