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

relative vorticity is -0.868 ×
`10^(-5)` s-1

Step-by-step 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