On the origins of steady streaming in precessing fluids

Abstract

Abstract

Zonal flow in a resonant precessing cylinder

“…Using this value and (4.25), the total kinetic energy is found to be E = 0.0025. This kinetic energy is approximately 30 % lower than the kinetic energy found in numerical simulations by isolating the azimuthal wavenumber m = 1 (Albrecht et al 2021). Equation (5.1) thus underestimates the amplitude A by approximately 14 % in this case.…”

“…In order to compare our theoretical results with the numerical results of Albrecht et al (2021), we focus on the aspect ratio h = 1.62 for which the (1, 1) resonance is obtained at a forcing frequency ω 1,1 = 1.181 (table 1). The tilt angle is small, ϕ = 0.4 • , and corresponds to a forcing amplitude ε = −0.00127, such that there is no instability in the numerical simulations at Ek = 1.538 × 10 −4 .…”

“…In geophysical fluid dynamics, a zonal flow is defined as an axisymmetric azimuthal velocity. This zonal flow has also been called mean streaming flow (Albrecht et al 2021) since it is mostly generated by streaming through the action of Reynolds stresses (Riley 2001). It is important to note that this zonal flow may not be invariant along the axial direction.…”

“…We then calculate, with an asymptotic approach, the five components of the zonal flow in § 4. The proposed theoretical solution is then compared with the numerical results of Albrecht et al (2021) in § 5 and the experimental results of Meunier et al (2008) in § 6. The sign of the angular momentum of the zonal flow (prograde or retrograde) is discussed in § 7.…”

Shaken and Stirred: When Bond Meets Suess–de Vries and Gnevyshev–Ohl

“…To the best of our knowledge, there have been no serious attempts to tackle this problem in its full beauty, including a realistic orbital motion, the 7 degree inclination of the Sun's rotation axis, and an alleged non-sphericity of the tachocline with a prolateness that might even vary with the magnetic field strength (Dikpati and Gilman, 2001). In this respect, we recall a relatively recent result on the similar problem of precession, for which a significant braking of the (solid body like) rotational profile was observed already for weak precessional forcing (Giesecke et al, 2018(Giesecke et al, , 2019Albrecht et al, 2021). If such a braking effect would also occur in the solar spin-orbit coupling problem (cf.…”