Temperature and velocity measurements of a rising thermal plume

Abstract

The three-dimensional velocity and temperature fields surrounding an isolated thermal plume in a fluid with temperature-dependent viscosity are measured using Particle-Image Velocimetry and thermochromatic liquid crystals, respectively. The experimental conditions are relevant to a plume rising through the mantle. It is shown that while the velocity and the isotherm surrounding the plume can be used to visualize the plume, they do not reveal the finer details of its structure. However, by computing the Finite-Time Lyapunov Exponent fields from the velocity measurements, the material lines of the flow can be found, which clearly identify the shape of the plume head and characterize the behavior of the flow along the plume stem. It is shown that the vast majority of the material in the plume head has undergone significant stretching and originates from a wide region very low in the fluid domain, which is proposed as a contributing factor to the small-scale isotopic variability observed in ocean-island basalt regions. Lastly, the Finite-Time Lyapunov Exponent fields are used to calculate the steady state rise velocity of the thermal plume, which is found to scale linearly with the Rayleigh number, in contrast to some previous work. The possible cause and the significance of these conflicting results are discussed, and it is suggested that the scaling relationship may be affected by the temperature-dependence of the fluid viscosity in the current work.

Constraining the source of mantle plumes

“…We derive the plume height from the tracer fields; y p is defined as the highest point at which the local tracers originated from below the PIV domain (y  1.39 mm). This was found to be consistent with the definitions based on the maxima of f (Cagney et al, 2015) and the gradient of the radial velocity (Davaille et al, 2011), but contained less scatter. The rise velocity signal, u r (t), was then found by di↵erentiating y p (t) using the least-squares method.…”

“…The density and viscosity were measured in the laboratory (see Cagney et al (2015) for more details). The syrup had a density, ⇢ of 1439 kg/m 3 at 25.2 C and a coe cient of thermal expansion, ↵, of 3.1 ⇥ 10 4 C 1 .…”

“…The velocity fields are also analysed using a Lagrangian approach, which has been shown to be an e↵ective means of visualising the plume structure (Farnetani et al, 2002;Lin and van Keken, 2006;Cagney et al, 2015). The Lagrangian Coherent Structures (LCSs) can be estimated using the FiniteTime Lyapunov Exponent (FTLE) (Haller, 2015), which is a measure of the maximum rate of separation of neighbouring fluid particles over the period t 0 to t. The FTLE therefore also serves as an indicator of regions of strong fluid stretching.…”

“…The variation in the FTLE fields throughout the growth and rise of a thermal plume is described in detail elsewhere (Cagney et al, 2015), and the current discussion focuses on its relation to the VRB. Ridges in the FTLE tend to separate qualitatively distinct regions of the flow; therefore, any definition of the structures within a flow is required to be consistent with the estimated FTLE fields.…”

“…However, the numerical simulations of Farnetani and Richards (1995) and experiments by Cagney et al (2015) found that the contribution of mechanical stirring to the entrainment process was relatively insignificant when the plume was generated from an isolated heat source. Farnetani and Richards (1995) argued that the high rates observed by Gri ths and Campbell (1990) were a result of their experimental system, which involved the injection of a buoyant fluid into a vessel of fluid with a higher viscosity, rather than the use of a heater.…”