Initial-amplitude dependence of strong-shock-driven interfacial instability in reflected-shock configurations

Shock-tube experiments are conducted to examine the initial-amplitude dependence of strong-shock-driven interfacial instability in reflected-shock configurations at Mach numbers ( upper M Subscript s <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> $M_s$ ) exceeding 3.0. Qualitative observations reveal a marked suppression (enhancement) of bubble (spike) growth under strong shocks, with stronger effects at higher dimensionless initial amplitudes ( k a 0 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>k</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> $ka_0$ ). The initial-amplitude effect on linear growth exhibits a non-monotonic dependence on upper M Subscript s <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> $M_s$ , contrary to the previously anticipated saturation behaviour, arising from the upper M Subscript s <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> $M_s$ dependence of compressibility and vorticity-deposition contributions. Compressibility suppresses bubble growth via a shock-proximity mechanism while promoting spike evolution through a newly identified Mach-reflection mechanism, with their competition yielding a saturation dependence on upper M Subscript s <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> $M_s$ . In contrast, the effectiveness of vorticity deposition is modulated by the Mach-reflection structure, with reduced contributions at high upper M Subscript s <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> $M_s$ due to geometric separation. Based on these insights, an empirical factor is proposed to quantify the initial-amplitude effect across a wide range of k a 0 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>k</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> $ka_0$ and upper M Subscript s <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>