TY - JOUR

T1 - Spontaneous singularity formation in converging cylindrical shock waves

AU - Mostert, W.

AU - Pullin, D. I.

AU - Samtaney, Ravi

AU - Wheatley, V.

N1 - KAUST Repository Item: Exported on 2021-02-19
Acknowledged KAUST grant number(s): URF/1/2162-01
Acknowledgements: This research was supported by the KAUST Office of Sponsored Research under Award No. URF/1/2162-01.

PY - 2018/7/23

Y1 - 2018/7/23

N2 - We develop a nonlinear, Fourier-based analysis of the evolution of a perturbed, converging cylindrical strong shock using the approximate method of geometrical shock dynamics (GSD). This predicts that a singularity in the shock-shape geometry, corresponding to a change in Fourier-coefficient decay from exponential to algebraic, is guaranteed to form prior to the time of shock impact at the origin, for arbitrarily small, finite initial perturbation amplitude. Specifically for an azimuthally periodic Mach-number perturbation on an initially circular shock with integer mode number q and amplitude proportional to ϵ1, a singularity in the shock geometry forms at a mean shock radius Ru,c∼(q2ϵ)-1/b1, where b1(γ)

AB - We develop a nonlinear, Fourier-based analysis of the evolution of a perturbed, converging cylindrical strong shock using the approximate method of geometrical shock dynamics (GSD). This predicts that a singularity in the shock-shape geometry, corresponding to a change in Fourier-coefficient decay from exponential to algebraic, is guaranteed to form prior to the time of shock impact at the origin, for arbitrarily small, finite initial perturbation amplitude. Specifically for an azimuthally periodic Mach-number perturbation on an initially circular shock with integer mode number q and amplitude proportional to ϵ1, a singularity in the shock geometry forms at a mean shock radius Ru,c∼(q2ϵ)-1/b1, where b1(γ)

UR - http://hdl.handle.net/10754/631521

UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.071401

UR - http://www.scopus.com/inward/record.url?scp=85051138830&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.3.071401

DO - 10.1103/PhysRevFluids.3.071401

M3 - Article

AN - SCOPUS:85051138830

VL - 3

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 7

ER -