Physics of singularities in pressure-impulse theory

R. Krechetnikov
Phys. Rev. Fluids 3, 054003 – Published 16 May 2018

Abstract

The classical solution in the pressure-impulse theory for the inviscid, incompressible, and zero-surface-tension water impact of a flat plate at zero dead-rise angle exhibits both singular-in-time initial fluid acceleration, v/tt=0δ(t), and a near-plate-edge spatial singularity in the velocity distribution, vr1/2, where r is the distance from the plate edge. The latter velocity divergence also leads to the interface being stretched infinitely right after the impact, which is another nonphysical artifact. From the point of view of matched asymptotic analysis, this classical solution is a singular limit when three physical quantities achieve limiting values: sound speed c0, fluid kinematic viscosity ν0, and surface tension σ0. This leaves open a question on how to resolve these singularities mathematically by including the neglected physical effects—compressibility, viscosity, and surface tension—first one by one and then culminating in the local compressible viscous solution valid for t0 and r0, demonstrating a nontrivial flow structure that changes with the degree of the bulk compressibility. In the course of this study, by starting with the general physically relevant formulation of compressible viscous flow, we clarify the parameter range(s) of validity of the key analytical solutions including classical ones (inviscid incompressible and compressible, etc.) and understand the solution structure, its intermediate asymptotics nature, characteristics influencing physical processes, and the role of potential and rotational flow components. In particular, it is pointed out that sufficiently close to the plate edge surface tension must be taken into account. Overall, the idea is to highlight the interesting physics behind the singularities in the pressure-impulse theory.

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  • Received 22 August 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.054003

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

R. Krechetnikov

  • Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

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Vol. 3, Iss. 5 — May 2018

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