Question

Consider an air parcel at latitude = 18◦N, moving northward (conserving absolute vorticity), with initial relative vorticity = 5.8 × 10−5 s −1 . Please calculate the relative vorticity of the air parcel when it reaches 50◦N.

Answer 1

Answer:

relative vorticity is  -0.868 × $10^{-5}$ s-1

Explanation:

given data

air parcel at latitude = 18◦N

relative vorticity = 5.8 × 10^−5 s−1

to find out

relative vorticity

solution

we will apply here conservation of vorticity that is

ζ + f = constant

we know ζ initial = 2Ωsin(5π/18)

and  f initial = 5.8 × $10^{-5}$

and f final =  2Ωsin(π/18)

and here angular frequency Ω = 0.7272 × $10^{-4}$ s-1

its mean

ζ initial -  ζ final = f final - f initial

so

ζ final =  ζ initial - f final + f initial

ζ final =  - 2Ωsin(5π/18) + ( 2Ωsin(π/18) +  5.8 × $10^{-5}$  )

ζ final =  - 2(0.7272 × $10^{-4}$) sin(5π/18) + ( 2(0.7272 × $10^{-4}$)sin(π/18) +  5.8 × $10^{-5}$  )

ζ final = -0.868 × $10^{-5}$ s-1

so relative vorticity is  -0.868 × $10^{-5}$ s-1