Constraining the source of mantle plumes

© The Author(s), 2016. This is the author's version of the work and is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Earth and Planetary Science Letters 453 (2016): 55-63, doi:10.1016/j.epsl.2015.12.008.In order to link the geochemical signature of hot spot basalts to Earth’s deep interior, it is first necessary to understand how plumes sample different regions of the mantle. Here, we investigate the relative amounts of deep and shallow mantle material that are entrained by an ascending plume and constrain its source region. The plumes are generated in a viscous syrup using an isolated heater for a range of Rayleigh numbers. The velocity fields are measured using stereoscopic Particle-Image Velocimetry, and the concept of the ‘vortex ring bubble’ is used to provide an objective definition of the plume geometry. Using this plume geometry, the plume composition can be analysed in terms of the proportion of material that has been entrained from different depths. We show that the plume composition can be well described using a simple empirical relationship, which depends only on a single parameter, the sampling coefficient, Sc. High-Sc plumes are composed of material which originated from very deep in the fluid domain, while low-Sc plumes contain material entrained from a range of depths. The analysis is also used to show that the geometry of the plume can be described using a similarity solution, in agreement with previous studies. Finally, numerical simulations are used to vary both the Rayleigh number and viscosity contrast independently. The simulations allow us to predict the value of the sampling coefficient for mantle plumes; we find that as a plume reaches the lithosphere, 90% of its composition has been derived from the lowermost 260−750 km in the mantle, and negligible amounts are derived from the shallow half of the lower mantle. This result implies that isotope geochemistry cannot provide direct information about this un-sampled region, and that the various known geochemical reservoirs must lie in the deepest few hundred kilometres of the mantle.This work was funded by the National Science Foundation (grant EAR-055199), the MAPS Dean’s Office at UCL and the CIDER workshop (EAR-1135452).2016-12-2

Renewing the Exploration Approach for Mid-Enthalpy Systems: Examples from Northern England and Scotland

After a promising start in the 1970s and 80s, the UK rather fell behind other countries in the search for viable mid-enthalpy geothermal resources. This situation began to turn around in 2004, when the first of three deep geothermal exploration boreholes were drilled in northern England. What distinguished these from earlier drilling in Cornwall was the deliberate search for naturallyhigh permeability associated with major faults, especially those that have undergone strike-slip reactivation during the Cenozoic. Boreholes at Eastgate in the North Pennines targeted buried radiothermal granite, whereas the 1,821m-deep Science Central Borehole in Newcastle upon Tyne targeted a postulated deep sedimentary aquifer (the Fell Sandstones), which were inferred to be connected laterally to the granitic heat source by a major fault (the reactivation of the Iapetus geo-suture). The drilling was in both cases rewarded with impressive heat flows, and in the case of Eastgate with what is believed to be the highest permeability yet found in a deep granite batholith anywhere in the world. In parallel with these developments, a re-assessment was made of the preexisting geothermal heat flow database for the UK, applying newly-standardised correction protocols for palaeoclimatic and topographic distortions, which were found to be particularly marked in Scotland (where only shallow boreholes had been used to establish geothermal gradients in the original 1980s analysis), Similar prospects in northern England (similar to that drilled at Science Central) are now the focus of commercial exploration efforts. Appraisal of fault dispositions relative to the present-day maximum compressive stress azimuth are being used to identify the most promising areas for intersecting fault-related permeability at depth. New geophysical tools – most notably atomic dielectric resonance scanning – are also being appraised for their ability to directly detect features (such as hot brines) which are indicative of localised convection in target fault zones and aquifers

