Viscous Linear Instability of an Incompressible Round Jet T.M. ...

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omega/alpha_r -alpha_i 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 omega R=50 R=100 R=200 R=1000 Figure 4.1: Phase Velocity as a function of ω and R for n = 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 omega R=50 R=100 R=200 R=1000 Figure 4.2: Amplification factor as a function of ω and R for n = 1 19
4.2 Critical Reynolds Number To obtain the critical Reynolds number, we have plotted (figure (4.3)) the amplification factor for some values of R close to the critical Reynolds number predicted by other researchers. The critical Reynolds number is the point where the curve −αi(ω) becomes tangent to the αi = 0 line. -alpha_i 2e-05 0 -2e-05 -4e-05 -6e-05 -8e-05 -0.0001 0.095 0.1 0.105 0.11 0.115 omega R = 37.63 R = 37.64 R = 37.65 R = 37.66 R = 37.67 R = 37.68 R = 37.681 Figure 4.3: Amplification factor as a function of Reynolds number and ω 20
Page 1 and 2: Viscous Linear Instability of an In
Page 3 and 4: INSTITUTE OF SOUND AND VIBRATION RE
Page 5 and 6: 1 Introduction The main objective o
Page 7 and 8: 2 Theory In this section we develop
Page 9 and 10: 2.2 Linearized Navier-Stokes Equati
Page 11 and 12: In order to solve the linear system
Page 13 and 14: 2.5 Asymptotic solutions of the sta
Page 15 and 16: 2.5.2 Far away from the axis of the
Page 17 and 18: 3 Numerical Scheme The equations de
Page 19 and 20: to r = rs, compute detF at rs and f
Page 21: method converges well for low Reyno
Page 25 and 26: 5 Summary • The linear stability
Page 27 and 28: References [1] V.K. Garg and W.T Ro
Page 29 and 30: Laplacian of a Vector, ∇ 2 V ∇
Page 31 and 32: From the above expressions for F an
Page 33: Components w ′ i w ′ 1 = − 1

Viscous Linear Instability of an Incompressible Round Jet T.M. ...

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