The concept of cluster evolution minerageny in the Earth’s history

The new concept of cluster evolutionary mineralogy is based on the idea of the formation of the Earth from the primary stellar matter, which was preserved in the cores of the planets. The consequent destruction of it, as a result of the decay of heavy nuclear matter, leads to fragmentation of the substance until the appearance of superheavy elements with their further nuclear dissociation. As a result, a protomagma emerges, which enters the upper mantle in the form of plume flows. This process supports the reactions that result in the formation of chemical elements, minerals, ores and rocks, from which the upper mantle and the crust are formed. The processes of nuclear dissociation lead to the release of energy and the decomposition of matter, which initiates the growth of the earth's volume, its geotectonic activity, and the appearance of the hydrosphere and the atmosphere.

Merging of two or more plumes arranged around a circle

A model is presented of merging turbulent plumes from sources evenly spaced around a horizontal circle in a quiescent, unstratified background. This follows the previously developed method of (i) identifying the boundaries of interacting plumes with velocity-potential contours of line sinks and (ii) closing the generalised plume equations with an entrainment assumption based on the integrated flux across the plume boundaries. It includes the simplest case of two merging plumes, as well as being applicable to plume flows in restricted corner configurations. The model is shown to display the expected limiting behaviour for the source plumes and the merged plume. Consideration of the plume fluxes in the merging region leads to a revision of the entrainment assumption. The resulting revised model compares satisfactorily with previous estimates of volume flux in two merging plumes.

Plume flows in porous media driven by horizontal differential heating

In this paper we describe flow through a porous medium in a two-dimensional rectangular cavity driven by differential heating of the impermeable lower surface. The upper surface is held at constant pressure and at a constant temperature equal to the minimum temperature of the lower surface, while the sidewalls are impermeable and thermally insulated. Numerical results for general values of the Darcy–Rayleigh number $R$ and the cavity aspect ratio $A$ are compared with theoretical predictions for the small Darcy–Rayleigh number limit $(R\ensuremath{\rightarrow} 0)$ where the temperature field is conduction-dominated, and with a boundary-layer theory for the large Darcy–Rayleigh number limit $(R\ensuremath{\rightarrow} \infty )$ where convection is significant. In the latter case a horizontal boundary layer near the lower surface conveys fluid to the hot end of the cavity where it rises to the upper surface in a narrow plume. Predictions are made of the vertical heat transfer through the cavity.