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125. 3. W. H. Reid, Sfudies Appl. Mark, 51, 341 (1972). 4. A. Davey, Quart. J. Mech. Appl. Math, 26, 401 (1973). 5. A. S . Eddington, The Infernal Consfifufionof the Stars J. Mech. Appl. , 26, 401 (1973), Camljridge, University Press (Second Impression), 1930, p. 201. 6. A. Davey, J. Fluid Mech, 57, 369 (1973). 7. Roberts, G. , Unpublished work; 1968; see also J. L. Robinson, J. Fluid Mech, 30,579 (1967). 8. J. W. Deardorff, J. Afmos. , 21, 419 (1964). J. W. Deardorff, J. Amos. , 22, 419 (1965).
This appears on the right-hand side of (25), and gives rise to a new term in A B on the right of (26) and (27). These equations must then be supplemented by an additional evolutionary equation for B. CONCEPTS IN HYDRODYNAMIC STABILITY THEORY 29 in Fig. 3b. For R < R,, two steady values of IA12 are possible, one (dotted) corresponding to an unstable state and the other (solid line) to a stable situation. The small amplitude theory described here is only competent to locate the less interesting unstable state.
V. Application of the Local Potential Finite Element Iterative Scheme to the Slow Viscous Flow of a Compressible Fluid betweenFiniteEccentric Permeablecylinders . . . VI. Local Potential Formulation for the Slow Viscous Flow of Non-Newtonian Fluid between Nonparallel Plates . . VII. A Variational Formulation for Certain Free Boundary Problems . . . . . . . . . VIII. SomeParticular FreeBoundary Problems . . . IX. Applications to Stability Theory . . . . . X. Conclusions . . .