Resonant and non-resonant flows in longitudinally and latitudinally librating spheres

Lin，Yufeng1; Hollerbach，Rainer2,3; Noir，Jérome4; Vantieghem，Stijn4

2023-07-01

10.1063/5.0142705

Physics of Fluids   Impact Factor & Quartile

1070-6631

1089-7666

We investigate the linear response to longitudinal and latitudinal libration of a rapidly rotating fluid-filled sphere. Asymptotic methods are used to explore the structure of resonant modes in both cases, provided that the nondimensional libration frequency is in the range ω ∈ [ 0 , 2 ] . High-resolution numerics are then used to map out this entire frequency range, picking out both the resonant peaks as well as the non-resonant troughs in between. The kinetic energy is independent of the Ekman number E at the peaks and scales as E 1 / 2 at the troughs. As the Ekman number is reduced, down to E = 10 − 10 for longitudinal libration and E = 10 − 9 for latitudinal libration, the frequency response also exhibits an increasingly fractal structure, with more and more peaks and troughs emerging. The spacing between peaks is seen to follow an E 1 / 2 self-similarity factor. However, detailed examinations of some of the more prominent troughs shows that their widths follow an E ∼ 0.23 self-similarity factor.

SCI

English

First

NSFC["42174215","12250012"] ; National Key Ramp;D Program of China[2022YFF0503200] ; STFC["ST/S000275/1","ST/W000873/1"] ; EPSRC[EP/R014604/1] ; SNSF["200021_140708","200021_185088"] ; Swiss National Supercomputer Centre (CSCS)[s1111] ; Swiss National Science Foundation (SNF)["200021_185088","200021_140708"]

Mechanics ; Physics

Mechanics ; Physics, Fluids & Plasmas

WOS:001034275700003

AIP Publishing

PHYSICS

2-s2.0-85166087475

Scopus

1.Department of Earth and Space Sciences,Southern University of Science and Technology,Shenzhen,518055,China
2.Department of Applied Mathematics,University of Leeds,Leeds,LS2 9JT,United Kingdom
3.Isaac Newton Institute for Mathematical Sciences,Cambridge,20 Clarkson Road,CB3 0EH,United Kingdom
4.Institut für Geophysik,ETH Zürich,Zürich,Sonneggstrasse 5,CH-8092,Switzerland

Lin，Yufeng,Hollerbach，Rainer,Noir，Jérome,et al. Resonant and non-resonant flows in longitudinally and latitudinally librating spheres[J]. Physics of Fluids,2023,35(7).

Lin，Yufeng,Hollerbach，Rainer,Noir，Jérome,&Vantieghem，Stijn.(2023).Resonant and non-resonant flows in longitudinally and latitudinally librating spheres.Physics of Fluids,35(7).

Lin，Yufeng,et al."Resonant and non-resonant flows in longitudinally and latitudinally librating spheres".Physics of Fluids 35.7(2023).