This article was originally published online and in print with typographical errors in Table I; certain diacritical accents, such as the tilde and circumflex, needed to denote either rotational or irrotational components, were missing. AIP apologizes for this error. All online versions of the article have been corrected. The correct table appears below:

Table I.

Linear growth rate corrections and the critical parameters delineating stability boundaries.

 Improved rotational set in general formEvaluated growth rates (dimensionless)
  Em2=12∫∫∫[(p̂m)2+ûmûm+2ûmũmi+ũmrũmr+ũmiũmi]dV 
α1: Pressure coupling Em2exp(2αmt)∫∫∫V[p̂û+12MbU(p̂)2]+Mb[û(Uû)]dV 45Mb[Ab(r)γ] 
α2: Dilatational Em2exp(2αmt)∫∫∫V43δ2û(û)dV 815ξMb3O(1) 
α3: Acoustic mean Em2exp(2αmt)∫∫∫VMb{û(û×Ω)}dV 
α4: Flow turning Em2exp(2αmt)∫∫∫VMbû(U×ω)dV 45Mb(1+π2Mb2ξ2l2m2)1 
α5: Rotational flow Em2exp(2αmt)∫∫∫Vũp̂dV 45Mb(1+π2Mb2ξ2l2m2)1 
α6: Mean vorticity Em2exp(2αmt)∫∫∫VMbũ(U×ω)dV 25Mb 
α7: Viscosity Em2exp(2αmt)∫∫∫Vδ2(û+ũ)(×ω)dV 415Mbξ[112ξ+15ξ2115ξ3+O(ξ4)] 
α8: Pseudo acoustic Em2exp(2αmt)∫∫∫Vûp̃dV 25(Mb3l2m2)O(1) 
α9: Pseudo vorticity Em2exp(2αmt)∫∫∫Vũp̃dV 9125πMb[(ξ232)exp(2ξ)+323ξ+2ξ2]ξ4 
α10: Unsteady nozzle Em2exp(2αmt)∫∫∫VMb(û+ũ)(Uũ)dV 43πMb{[π2+4(ξ+2)2]11500} 
Critical damping parameter ξr=3γb+9γb2+12Mb2(4Mb2) 
Critical aspect ratio lr=mπδMb3256+353sinh(13sinh1{4[3254+27(15215γb)](3535)}) 
Critical Mach number Mbr=6{12γb[14ξ2(12ξ+2ξ2e2ξ)]}(4ξ3l2m2) 
 Improved rotational set in general formEvaluated growth rates (dimensionless)
  Em2=12∫∫∫[(p̂m)2+ûmûm+2ûmũmi+ũmrũmr+ũmiũmi]dV 
α1: Pressure coupling Em2exp(2αmt)∫∫∫V[p̂û+12MbU(p̂)2]+Mb[û(Uû)]dV 45Mb[Ab(r)γ] 
α2: Dilatational Em2exp(2αmt)∫∫∫V43δ2û(û)dV 815ξMb3O(1) 
α3: Acoustic mean Em2exp(2αmt)∫∫∫VMb{û(û×Ω)}dV 
α4: Flow turning Em2exp(2αmt)∫∫∫VMbû(U×ω)dV 45Mb(1+π2Mb2ξ2l2m2)1 
α5: Rotational flow Em2exp(2αmt)∫∫∫Vũp̂dV 45Mb(1+π2Mb2ξ2l2m2)1 
α6: Mean vorticity Em2exp(2αmt)∫∫∫VMbũ(U×ω)dV 25Mb 
α7: Viscosity Em2exp(2αmt)∫∫∫Vδ2(û+ũ)(×ω)dV 415Mbξ[112ξ+15ξ2115ξ3+O(ξ4)] 
α8: Pseudo acoustic Em2exp(2αmt)∫∫∫Vûp̃dV 25(Mb3l2m2)O(1) 
α9: Pseudo vorticity Em2exp(2αmt)∫∫∫Vũp̃dV 9125πMb[(ξ232)exp(2ξ)+323ξ+2ξ2]ξ4 
α10: Unsteady nozzle Em2exp(2αmt)∫∫∫VMb(û+ũ)(Uũ)dV 43πMb{[π2+4(ξ+2)2]11500} 
Critical damping parameter ξr=3γb+9γb2+12Mb2(4Mb2) 
Critical aspect ratio lr=mπδMb3256+353sinh(13sinh1{4[3254+27(15215γb)](3535)}) 
Critical Mach number Mbr=6{12γb[14ξ2(12ξ+2ξ2e2ξ)]}(4ξ3l2m2)