Skimming impacts and rebounds of smoothly shaped bodies on shallow liquid layers

• Published in: Journal of engineering mathematics 2020-10, Vol.124 (1), p.41-73
• Main Authors: Palmer, Ryan A., Smith, Frank T.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational fluid dynamics; Computational Mathematics and Numerical Analysis; Fluid flow; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Physical simulation; Qualitative analysis; Skimming; Theoretical and Applied Mechanics; Thickness; Trailing edges; Underbodies
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-020-10063-6

Investigated in this paper is the coupled fluid–body motion of a thin solid body undergoing a skimming impact on a shallow-water layer. The underbody shape (the region that makes contact with the liquid layer) is described by a smooth polynomic curve for which the magnitude of underbody thickness is represented by the scale parameter C . The body undergoes an oblique impact (where the horizontal speed of the body is much greater than its vertical speed) onto a liquid layer with the underbody’s trailing edge making the initial contact. This downstream contact point of the wetted region is modelled as fixed (relative to the body) throughout the skimming motion with the liquid layer assumed to detach smoothly from this sharp trailing edge. There are two geometrical scenarios of interest: the concave case ( C < 0 producing a hooked underbody) and the convex case ( C > 0 producing a rounded underbody). As C is varied the rebound dynamics of the motion are predicted. Analyses of small-time water entry and of water exit are presented and are shown to be broadly in agreement with the computational results of the shallow-water model. Reduced analysis and physical insights are also presented in each case alongside numerical investigations and comparisons as C is varied, indicating qualitative analytical/numerical agreement. Increased body thickness substantially changes the interaction structure and accentuates inertial forces in the fluid flow.