A theory of convection: Modelling by two buoyant interacting fluids

Abstract

A new model of convection and mixing is presented. The fluid is envisioned as being composed of two buoyant interacting fluids, called thermals and anti-thermals. In the context of the Boussinesq approximation, pairs of governing equations are derived for thermals and anti-thermals. Each pair meets an Invariance Principle as a consequence of the reciprocity in the roles played by thermals and anti-thermals. Each pair is transformed into an average equation for which interaction terms cancel and another very simple equation linking the two fluid properties. An important parameter of the model is the fraction, f, of area occupied by thermals to the total area. A dynamic saturation equilibrium between thermals and antithermals is assumed. This implies a constant values of f throughout the system. The set of equations is written in terms of mean values and root-mean-square fluctuations, in keeping with equations of turbulence theories. The final set consists of four coupled non-linear differential equations. The model neglects dissipation and can be applied to any convective situations where molecular viscosity and diffusivity may be neglected. Applications of the model to mixed-layer deepening and penetrative convection are presented in subsequent papers.     

<Emphasis Type="Italic">In Situ</Emphasis> Signatures of Interchange Reconnection between Magnetic Clouds and Open Magnetic Fields: A Mechanism for the Erosion of Polar Coronal Holes?

We outline a method to determine the direction of solar open flux transport that results from the opening of magnetic clouds (MCs) by interchange reconnection at the Sun based solely on in-situ observations. This method uses established findings about i) the locations and magnetic polarities of emerging MC footpoints, ii) the hemispheric dependence of the helicity of MCs, and iii) the occurrence of interchange reconnection at the Sun being signaled by uni-directional suprathermal electrons inside MCs. Combining those observational facts in a statistical analysis of MCs during solar cycle 23 (period 1995 – 2007), we show that the time of disappearance of the northern polar coronal hole (1998 – 1999), permeated by an outward-pointing magnetic field, is associated with a peak in the number of MCs originating from the northern hemisphere and connected to the Sun by outward-pointing magnetic field lines. A similar peak is observed in the number of MCs originating from the southern hemisphere and connected to the Sun by inward-pointing magnetic field lines. This pattern is interpreted as the result of interchange reconnection occurring between MCs and the open field lines of nearby polar coronal holes. This reconnection process closes down polar coronal hole open field lines and transports these open field lines equatorward, thus contributing to the global coronal magnetic field reversal process. These results will be further constrainable with the rising phase of solar cycle 24.     

Hydrous partial melting in the sheeted dike complex at fast spreading ridges: experimental and natural observations

In ophiolites and in present-day oceanic crust formed at fast spreading ridges, oceanic plagiogranites are commonly observed at, or close to the base of the sheeted dike complex. They can be produced either by differentiation of mafic melts, or by hydrous partial melting of the hydrothermally altered sheeted dikes. In addition, the hydrothermally altered base of the sheeted dike complex, which is often infiltrated by plagiogranitic veins, is usually recrystallized into granoblastic dikes that are commonly interpreted as a result of prograde granulitic metamorphism. To test the anatectic origin of oceanic plagiogranites, we performed melting experiments on a natural hydrothermally altered dike, under conditions that match those prevailing at the base of the sheeted dike complex. All generated melts are water saturated, transitional between tholeiitic and calc-alkaline, and match the compositions of oceanic plagiogranites observed close to the base of the sheeted dike complex. Newly crystallized clinopyroxene and plagioclase have compositions that are characteristic of the same minerals in granoblastic dikes. Published silicic melt compositions obtained in classical MORB fractionation experiments also broadly match the compositions of oceanic plagiogranites; however, the compositions of the coexisting experimental minerals significantly deviate from those of the granoblastic dikes. Our results demonstrate that hydrous partial melting is a likely common process in the root zone of the sheeted dike complex, starting at temperatures exceeding 850°C. The newly formed melt can either crystallize to form oceanic plagiogranites or may be recycled within the melt lens resulting in hybridized and contaminated MORB melts. It represents the main MORB crustal contamination process. The residue after the partial melting event is represented by the granoblastic dikes. Our results support a model with a dynamic melt lens that has the potential to trigger hydrous partial melting reactions in the previously hydrothermally altered sheeted dikes. A new thermometer using the Al content of clinopyroxene is also elaborated.     

Determination of Trace Element Mass Fractions in Ultramafic Rocks by HR‐ICP‐MS: A Combined Approach Using a Direct Digestion/Dilution Method and Preconcentration by Coprecipitation

A procedure is described for the determination of thirty‐seven minor and trace elements (LILE, REE, HFSE, U, Th, Pb, transition elements and Ga) in ultramafic rocks. After Tm addition and acid sample digestion, compositions were determined both following a direct digestion/dilution method (without element separation) and after a preconcentration procedure using a double coprecipitation process. Four ultramafic reference materials were investigated to test and validate our procedure (UB‐N, MGL‐GAS [GeoPT12], JP‐1 and DTS‐2B). Results obtained following the preconcentration procedure are in good agreement with previously published work on REE, HFSE, U, Th, Pb and some of the transition elements (Sc, Ti, V). This procedure has two major advantages: (a) it avoids any matrix effect resulting from the high Mg content of peridotite, and (b) it allows the preconcentration of a larger trace element set than with previous methods. Other elements (LILE, other transition elements Cr, Mn, Co, Ni, Cu, Zn, as well as Ga) were not fully coprecipitated with the preconcentration method and could only be accurately determined through the direct digestion/dilution method.