• rotation rate,
• high voltage,
• temperature difference and
• cold side temperature.

In all the experiment runs described in the present document, solid body rotation with varying rotation rate, fixed high voltage of 6 kV (or higher if available) and varying temperature difference and cold side temperature will be applied. For all the objectives, the flow pattern shall be observed by Wollaston Shearing Interferometry (WSI) and by an optional technique.

Objective 1:
Thermal convection between non-rotating spherical shells, under a central force field. This objective shall include hysteresis effects investigation (i. e. sequence of experiment points with decreasing temperature difference across the spheres).
Objective 2:
Thermal convection between rotating spherical shells, regime of low rotation (0.008 to 0.16 Hz), under a central force field.
Objective 3:
Thermal convection between rotating spherical shells, regime of medium rotation (0.2 to 1 Hz), under a central force field.
Objective 4:
Thermal convection between rotating spherical shells, regime of high rotation (1.2 to 2 Hz) where high centrifugal effects are expected (high Froude numbers), under a central force field.
Besides WSI, an additional optical diagnostic for each experimental point for a better analysis of the observed fluid flow state and its dynamic behaviour is considered. [see: F6-PR-BTU-0010, Scientific Justification of using Shadowgraphy in GeoFlow experiments, Issue 1, 15/3/2007].

BACKGROUND

The main feature of GeoFlow II is its geometry. That is, at variance with experiments that are performed in planar, cartesian geometries, GeoFlow II aims at observing flows in spherical geometries that are subjected to a central force field.
Such a condition, obviously impossible to reach on ground, is achieved by simulating buoyancy driven convection through a central dielectrophoretic field in reduced gravity conditions, providing a benchmark for a rich variety of numerical problems which are still a challenge for scientific research.
The present project forms a follow up of the first GeoFlow I experiment. For a detailed description of the experiment and an overview of the preparatory activities, see here and references. [Ref. 1- Ref. 11]. The activity here described is to be carried out in the same configuration (geometry, range of accessible Rayleigh numbers, temperature difference) but with a sample that displays a pronounced temperature dependent viscosity. This topic is of high interest in mantle convection studies, as temperature dependent viscosity is believed to play a fundamental role in mantle convection [Ref. 12]. The extremely high temperature difference across the mantle generates a variation of viscosity up to a factor 105 that deeply influences the properties of the flow in the entire domain. In particular, it affects the properties of the upper boundary layer that, being very viscous, takes the form of a so-called stagnant lid, where convection is heavily depressed and conduction becomes an important heat transport mechanism. Viscosity contrast generated stagnant lids are an essential feature of mantle convection and are at the basis of the still not fully explained formation of plate tectonics [Ref. 13].
Temperature dependent viscosity convection has been subjected to numerous numerical studies [see Ref. 14 and references therein] mainly carried out in Cartesian box geometries, that elucidate the transition to different convective regimes as viscosity contrast is increased. A current limitation of these studies is the lack of experimental evidence and the few results obtained in spherical geometry. Purpose of GeoFlow II is to observe the basic properties of the flow in the small viscosity contrast regime, by achieving the maximal viscosity variation allowed with the hardware limitation of the GeoFlow insert of the Fluid Science Laboratory. Even if the flow parameters are far from representing the actual ones found inside the mantle (a condition that poses an insurmountable experimental challenge), they are to be considered as the very first verification of present spherical numerical models. This will contribute to the extension of state of the art simulations to more realistic threedimensional spherical geometry, a clear trend of present research activities in the study of Earth mantle evolution [Ref. 14].

Experiments on thermal convection with a simulated central force field (similar to the gravity field acting on planets) are needed to understand large scale geophysical motions. Such a central symmetric force field can be produced by applying a high voltage potential between an inner and an outer sphere using the effect of dielectrophoretic force field. The simulated central gravity acceleration is of the order
of 10^-1 g₀ [Ref. 1], where g₀ is the terrestrial gravity acceleration. Such kinds of experiments are therefore impossible to be carried out on ground, and require a reduced gravity environment where the uniaxial acceleration is order of magnitudes smaller than the central symmetric one.

Previous flight experiments (precursors)
– Drop tower: Egbers, C., Liu, M., Rath, H.J.: Microgravity sci. technol. 4 1993.

– Parabolic flights: Sitte, B., et. al., ZARM, University of Bremen, DLR parabolic flight campaign, Dec. 2000, (investigation of dielectrophoretic effect in microgravity).

– Sounding rockets: TCM-Wolna flown in 1995.

– ISS: GeoFlow I, 2008.

Expected results
The overall convective behaviour is expected to be very different from the results achievable by GeoFlow I, where a fluid with a negligible temperature dependent viscosity is used. Nevertheless for a scientific impact, scientific analyses are comparable to those for GeoFlow I, i.e.:

• The stability of the basic states and its transitions will be studied for both the non-rotating and rotating situations;
• The characteristics of the convection flows and in particular their symmetries will be determined;
• The critical Rayleigh number which denotes linear stability and marks the onset of thermal convection should be detected;
• The stability diagram for the different states should be measured and the occurrence of multistability will be investigated;
• The energy transport from the inner sphere to the outer sphere should be estimated;
• The characteristic wave numbers should be determined;
• Time dependent up to chaotic behaviour will be detected; drift velocities and non-linear dynamics such as mode interactions will be analysed.

As a result, a detailed description of the transition to turbulence and the transition scenarios to chaos should be obtained. Numerical simulations and comparisons of the experiment with theoretical predictions for the flow pattern bifurcating from trivial state will be conducted, as well as a comparison with theoretical work on the flow in the Earth’s interior.