Spontaneous singularity formation in converging cylindrical shock waves

Mostert, Wouter; Pullin, D. I.; Samtaney, Ravi; Wheatley, Vincent

doi:10.1103/physrevfluids.3.071401

Cited by 4 publications

(8 citation statements)

References 21 publications

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“…The initial shape of the CMS satisfies (3.9 a , b ), while the initial distribution of the shock Mach numbers is consistent with that of Mostert et al. (2018 b ), which can be expressed as where is periodic over CMS with a wavenumber , and is a perturbation amplitude, and . The cases with and are calculated by the FDTM, and the corresponding formation time of the kinks are extracted for comparisons with the literature.…”

Section: Front-disturbance Tracking Methodssupporting

confidence: 67%

“…For the converging CMS with a large and a sufficiently small perturbation, an asymptotic solution for the kink formation time and the corresponding shock radius was derived by Mostert et al. (2018 b ), which is adopted here to further illustrate the performance of the FDTM. The initial shape of the CMS satisfies (3.9 a , b ), while the initial distribution of the shock Mach numbers is consistent with that of Mostert et al.…”

Section: Front-disturbance Tracking Methodsmentioning

confidence: 99%

“…The asymptotic solution reported by Mostert et al. (2018 a , b ) using the nonlinear Fourier-based analysis method, and the numerical results obtained by the method of Schwendeman (1993) using GSD are superimposed on figure 9. It is obvious that and calculated by the FDTM agree well with the numerical results reported by Schwendeman (1993).…”

Section: Front-disturbance Tracking Methodsmentioning

confidence: 99%

“…Subsequently, Mostert et al. (2018 a , b ) found that the kink formation time is inversely proportional to the initial amplitude of the perturbation when assuming a sinusoidal distribution of the shock Mach numbers for an initially planar shock or CMS. As GSD is not formally derived from the Euler equations (Mostert et al.…”

Section: Introductionmentioning

confidence: 99%

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Kinks on elliptical convergent shock waves in hypersonic flow

Si,

2023

J. Fluid Mech.

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Kinks commonly appear on the convergent shock surface when an internal conical flow deviates from the axisymmetric state. In this paper, the formation mechanisms of kinks on internal conical shocks (ICSs) generated by elliptical ring wedges with typical entry aspect ratios ( $AR{\rm s}$ ) in a Mach 6 flow are revealed using a theoretical method, in which the spatial evolution of the three-dimensional elliptical ICS is converted into a temporal evolution of a two-dimensional elliptical moving shock (EMS) using the hypersonic equivalence principle. To simultaneously track the shock front of the EMS and the disturbances propagating along it, a front-disturbance tracking method (FDTM) based on geometrical shock dynamics is proposed. It is found that the shock–compression disturbances from the same family initially near the major axis catch up with the disturbance initially emitted from the major axis to form kinks on the EMS. The equivalent kink formation positions predicted by the FDTM always lag behind the real kink formation positions on the elliptical ICS because the applicability of the hypersonic equivalence principle decays as the shock strengthens along the incoming flow direction. The accuracy of the equivalent kink formation positions predicted by the FDTM gradually declines with the reduction in $AR$ , but it can be significantly improved for all $AR{\rm s}$ after a modification of the equivalent relationship using the shock angle in the major plane of the elliptical ICS, which provides a new way to solve the kinks on the elliptical ICS.

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Section: Front-disturbance Tracking Methodssupporting

confidence: 67%

Section: Front-disturbance Tracking Methodsmentioning

confidence: 99%

Section: Front-disturbance Tracking Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kinks on elliptical convergent shock waves in hypersonic flow

Si,

2023

J. Fluid Mech.

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“…Mostert et al. (2018 a , b ) hypothesized a sinusoidal perturbation in the Mach-number distribution for both initially flat and cylindrical shock geometry, finding that a shock curvature singularity, as a prelude to the formation of a triple point, occurs at a critical time that is inversely proportional to the initial perturbation amplitude, . This result is obtained analytically via weakly nonlinear Fourier analysis using Whitham's GSD approximation.…”

Section: Introductionmentioning

confidence: 98%

Evolution of a shock generated by an impulsively accelerated, sinusoidal piston

et al. 2020

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Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock

et al. 2019

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The Richtmyer–Meshkov (RM) instability is numerically investigated on an unperturbed interface subjected to a diffracted convergent shock created by diffracting an initially cylindrical shock over a rigid cylinder. Four gas interfaces are considered with Atwood number ranging from $-0.18$ to 0.67. Results indicate that the diffracted convergent shock increases its strength gradually and reduces its amplitude quickly when it propagates towards the convergence centre. After the strike of the diffracted convergent shock, the initially unperturbed interface deforms with a bulge structure at the centre and two interface steps at both sides, which can be ascribed to the non-uniformity of the pressure distribution behind the diffracted convergent shock. With the decrease of Atwood number, the bulge structure becomes more pronounced. Quantitatively, the interface amplitude experiences a fast but short growing stage and then enters a linear stage. A good collapse of the dimensionless amplitude is found for all cases, which indicates a weak dependence of the growth rate on Atwood number in the deformed shock-induced RM instability. Then the impulsive theory is modified by eliminating the Atwood number and considering the geometry convergence, which well predicts the amplitude growth for the deformed shock-induced RM instability. Finally, the underlying mechanism is decoupled into three parts, and it is found that both the impulsive pressure perturbation and the geometry convergence promote the growth of interface perturbation while the continuous pressure perturbation inhibits the growth. As the Atwood number decreases, the impulsive perturbation plays an increasingly important role, which suggests that the impulsive perturbation dominates the deformed shock-induced RM instability at the linear stage.

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Spontaneous singularity formation in converging cylindrical shock waves

Cited by 4 publications

References 21 publications

Kinks on elliptical convergent shock waves in hypersonic flow

Kinks on elliptical convergent shock waves in hypersonic flow

Evolution of a shock generated by an impulsively accelerated, sinusoidal piston

Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock

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