Experiments on steady buoyancy transfer through turbulent fluid layers separated by density interfaces

A laboratory experiment was performed to investigate mixing across a density interface which separates two turbulent fluid layers and coexists with a stabilizing buoyancy flux. It was found that the buoyancy flux (q₀) across the interface and through the turbulent layers (of depth D) becomes steady and constant in magnitude in the vertical direction, only when , where u is the horizontal r.m.s. velocity at the base of the mixed layers. The results suggest that mixing across the density interface is controlled by a dynamically important buoyancy gradient induced in the turbulent layers and that parameters such as the bulk Richardson number, , where Δb is the interfacial buoyancy jump, are of secondary importance. Measurements are used to infer the mixing mechanism at the interface, the mixing efficiency of stratified fluids and the entrainment law. Some geophysical applications of the results are also discussed.     

Eclogite thermobarometry: The consistency between conventional thermobarometry and forward phase-equilibrium modelling

Eclogite thermobarometry is crucial for constraining the depths and temperatures to which oceanic and continental crust subduct. However, obtaining the pressure and temperature (P–T) conditions of eclogites is complex as they commonly display high-variance mineral assemblages, and the mineral compositions only vary slightly with P–T. In this contribution, we present a comparison between two independent and commonly used thermobarometric approaches for eclogites: conventional thermobarometry and forward phase-equilibrium modelling. We assess how consistent the thermobarometric calculations are using the garnet–clinopyroxene–phengite barometer and garnet–clinopyroxene thermometer with predictions from forward modelling (i.e. comparing the relative differences between approaches). Our results show that the overall mismatch in methods is typically ±0.2–0.3 GPa and ±29–42°C although differences as large as 80°C and 0.7 GPa are possible for a few narrow ranges of P–T conditions in the forward models. Such mismatch is interpreted as the relative differences among methods, and not as absolute uncertainties or accuracies for either method. For most of the investigated P–T conditions, the relatively minor differences between methods means that the choice in thermobarometric method itself is less important for geological interpretation than careful sample characterization and petrographic interpretation for deriving P–T from eclogites. Although thermobarometry is known to be sensitive to the assumed X_Fe³⁺ of a rock (or mineral), the relative differences between methods are not particularly sensitive to the choice of bulk-rock X_Fe³⁺, except at high temperatures (>650°C, amphibole absent) and for very large differences in assumed X_Fe³⁺ (0–0.5). We find that the most important difference between approaches is the activity–composition (a–x) relations, as opposed to the end-member thermodynamic data or other aspects of experimental calibration. When equivalent a–x relations are used in the conventional barometer, P calculations are nearly identical to phase-equilibrium models (ΔP < 0.1). To further assess the implications of these results for real rocks, we also evaluate common mathematical optimizations of reaction constants used for obtaining the maximum P–T with conventional thermobarometric approaches (e.g. using the highest aGrs² × aPrp in garnet and Si content in phengite, and the lowest aDi in clinopyroxene). These approaches should be used with caution, because they may not represent the compositions of equilibrium mineral assemblages at eclogite facies conditions and therefore systematically bias P–T calculations. Assuming method accuracy, geological meaningful P_max at a typical eclogite facies temperature of ~660°C will be obtained by using the greatest aDi, aCel, and aPrp and lowest aGrs and aMs; garnet and clinopyroxene with the lowest Fe²⁺/Mg ratios may yield geological meaningful T_max at a typical eclogite facies pressure of 2.5 GPa.     

Physical processes contributing to the water mass transformation of the Indonesian Throughflow

The properties of the waters that move from the Pacific to the Indian Ocean via passages in the Indonesian archipelago are observed to vary with along-flow-path distance. We study an ocean model of the Indonesian Seas with reference to the observed water property distributions and diagnose the mechanisms and magnitude of the water mass transformations using a thermodynamical methodology. This model includes a key parameterization of mixing due to baroclinic tidal dissipation and simulates realistic water property distributions in all of the seas within the archipelago. A combination of air–sea forcing and mixing is found to significantly change the character of the Indonesian Throughflow (ITF). Around 6 Sv (approximately 1/3 the model net ITF transport) of the flow leaves the Indonesian Seas with reduced density. Mixing transforms both the intermediate depth waters (transforming 4.3 Sv to lighter density) and the surface waters (made denser despite the buoyancy input by air–sea exchange, net transformation?=?2 Sv). The intermediate transformation to lighter waters suggests that the Indonesian transformation contributes significantly to the upwelling of cold water in the global conveyor belt. The mixing induced by the wind is not driving the transformation. In contrast, the baroclinic tides have a major role in this transformation. In particular, they are the only source of energy acting on the thermocline and are responsible for creating the homostad thermocline water, a characteristic of the Indonesian outflow water. Furthermore, they cool the sea surface temperature by between 0.6 and 1.5°C, and thus allow the ocean to absorb more heat from the atmosphere. The additional heat imprints its characteristics into the thermocline. The Indonesian Seas cannot only be seen as a region of water mass transformation (in the sense of only transforming water masses in its interior) but also as a region of water mass formation (as it modifies the heat flux and induced more buoyancy flux). This analysis is complemented with a series of companion numerical experiments using different representations of the mixing and advection schemes. All the different schemes diagnose a lack of significant lateral mixing in the transformation.     

Some approaches for location of centroids of quartz grain outlines to increase homology between Fourier amplitude spectra

The ability to test for similarities and differences among families of shapes by closed-form Fourier expansion is greatly enhanced by the concept of homology. Underlying this concept is the assumption that each term of a Fourier series, when compared to the same term in another series, represents the same thing. A method that ensures homology is one which minimizes the centering error, as reflected in the first harmonic term of the Fourier expansion. The problem is to chose a set of edge points derived from a much larger, but variable, number of edge points such that a valid homologous Fourier series can be calculated. Methods are reviewed and criteria given to define a proper solution. An algorithm is presented which takes advantage of the fact that minimization of the error term can be accomplished by minimizing the distance between the origin of the polar coordinate system in the calculation of the Fourier series and the shape centroid. The use of this algorithm has produced higher quality solutions for quartz grain provenance studies.     

The termination of the solar wind

It has previously been suggested that the solar wind might terminate at distances of 5 AU to 20 AU from the Sun, and that the solar wind might be drastically slowed down by charge exchange and photoionization of interstellar hydrogen atoms which approach the Sun. However, recent satellite measurements of resonantly scattered Lyman alpha radiation, together with pulsar dispersion and Faraday rotation measures, imply very small values for the interstellar hydrogen density (0.05 cm⁻³) and magnetic field strength (3 μG). As a result, the solar wind is not expected to be slowed down by more than about 30% inside the termination distance, which is expected to be about 100 AU.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.