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Deriving the expression for wind velocity around low pressure area

  1. Jun 14, 2013 #1
    Hi
    Can somebody tell me the steps and assumptions made in deriving the equation to calculate the wind velocity around a low pressure area ? (see the attachment fro Kleppner & Kolenkow).
    I tried to derive like this :
    Coordinate system located on earth's surface with i direction towards E, j direction towards N and k direction upwards.
    Initial wind velocity V = Vx i + Vy j
    Ω = Ω sin λ j + Ω cos λ k where λ is the latitude of the place considered.
    Position vector of parcel of air r = rx i + ryj

    Eqn for the rotating system is
    marot = mainertial - 2m Ω * V - Ω * (Ω * r) ----- (1)

    mainertial = -(ΔP)S j where S = cross sectional area of parcel of air

    As the flow is assumed to be steady, LHS of equation 1 i.e. marot = 0

    RHS evaluated vectorially.

    However, I cannot get the expression shown in the attachment.

    Please help out. Is there any other text which shows this derivation ?

    TIA
     

    Attached Files:

    • K&K.pdf
      K&K.pdf
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  2. jcsd
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