Contour Dynamics Methods

In an early paper on the stability of fluid layers with uniform vorticity Rayleigh (1880) remarks: "... In such cases, the velocity curve is composed of portions of straight lines which meet each other at finite angles. This state of things may be supposed to be slightly disturbed by bending the surfaces of transition, and the determination of the subsequent motion depends upon that of the form of these surfaces. For co retains its constant value throughout each layer unchanged in the absence of friction, and by a well-known theorem the whole motion depends upon [omega]." We can now recognize this as essentially the principal of contour dynamics (CD), where [omega] is the uniform vorticity. The theorem referred to is the Biot-Savart law. Nearly a century later Zabusky et al (1979) presented numerical CD calculations of nonlinear vortex patch evolution. Subsequently, owing to its compact form conferring a deceptive simplicity, CD has become a widely used method for the investigation of two-dimensional rotational flow of an incompressible inviscid fluid. The aim of this article is to survey the development, technical details, and vortex-dynamic applications of the CD method in an effort to assess its impact on our understanding of the mechanics of rotational flow in two dimensions at ultrahigh Reynolds numbers. The study of the dynamics of two- and three-dimensional vortex mechanics by computational methods has been an active research area for more than two decades. Quite apart from many practical applications in the aerodynamics of separated flows, the theoretical and numerical study of vortices in incompressible fluids has been stimulated by the idea that turbulent fluid motion may be viewed as comprising ensembles of more or less coherent laminar vortex structures that interact via relatively simple dynamics and by the appeal of the vorticity equation, which does not contain the fluid pressure. Two-dimensional vortex interactions have been perceived as supposedly relevant to the origins of coherent structures observed experimentally in mixing layers, jets, and wakes, and for models of large-scale atmospheric and oceanic turbulence. Interest has often focused on the limit of infinite Reynolds number, where in the absence of boundaries, the inviscid Euler equations are assumed to properly describe the flow dynamics. The numerous surveys of progress in the study of vorticity and the use of numerical methods applied to vortex mechanics include articles by Saffman & Baker (1979) and Saffman (1981) on inviscid vortex interactions and Aref (1983) on two-dimensional flows. Numerical methods have been surveyed by Chorin (1980), and Leonard (1980, 1985). Caflisch (1988) describes work on the mathematical aspects of the subject. Zabusky (1981), Aref (1983), and Melander et al (1987b) discuss various aspects of CD. The review of Dritschel (1989) gives emphasis to numerical issues in CD and to recent computations with contour surgery. This article is confined to a discussion of vortices on a two-dimensional surface. We generally follow Saffman & Baker (1979) in matters of definition. In two dimensions a vortex sheet is a line of discontinuity in velocity while a vortex jump is a line of discontinuity in vorticity. We shall, however, use filament to denote a two-dimensional ribbon of vorticity surrounded by fluid with vorticity of different magnitude (which may be zero), rather than the more usual three-dimensional idea of a vortex tube. The ambiguity is unfortunate but is already in the literature. Additionally, a vortex patch is a finite, singly connected area of uniform vorticity while a vortex strip is an infinite strip of uniform vorticity with finite thickness, or equivalently, an infinite filament. Contour Dynamics will refer to the numerical solution of initial value problems for piecewise constant vorticity distributions by the Lagrangian method of calculating the evolution of the vorticity jumps. Such flows are often related to corresponding solutions of the Euler equations that are steady in some translating or rotating frame of reference. These solutions will be called vortex equilibria, and the numerical technique for computing their shapes based on CD is often referred to as contour statics. The mathematical foundation for the study of vorticity was laid primarily by the well-known investigations of Helmholtz, Kelvin, J. J. Thomson, Love, and others. In our century, efforts to produce numerical simulations of flows governed by the Euler equations have utilized a variety of Eulerian, Lagrangian, and hybrid methods. Among the former are the class of spectral methods that now comprise the prevailing tool for large-scale two- and three-dimensional calculations (see Hussaini & Zang 1987). The Lagrangian methods for two-dimensional flows have been predominantly vortex tracking techniques based on the Helmholtz vorticity laws. The first initial value calculations were those of Rosenhead (193l) and Westwater (1935) who attempted to calculate vortex sheet evolution by the motion of O(10) point vortices. Subsequent efforts by Moore (1974) (see also Moore 1983, 1985) and others to produce more refined computations for vortex sheets have failed for reasons related to the tendency for initially smooth vortex sheet data to produce singularities (Moore 1979). Discrete vortex methods used to study the nonlinear dynamics of vortex patches and layers have included the evolution of assemblies of point vortices by direct summation (e.g. Acton 1976) and the cloud in cell method (Roberts & Christiansen 1972, Christiansen & Zabusky 1973, Aref & Siggia 1980, 1981). For reviews see Leonard (1980) and Aref (1983). These techniques have often been criticized for their lack of accuracy and numerical convergence and because they may be subject to grid scale dispersion. However, many qualitative vortex phenomena observed in nature and in experiments, such as amalgamation events and others still under active investigation (e.g. filamentation) were first simulated numerically with discrete vortices. The contour dynamics approach is attractive because it appears to allow direct access, at least for small times, to the inviscid dynamics for vorticity distributions smoother than those of either point vortices or vortex sheets, while at the same time enabling the mapping of the two-dimensional Euler equations to a one-dimensional Lagrangian form. In Section 2 we discuss the formulation and numerical implementation of contour dynamics for the Euler equations in two dimensions. Section 3 is concerned with applications to isolated and multiple vortex systems and to vortex layers. An attempt is made to relate this work to calculations of the relevant vortex equilibria and to results obtained with other methods. Axisymmetric contour dynamics and the treatment of the multi-layer model of quasigeostrophic flows are described in Section 4 while Section 5 is devoted to a discussion of the tendency shown by vorticity jumps to undergo the strange and subtle phenomenon of filamentation

