Pears, MIB; (2015) Stall and Collapse in Mantle Plumes: An experimental and numerical fluid dynamics perspective. Doctoral thesis , UCL (University College London).

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Abstract

Collapsing thermal plumes were investigated through experimental and numerical simulations. Collapsing plumes are an uncommon fluid dynamical phenomenon, usually observed when the heat source is removed. A series of fluid dynamical experiments were conducted on thermal plumes at a variety of \nohyphens{temperature} and viscosity contrasts, in a cubic plexiglas tank of inner side dimension 26.5cm and no-slip sides. The fluid was heated by a small 2cm diameter heater. Experimental fluids included Lyle’s Golden syrup and ADM’s Liquidose 436 syrup, which have strongly temperature-dependent viscosities and high Prandtl numbers (10$^{3}$-10$^{5}$ at \nohyphens{experimental} conditions). Visualisation techniques included white light shadowgraphs and Stereoscopic \nohyphens{Particle} Image Velocimetry (SPIV) of the tank's central plane. Temperature \nohyphens{contrasts} ranged from 3-60$^{\circ}$C, and two differing forms of collapse were identified. At very low temperature differences \enquote{stalled} collapse was observed, where the plumes stall in the lower third of the tank before collapsing. At temperature differences between 7-23$^{\circ}$C normal plume evolution occurred, until \enquote{lenticular} collapse developed between midway and two-thirds of the distance from the base of the tank. The \enquote{lens shape} originated in the top of the head and was present throughout collapse. At temperatures above $\Delta$T=23$^{\circ}$C, the plumes followed the expected growth and shape and the head flattened out at the top of the tank. Thermal collapse remains difficult to explain given experimental conditions (continuous \nohyphens{heating}). Instead, it is possible that small density differences arising from crystallisation at ambient \nohyphens{temperatures} changes plume buoyancy and therefore induces \enquote{lenticular} collapse. The \nohyphens{evolution} of the refractive index of the syrup through time to ascertain this possibility was measured. \nohyphens{Additionally}, SPIV revealed the presence of a large, downwelling, low velocity mass in the tank that inhibited the growth of low temperature difference \enquote{stalled} collapse plumes. In the mantle it is likely that the \enquote{stalled} collapse plumes would be unable to be detected by tomography because they would be unable to traverse far from the thermal boundary layer and would collapse back to the base. This would mean that they would have little impact on redistributing material in the mantle. The plumes in this \enquote{stalled} collapse regime had rise times comparable to diffusion times, which is an additional reason for the collapse. The \enquote{lenticular} collapse in the mantle could cause depletion of a deep-source and redistribute the material in the region where the plume began to collapse with some material flowing back to the base of the mantle. Numerical simulations using Fluidity\footnote{Fluidity, is an adaptive mesh finite element package} were undertaken to explore the parameter range where the two collapse phenomena were observed experimentally. These simulated plumes did not show signs of collapse in the purely thermal simulation but at temperature differences up to 14$^{\circ}$C the plumes stalled and were unable to ascend to the top of the tank. The aspect ratio of the tank was changed to explore the effect this had on plume stalling. At increased tank height the plume ascended further in the tank whilst the conduit radius remained constant. However, the very low temperature difference plumes remained unable to reach the upper surface of the tank. In contrast, when the tank width was increased the plumes ascended a little further in the tank but stalled at an earlier time and the plume conduit width generally increased. This implied that the tank width was inhibiting the growth of the plume marginally. Therefore, changing the aspect ratio of the tank does not inhibit the stalling of the simulated plumes and is unlikely to be influencing the experimental plumes growth, stalling and collapse.

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