We present new experiments focussing on the transient behaviour of thermal plumes. In a fluid heated from below, plumes develop once the hot thermal boundary layer (TBL) reaches a critical thickness (Howard, 1964). They rise through the fluid owing to their thermal buoyancy and comprise TBL material which empties itself into the plumes. As the TBL becomes exhausted, plumes start disappearing from the bottom up, sometimes even before reaching the upper boundary, depending on the convection intensity. Then, they finally fade away by thermal diffusion. This sequence of events shows that time‐dependence is a key‐factor when interpreting present‐day tomographic images of mantle upwellings. In particular, it could be erroneous to identify the depth of a present‐day slow seismic anomaly with the depth of its origin, or to interpret the absence of a long tail as the absence of a plume.

[1] The Amsterdam-Saint Paul plateau results from a 10 Myr interaction between the South East Indian Ridge and the Amsterdam-Saint Paul hot spot. During this period of time, the structure of the plateau changed as a consequence of changes in both the ridge-hot spot relative distance and in the strength of the hot spot source. The joint analysis of gravity-derived crust thickness and bathymetry reveals that the plateau started to form at ∼10 Ma by an increase of the crustal production at the ridge axis, due to the nearby hot spot. This phase, which lasted 3-4 Myr, corresponds to a period of a strong hot spot source, maybe due to a high temperature or material flux, and decreasing ridge-hot spot distance. A second phase, between ∼6 and ∼3 Ma, corresponds to a decrease in the ridge crustal production. During this period, the hot spot center was close to the ridge axis and this reduced magmatic activity suggests a weak hot spot source. At ∼3 Ma, the ridge was located approximately above the hot spot center. An increase in the hot spot source strength then resulted in the building of the shallower part of the plateau. The variations of the melt production at the ridge axis through time resulted in variations in crustal thickness but also in changes in the ridge morphology. The two periods of increased melt production correspond to smooth ridge morphology, characterized by axial highs, while the intermediate period corresponds to a rougher, rift-valley morphology. These variations reveal changes in axial thermal structure due to higher melting production rates and temperatures.

[1] A detailed comparison of starting laminar plumes in viscous fluids is provided using the complementary approaches of laboratory modeling and numerical simulation. In the laboratory experiments the plumes are started in a nearly isoviscous silicone oil with heat supplied through a fixed circular source. The temperature field is measured by differential interferometry and thermochromic liquid crystals. The velocity field is determined by particle image velocimetry. Numerical simulations of the laboratory experiments are performed using a finite element method that employs the measured properties of the physical oil and the heating history. No further adjustments are made to match the laboratory results. For fluids at two different viscosities and for variable power supplied to the plume there is excellent agreement in the temporal evolution and fine spatial detail of the plume. Minor differences remain, particulary in the transient stage of the plume in the low-viscosity fluid, but the differences are within the experimental uncertainties. In contrast, the assumption of constant viscosity in the numerical models leads to differences that are larger than the experimental uncertainties, demonstrating that these near-isoviscous fluids should not be considered to have constant viscosity.

No abstract

We study experimentally the influence of the transverse dimension on film flow in relatively wide channels with sidewalls. Large deviations from two-dimensional predictions are observed in the primary instability and in the post-threshold traveling waves, and the deviations are presently shown to depend strongly on fluid physical properties. Measurements for a wide range of fluid properties are found to correlate with the Kapitza number, which represents the ratio of capillary to viscous stresses. These observations point to an unexpected long-range effect of surface tension that provides transverse coherence to the flow.

Traveling waves in inclined film flow in channels of finite width are never truly two-dimensional (2D) because of a long-range effect of sidewalls. The present study documents the characteristics of the first waves that are observed beyond the primary instability (termed nominally 2D) by taking measurements in a 3000 mm long inclined facility with adjustable width up to 450 mm using a fluorescence imaging technique. It is observed that nominally 2D waves are very persistent structures with their crests attaining a parabolic shape, which is symmetric with respect to the channel centerplane irrespective of the 3D content of the inlet forcing. The apex curvature of the parabola varies inversely with channel width and Reynolds number. The wave height is maximum at the centerplane and decreases to zero at the sidewalls, irrespective of the wetting properties of the system. The linear phase velocity of nominally 2D waves is always lower than predicted by the theory for small amplitude, 2D waves, and significantly in narrow channels and/or small inclinations. The above characteristics are shown to explain discrepancies between theory and observations, in particular the recently reported deviation of the onset of the primary instability from the classical prediction [M. Vlachogiannis et al., Phys. Fluids 22, 012106 (2010)].

[1] The steady state structure of thermal plumes rising from a small heater is studied in high Prandtl number fluids. We show good agreement between laboratory experiments and numerical simulations. We study the effect of the boundaries on the plume development by numerically simulating the plume rise in very large geometries. The thermal structure of the plume axis is similar for all box sizes considered, but the velocity structure changes strongly as box sizes are increased. We show that the effect of the side boundaries becomes unimportant for large aspect ratio, but that the free-slip top boundary has a strong influence on the velocity structure under all conditions. We show that the use of an outflow boundary condition significantly reduces the influence of the top boundary. Under these conditions we recover to good precision the theoretical predictions for plumes rising in an semi-infinite half-space. The strong influence of the boundaries in high Prandtl number fluids is important in the interpretation of laboratory experiments and numerical simulation for the dynamics of the Earth's mantle.Components: 9,800 words, 15 figures.

Particle Tracking Velocimetry (PTV) is applied to measure the flow in an oscillating grid stirred tank filled with either water or shear thinning dilute polymer solutions (DPS) of Xanthan Gum (XG). There are many interests of studying turbulence in such complex non-Newtonian fluids (e.g. in the pharmaceutical, cosmetic, or food industry), and grid stirred tanks are commonly used for fundamental studies of turbulence in Newtonian fluids. Yet the case of oscillating grid flows in shear thinning solutions has been addressed recently by Lacassagne et al. (Exp Fluids 61(1):15, Phys Fluids 31(8):083102, 2019a, b), with only a single two dimensional (2D) Particle Image Velocimetry (PIV) characterization of mean flow and turbulence properties in the central vertical plane of the tank. Here, PTV data processed by the Shake The Box algorithm allows for the time resolved, three dimensional (3D) 3 components (3C) measurement of Lagrangian velocities for a large number of tracked particles in a central volume of interest of the tank. The possibility of projecting this Lagrangian information on an Eulerian grid is explored, and projected Eulerian results are compared with 2D PIV data from the previous work. Even if the mean flow is difficult to reproduce at the lowest polymer concentrations, a good agreement is found between measured turbulent decay laws, thus endorsing the use of this 3D-PTV metrology for the study of oscillating grid turbulence in DPS. The many possibilities of further analysis offered by the 3D3C nature of the data, either in the original Lagrangian form or in the projected Eulerian one, are finally discussed. Graphic Abstract