Revisiting diagenesis on the Ontong-Java plateau: Evidence for authigenic crust precipitation in Globorotalia tumida

The calcite tests of foraminifera lie in marine sediments for thousands to millions of years, before being analysed to generate trace element and isotope palaeoproxy records. These sediments constitute a distinct physio-chemical environment from the conditions in which the tests formed. Storage in sediments can modify the trace element and isotopic content of foraminiferal calcite through diagenetic alteration, which has the potential to confound their palaeoceanographic interpretation. A previous study of G. tumida from the Ontong Java Plateau, western equatorial Pacific, found that preferential dissolution of higher-Mg chamber calcite, and the preservation of a low-Mg crust on the tests significantly reduced whole-test Mg/Ca and Sr/Ca [Brown and Elderfield, 1996]. Here, we revisit these specimens with a combination of synchrotron X-ray computed tomography (sXCT) and electron probe micro-analyses (EPMA) to re-evaluate the nature of their diagenetic alteration. The dissolution of higher-Mg calcite with depth was directly observed in the sXCT data, confirming the inference of the previous study. The sXCT data further reveal a thickening of the chemically and structurally distinct calcite crust with depth. We propose that these crusts have a diagenetic origin, driven by the simultaneous dissolution of high-Mg chamber calcite and precipitation of low-Mg crust from the resulting modified pore-water solution. While the breadth of the study is limited by the nature of the techniques, the observation of both dissolution and re-precipitation of foraminiferal calcite serves to demonstrate the action of two simultaneous diagenetic alteration processes, with significant impacts on the resulting palaeoproxy signals.The authors would like to acknowledge Aleksey Sadekov, Gerald Langer, India Weidle, Alberto de Fanis, Andrew Bodey, Joan Vila-Comamala and Ulrich Wagner for their help with the project. The work was funded by the Diamond Light Source and by the ERC (2010-NEWLOG ADG-267931 grant to HE).This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1002/2014PA00275

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Dynamics and parameterization of stably stratified turbulence: implications for estimates of mixing in geophysical flows

