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14 Feb 2013: 24] An upscaled model for convective dissolution canthen be incorporated into models such as equation (1) byintroducing a constant loss or sink term [Gasda et al.,2011 ; MacMinn et al., 2011],.

9 Feb 2004: 5H1 2(H0U1)′=0, (24)3U1 H ′1 H ′0ϕ1. 1. 2H0ϕ. ′1=0, (25)ϕ1=2720. ... 4y2)], (38). and then subsequent substitution into (24) yields a second-order differential equation forH1(y), namely(1.

16 Jan 2007: J. Fluid M e c h. (1990). vol. 212, p p. 209-240. Printed in Great Britain 209. The fluid mechanics of solidification. By H E R B E R T E. H U P P E R T Institute of Theoretical Geophysics and Department of Applied Mathematics and Theoretical.

25 Jan 2007: 0.01 (for Ra, = lo@), convection continues in the melt until t = 0.24, by which time the system is about 40% solidified.

21 Dec 2012: Carbon budgets have been introduced to capemissions [24] (Figure 1). The power sector is the single largest emitter. ... and are designed to capemissions [24] (green line).

29 Jul 2010: JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B9, PAGES 15,891-15,901, SEPTEMBER 10, 1993. The Crystallization of Lava Lakes. M. GRAE WORSTER AND HERBERT E. HUPPERT. Institute of Theoretical Geophysics, Department of Applied Mathematics and

9 Mar 2004: e-mail: grae@esc.cam.ac.uk; heh1@esc.cam.ac.uk. (Received 24 July and in revised form 27 March 1997). ... 24/3λRa1/3 (3.1). between the Nusselt number Nu for thermal convection in the liquid region and theRayleigh number.

9 Mar 2004: Received 24 April 2000 and in revised form 7 December 2000).

30 Jul 2013: 24). The perturbation equations are given, at O(βN), by. 1. η.

18 Jul 2014: Email address for correspondence: ssp23@cam.ac.uk. first published online 24 March 2014). ... upper fluid to speeds above those induced by the background-pressure-driven flow (3.24) alone.

16 Jul 2010: nly. 24 HUPPERT & SPARKS. compositional film is to substitute the film thickness into the compositional Rayleigh number, which can be re-expressed as. ... 24. I. A. -.:---n;o • • Pl AA GIOCl A S E.

23 Dec 2021: 2πϕ r0. 0. h00. s0[h0(r), z]dzr dr =V, (2.24). where s0[h0(r), z] is the initial saturation distribution. ... By applying scaling analysis to (2.14) and (2.24) and rearranging, we find thefollowing relations between the dimensions of radius, height,

5 May 2006: We areinterested in cases with small C2H because otherwise the distance of propagation issmall, see (3.24), and no real gravity current appears. ... Using the approximations (3.19)–(3.24), we find: (i) for S < 1.

26 Apr 2006: Ẇφ̇′. )=(. R 1+ S/C SVC1 V. )(Wφ′. ), (24). whereφ′ = φφe. ... The characteristics of the eigenso-lutions of Equation 24 are shown in Figure 6, the topology of which is preservedby the full system of Equations 9–12 (Anderson & Worster 1996

14 Sep 2009: casting [17,24]) to natural (e.g. for-. All rights reserved. Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, United Kingdom.

19 Jul 2010: JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B9, PAGES 15,891-15,901, SEPTEMBER 10, 1993. The Crystallization of Lava Lakes. M. GRAE WORSTER AND HERBERT E. HUPPERT. Institute of Theoretical Geophysics, Department of Applied Mathematics and

9 Mar 2004: 6 1.9 1.7ID 20 26.5 1.4 1.3IE 23 20 3.9 10.5IF 12 18 4.0 11.25IG 24 20 4.1 11.5. ... IIA 23 26 5.22 2.62 29 48IIB 17.5 24 5.36 2.68 30 48IIC 15 21 5.94 2.01 25 24IID 28 15 7.02

30 May 2006: University of Cambridge, Silver Street, Cambridge CB3 9EW, UK. (Received 17 October 1994 and in revised form 24 May 1995). ... Each freezing experiment took on the order of 24 hours, after which the solid crystalline block was cut up into pieces and the

9 Mar 2004: Consequently, the relationships between the variables on the characteristics with. 24 M. ... v = r[1. (rinitr. )2]. (2.24). In particular, at the nose.

24 Sep 2009: J. Fluid Mech. (2009), vol. 631, pp. 419–440. c 2009 Cambridge University Pressdoi:10.1017/S0022112009007174 Printed in the United Kingdom. 419. Particulate gravity currents alongV-shaped valleys. JOE J. MONAGHAN1†, CATHERINE MÉRIEUX1,HERBERT E