A finite element analysis on fluid motion in librating triaxial ellipsoids

Chan, Kit H.; He, Ya‐Ling; Zhang, Keke; Zou, Jun

doi:10.1002/num.21833

Cited by 6 publications

(1 citation statement)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This method allows us to extend the weakly precessing regime (Po/ √ E < 1) to the strongly precessing regime [Po/ √ E O (1)]. Since the detail of the finite-element code, its validation against a constructed exact solution, and its convergence properties have been discussed in [23](see also [24] and [25]), this section is brief.…”

Section: A a Finite-element Methods In The Tetrahedralized Cylindermentioning

confidence: 99%

Precessing cylinders at the second and third resonance: Turbulence controlled by geostrophic flow

et al. 2015

Self Cite

View full text Add to dashboard Cite

We investigate, via both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in fluid-filled circular cylinders that rotate rapidly about their symmetry axis and precess about a different axis and that are marked by radius-height aspect ratios Γ=1.045945 and Γ=1.611089. At these radius-height aspect ratios, the Poincaré force resonates directly with the two special inertial modes that have the simplest vertical structure. An asymptotic analytical solution in closed form describing weakly precessing flow is derived in the mantle frame of reference for asymptotically small Ekman numbers, showing quantitative agreement with the result of direct nonlinear numerical simulation. Our numerical simulation makes use of a finite-element method with the three-dimensional tetrahedralization of a cylindrical cavity that allows the construction of dense nodes in the vicinity of the bounding surface of the cavity for resolving the thin viscous boundary layer. It is found that axisymmetric geostrophic flow in the alternating eastward and westward direction can be generated and maintained by nonlinear and viscous effects in the viscous boundary layer. It is also found that, when the precessing rate is moderate and, consequently, the geostrophic flow is weak, nonlinear interaction between the resonant inertial mode and the nonesonant inertial modes driven by the Poincaré force and the boundary-layer influx leads to strongly turbulent flow with irregular temporal-spatial fluctuation. When the cylinders are strongly precessing such that the geostrophic flow becomes predominant, however, the effect of the geostrophic flow controls/stabilizes its nonlinear dynamics, leading to weakly turbulent flow that can be largely described by a dominant quasisteady geostrophic component and a weak nonaxisymmetric component localized in the region where the geostrophic flow is weak.

show abstract