2014 Summer.Includes bibliographical references.This research focuses on the relationship between the observed length scales of overturns in stably-stratified shear-flow turbulence and the fundamental length scales constructed from dimensional analysis of basic physical quantities. In geophysical flows such as the ocean, overturns are relatively easy to observe while the basic quantities are not. As such, overturns provide a means of inferring basic quantities if the relationship between the observed and fundamental scales are known. In turn, inferred values of the basic quantities, namely the the turbulent kinetic energy k, and the dissipation rate of turbulent kinetic energy ϵ, can be used to estimate diapycnal diffusivity (i.e. turbulent mixing). Most commonly, the observed Thorpe length scale, LT, is assumed to scale linearly with the fundamental Ozmidov scale, LO =(ϵ/N3)1/2, so that inferred values of ϵ can be obtained and used to estimate mixing from the Osborn formulation for diapycnal diffusivity. A major goal of this research is to re-examine this and other possible scalings using dimensional analysis, direct numerical simulation (DNS), laboratory data, and field observations. The preliminary chapters constitute a fresh approach at dimensional analysis that presents the fundamental length scales, time scales, and dimensionless parameters relevant to the problem. The relationship between LT and the fundamental length scales is then examined for the simple case of homogeneously stratified turbulence (without shear) using DNS. A key finding is that the common practice of inferring ϵ from LT ~ LO, is valid at the transition between a buoyancy-dominated regime and an inertia-dominated regime where the time scale of the buoyancy oscillations, N-1, roughly matches that of the inertial motions, TL = k/ϵ. Regime definition is made possible using a non-dimensional buoyancy strength parameter NTL = Nk/ϵ. Next, the problem is generalized to consider mean shear, and thus, a shear strength parameter, STL = Sk/ϵ, and the gradient Richardson number, Ri = N2/S2, are considered along with NTL to define three regimes available to high Reynolds number stratified shear-flow turbulence: a buoyancy-dominated regime (NTL ≳ 1.7, Ri ≳ 0.25), a shear-dominated regime (STL ≳ 3.3, Ri ≲ 0.25), and an inertia-dominated regime (NTL ≲ 1.7, STL ≲ 3.3). The regimes constitute a multi-dimensional parameter space which elucidates the independent influences that shear and stratification have on the turbulence. Using a large database of DNS and laboratory results, overturns are shown to have unique scalings in the various regimes. Specifically, LT ~ k1/2N-1, LT ~ k1/2S-1, and LT ~ k3/2ϵ-1 in the buoyancy-, shear-, and inertia-dominated regimes, respectively. LT ~ LO is found only for the case of NTL = O(1) and STL ≲ 3.3, or for NTL = O(100), STL ≈ 3.3 and Ri ≈ 0.25 when shear is present. In all three regimes, LT is found to generally indicate k rather than ϵ. An alternative parameterization of turbulent diffusivity is developed based on inferred values of k with a practical eye toward field applications. When tested with DNS and laboratory data, the new model is shown to be more accurate than estimates based on inferred values of ϵ. The multi-parameter framework is broadened with consideration for the turbulent Reynolds number, ReL, thus allowing for an evaluation of existing parameterizations of diapycnal mixing efficiency, R*f. Select DNS and laboratory data sets are used in the analysis. A key finding is that descriptions of R*f based on a single-parameter are generally insufficient. It is found that Ri is an accurate parameter in the shear-dominated regime but fails in the inertia-dominated regime where turbulence is generated by external forcing (rather than mean shear). In contrast, the turbulent Froude number, FrT = (LO/LT)2/3, is an accurate parameter in the inertia-dominated regime but loses accuracy in the shear-dominated regime. Neither Ri or FrT sufficiently describe R*f in the buoyancy-dominated regime where additional consideration for ReL is needed. Another key finding is that the popular buoyancy Reynolds number, Reb = ReL(NTL)-2, is a particularly misleading parameter for describing R*f because it fails to distinguish between (i) a low-Reynolds number, weakly stratified regime of low efficiency (low ReL, low NTL, low R*f) typical of DNS flows and (ii) a high-Reynolds number, strongly stratified regime of high efficiency (high ReL, high NTL, high R*f) typical of geophysical flows. Finally, oceanic observations from Luzon Strait and the Brazil Basin are featured to examine the relationship between LT and LO in geophysical flows where turbulence is driven by overturns that are very large by open ocean standards. LT is found to increase with respect to LO as a function of the normalized overturn size LT = LTN1/2ν-1/2. When large overturns are present, dissipation rates inferred from LT ~ LO are generally larger than measured values on average. The overestimation is quantified over a spring tidal period at Luzon Strait where depth- and time-integration of inferred and measured values show that inferred energy dissipation is four times too large

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier–Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier–Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry