Dynamics of Thermal Plumes: Comparison of Laboratory and Numerical Models

Plumes originating from point sources have been widely studied by analytical, numerical and experimental techniques to better understand mantle plume dynamics using fluid mechanical constraints. However, a detailed comparison is made difficult due to the widely different contexts (injection of hot fluids or conductive heating, use of different heating modes) and assumptions of fluid dynamical parameters. This has led to a wide range of different scaling laws, diverse ideas about plume shapes and sizes, and diverging thoughts about entrainment in the plume head and tail. It is essential to investigate how the technical differences and underlying assumptions influence our understanding of plume dynamics, in order to figure out which configuration should apply to mantle plumes in the Earth. To facilitate this study we compare laboratory experiments of a plume growing in a viscous fluid from a heated patch with numerical models that attempt to reproduce the laboratory conditions as closely as possible. A new method of visualization set up in the IPG laboratory allows to visualize in situ the thermal and dynamical structures of the convection patterns on a 2-D section of the tank, without interfering with the flow. The numerical simulations are axisymmetric finite element simulations of starting plumes where we use the measured properties of the laboratory fluids under the assumptions of infinite Prandtl number and laminar flow. We find excellent quantitative agreement between the two fully independent approaches, in both temperature and detailed velocity field. That suggests that the laboratory simulation can be accurately described by laminar Boussinesq low at infinite Prandtl number, at least for finite size boxes. We use the numerical models to understand the origin of remaining minor quantitative differences, especially to estimate the effects of the boundary conditions and the influence of the weak temperature-dependence of viscosity. We also quantify the power leakage from the heater in the laboratory setup by measuring the heat flux through the plume stem in the numerical models. The combination of these numerical analyses allows to find reasonable agreement with independently derived scaling laws for the conduit velocity and the head dynamics versus power for thermal plumes, depending on the geometry of the box.