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30 May 2006: Stability of a large gas bubble rising through liquid 417. 24. ... 1. oo 1.712 1.26 1.42 1.10 1.24. 13.61 1.200 0.79 1.06 1.

30 May 2006: a$'(@, SY), DPI = { P } [ 1 , 1 , S&I, (4.23) where yil) = P-1Bi/Ms$2) (4.24 a). ... 4.24 b) = 1 1 8 ) K21og K O ( K 2 ). Truncating a t n = N = 2 , we obtain the second approximation.

27 Apr 2006: r N = c ( ) (gS3/3v) 118 t (3 I)18 (2.24). ... 8 a n d using (2.24}. The results are:. S = 0.

30 May 2006: 2.21). (2.22). (2.23). (2.24). where EN is the value of [ at r = rN(t). ... Substituting (2.23) and (2.24) into (2.21) and (2.22), we find that $ ( z ) , where z = c/&, satisfies.

30 May 2006: J. Fluid Me&. (1981), vol. 106, p p. 299-329. Printed in Great Britain 399. Double-diffusive convection. By H E R B E R T E. H U P P E R T Department of Applied Mathematics and Theoretical Physics,. Silver Street, Cambridge CB3 9EW. A N D J. S T E W

30 May 2006: 24-2. 740 J. Y. Holyer and H. E. Huppert. model for energy dissipation. ... The wavelengths given by (6.3) and (6.4) are 6.1 cm on the lower interface and 24-1 cm on the upper interface.

30 May 2006: 0 69.5 24.6 30.4 40.8 47.3 62-5 29.2 37.2 51.9 41.7 23.7 29.7 36.5 42.2. ... 29.6 36.6 25.0 34.8 54.0 24.8 33-8 28.2 35.3 24.3. 1 0 3 dp.

30 May 2006: head. This Froude number should be 24 according to Benjamin, but Hoult suggests expressing it as a constant A, to be determined from experiment.

30 May 2006: J. F u i d Xech. (19761, VOZ. 78, part 4? pp. 821-854 Printed in Great Britain. 82 1. Nonlinear double-diffusive convection By H E R B E R T E. H U P P E R T A N D D A N I E L R. MOORE. Department of Applied Mathematics and Theoretical Physics,

11 Oct 2006: After some algebra and use of(2.24), we obtain. ρD. Dt. [1. ... 374 M. Ungarish and H. E. Huppert. t0 4 8 12 16 20 24.