Drag of a Plate Planing on the Shallow Water with Formation of Waves

• Published in: Fluid dynamics Vol. 53; no. 5; pp. 608 - 615
• Main Authors: Filatov, E. V., Yakimov, A. Yu
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-09-2018; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Classical Mechanics; Computational fluid dynamics; Critical flow; Deer hunting; Drag; Engineering Fluid Dynamics; Experiments; Fluid flow; Fluid- and Aerodynamics; Flying-machines; Incompressible flow; Mathematical analysis; Numerical analysis; Physics; Physics and Astronomy; Planing; Shallow water; Stagnation point; Submerging; potential flow; free surface; body drag; stagnation point; planing; water tunnel
• ISSN: 0015-4628; 1573-8507
• DOI: 10.1134/S0015462818050075

The plane problem of the plate planing at a constant velocity on the surface of a heavy, ideal, incompressible, finite-depth fluid is considered. The approximate, depth-independent expression for the force acting on the plate is derived from the linear distribution of the fluid velocity along the plate and the height of the flow stagnation point, without regard for jet formation near the leading edge. In this approximate formulation the plate drag depends on its velocity and the trailing edge immersion and does not depend on the planing angle. Experiments and numerical calculations in the exact formulation are performed in the near-critical flow regimes. It is shown that the wave patterns in the experiments and numerical calculations coincide, the formula for the drag being in agreement with the numerical experiments. An approximate criterion of the formation of waves going away from the plate in the forward direction is proposed.