A Laboratory Study of Vortical Structures in Rotating Convection Plumes

A laboratory study of the columnar vortex structure in rotating Rayleigh-B\'{e}nard convection is conducted. A rectangular water tank is uniformly heated from below and cooled from above, with $Ra=(6.35\pm 0.77)\times 10^{7}$, $Ta=9.84\times 10^{7}$, $\Pr =7.34$. The columnar vortices are vertically aligned and quasi steady. Two 2D PIV systems were used to measure velocity field. One system performs horizontal scans at 9 different heights every 13.6s, covering 62{\%} of the total depth. The other system scans vertically to obtain the vertical velocity profile. The measured vertical vorticity profiles of most vortices are quasi-linear with height while the vertical velocities are nearly uniform with only a small curvature. A simple model to deduce vertical velocity profile from vertical vorticity profile is proposed. Under quasi-steady and axisymmetric conditions, a ``vortex core'' assumption is introduced to simplify vertical vorticity equation. A linear ODE about vertical velocity is obtained whenever a vertical vorticity profile is given and solved with experimental data as input. The result is approximately in agreement with the measurement.