Ekman Spiral. Consider a local Cartesian coordinate system (X, Y, Z) in the nort

Question

Ekman Spiral. Consider a local Cartesian coordinate system (X, Y, Z) in the northern hemisphere where X Cartesian coordinate axis is assumed to be directed eastward and Y Cartesian coordinate axis is assumed to be directed northward (conventional geographic system). Calculate and plot Ekman-model x and y wind components, u(z) and v(z), and corresponding wind hodograph (Ekman spiral) for the range of z from 0 to 4000 m in the above specified coordinate system. Model parameters: x and y geostrophic wind components are U_g = -5 m s^-1 and V_g = 8 m s^-1, respectively; Coriolis parameter is f = 10^-4 s^-1; and eddy diffusivity is k = 50 m^2s^-1. Evaluate the planetary boundary layer depth scale. Calculate and plot Ekman-model wind components and corresponding wind hodograph (Ekman spiral) for the range of z from 0 to 4000 m and with the same values of f and k as in a, but in the Cartesian coordinate system with the X axis (denote it as X) directed along the geostrophic wind vector from case a. Calculate and plot Ekman-model wind components, and corresponding Ekman spiral for the range of z from 0 to 4000 m and with the same values of f and k as in a, but in the Cartesian coordinate system with the X axis (denote it as X") directed along the near-surface wind from case a.

Explanation / Answer

f = 10- 4 s¯¹

k= 50 m2 s¯¹

ae = SqareR(f/k)

  =0.000002 m-1

Planetary boundary-layer depth scale / ae=22/7*0.000002

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