On the entry of a wedge into water: The thin wedge and an all-purpose boundary-layer equation

Journal of Engineering Mathematics

Volumn 48, Issue 3-4, 2004, Pages 219-252

  Fraenkel, L E ^a   Keady, G ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Entry of wedge into water; Integral equations

Indexed keywords

BOUNDARY LAYERS; CONTACT ANGLE; EXTRAPOLATION; GRAVITATIONAL EFFECTS; INTEGRAL EQUATIONS; PROBLEM SOLVING; SURFACE TENSION; VISCOSITY;

VERTEX ANGLE; WEDGES;

FLUID DYNAMICS;

BOUNDARY LAYER; FLUID-STRUCTURE INTERACTION; MATHEMATICAL METHOD; SURFACE TENSION; VISCOSITY;

EID: 1942456513     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:engi.0000018157.35269.a2     Document Type: Article

References (14)

1. H. Wagner, Über Stoss- und Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12 (1932) 193-215.
2. J. B. McLeod and L. E. Fraenkel, On the vertical entry of a wedge into water. (In preparation.)
3. L. E. Fraenkel and J. B. McLeod, Some results for the entry of a blunt wedge into water. Phil. Trans. R. Soc. London A 355 (1997) 523-535.
4. Z. N. Dobrovol'skaya, On some problems of similarity flow of fluid with a free surface. J. Fluid Mech. 36 (1969) 805-829.
5. P. R. Garabedian, Asymptotic description of a free boundary at the point of separation. AMS Proc. Symp. Appl. Math. 17 (1965) 111-117.
6. A. G. Mackie, The water entry problem. Quart. J. Mech. Appl. Math. 22 (1969) 1-17.
7. R. Zhao and O. Faltinsen, Water entry of two-dimensional bodies. J. Fluid Mech. 246 (1993) 593-612.
8. G. Keady and N. D. Fowkes, The vertical entry of a wedge into water: integral equations and numerical results. In: E. O. Tuck and J. A. K. Scott (eds.), Proceedings of the Engineering Mathematics and Applications Conference. Adelaide: Institute of Engineers, Australia (1998) pp. 277-280.
9. A. G. Mackie, A linearised theory of the water entry problem. Quart. J. Mech. Appl. Math. 15 (1962) 137-151.
10. E. A. Johnstone and A. G. Mackie, The use of Lagrangian coordinates in the water entry and related problems. Proc. Camb. Phil. Soc. 74 (1973) 529-538.
11. E. C. Titchmarsh, Eigenfunction Expansions, part II. Oxford: Clarendon (1958) 404 pp.
12. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals. Oxford: Clarendon (1948) 394 pp.
13. J. C. Burkill, The Theory of Ordinary Differential Equations. London: Longman (1975) 121 pp.
14. G. Keady, On a boundary layer in the problem of a wedge entering water. In: S. Wang and N. D. Fowkes (eds.), Proceedings of the BAIL2002 Conference. Perth: University of Western Australia (2002) pp. 153-158.