Nonlinear spin-up of a thermally stratified fluid in cylindrical geometries

TL;DR

This study visualizes the complex three-dimensional flow evolution during the spin-up of a thermally stratified fluid in cylindrical geometries, highlighting the transition from axisymmetric to non-axisymmetric flow patterns.

Contribution

It demonstrates the feasibility of transitioning from axisymmetric to non-axisymmetric flow during spin-up in thermally stratified fluids within cylindrical containers.

Findings

Transition from axisymmetric to non-axisymmetric flow observed

Flow patterns depend on spin-up time and stratification

Visualization confirms theoretical predictions of flow behavior

Abstract

This is an entry for the Gallery of Fluid Motion of the 62nd Annual Meeting of the APS-DFD (fluid dynamics videos). This video shows the three-dimensional time-dependent incremental spin-up of a thermally stratified fluid in a cylinder and in an annulus. The rigid bottom/side wall(s) are non-slip, and the upper surface is stress-free. All the surfaces are thermally insulated. The working fluid is water characterized by the kinematic viscosity $\nu$ and thermal diffusivity $\kappa$. Initially, the fluid temperature varies linearly with height and is characterized by a constant buoyancy frequency $N$, which is proportional to the density gradient. The system undergoes an abrupt change in the rotation rate from its initial value $\Omega_i $, when the fluid is in a solid-body rotation state, to the final value $\Omega_f$. Our study reveals a feasibility for transition from an axisymmetric initial circulation to non-axisymmetric flow patterns at late spin-up times.