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In this paper, the Green function method is used to obtain the exact solution of Couette flow. By defining the Couette flow energy, the relative energy and the energy increase ratio, we discuss the relations between the structure of initial field and the evolution of Couette flow energy, the relations between the time corresponding to Couette flow energy attaining to its maximum and the structure of initial field together with the structure of initial field which can optimal excitated Couette flow energy increasing within a finite time interval. We further investigate the relations between the perturbed initial field and the evolution of Couette flow energy. The conclusions of this paper are supplementary to Farrell’s conclusions.
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Keywords:
- Couette flow /
- Green function method /
- normal mode /
- initial value problem
[1] ［1]Orr W M 1907 Proc.R.Irich Acad. A 27 69
[2] ［2]Lin C C 1955 The theory of hydrodynamic instability（Cambridge Univ. Press） 155
[3] ［3]Eliassen A E 1953 Inst.Weather Climate Res. 1
[4] ［4]Holland E 1953 Geofys,Publ. 18 1
[5] ［5]Case K M 1960 Phys.Fluids 3 43
[6] ［6]Pedlosky J 1964 Tellus 16 12
[7] ［7]Burger A P 1966 J.Atmos.Sci. 23 272
[8] ［8]Zeng Q C 1983 J.Atmos.Sci. 40 73
[9] ［9]Yamagata T 1980 J.Meteorol.Soc. Japan 58 160
[10] ［10]Tung K K 1983 J.Fluid Mech. 133 443
[11] ［11]O’Brien E 1992 J.Atmos.Sci. 49 1557
[12] ［12]Boyd J P 2002 J.Phys,Oceanogr. 32 2589
[13] ［13]Rosen G 1971 Phy.Fluids 14 2767
[14] ［14]Farrell B F 1982 J.Atmos.Sci. 39 1663
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[1] ［1]Orr W M 1907 Proc.R.Irich Acad. A 27 69
[2] ［2]Lin C C 1955 The theory of hydrodynamic instability（Cambridge Univ. Press） 155
[3] ［3]Eliassen A E 1953 Inst.Weather Climate Res. 1
[4] ［4]Holland E 1953 Geofys,Publ. 18 1
[5] ［5]Case K M 1960 Phys.Fluids 3 43
[6] ［6]Pedlosky J 1964 Tellus 16 12
[7] ［7]Burger A P 1966 J.Atmos.Sci. 23 272
[8] ［8]Zeng Q C 1983 J.Atmos.Sci. 40 73
[9] ［9]Yamagata T 1980 J.Meteorol.Soc. Japan 58 160
[10] ［10]Tung K K 1983 J.Fluid Mech. 133 443
[11] ［11]O’Brien E 1992 J.Atmos.Sci. 49 1557
[12] ［12]Boyd J P 2002 J.Phys,Oceanogr. 32 2589
[13] ［13]Rosen G 1971 Phy.Fluids 14 2767
[14] ［14]Farrell B F 1982 J.Atmos.Sci. 39 1663
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