Required:
1. Find the Coriolis acceleration component in the x-y plane. Also prove that the component of the
Coriolis force per unit volume and its acceleration in the x-y plane point radially outward
from center of h
...
Required:
1. Find the Coriolis acceleration component in the x-y plane. Also prove that the component of the
Coriolis force per unit volume and its acceleration in the x-y plane point radially outward
from center of hurricane.
2. Find a relation between ∆P, jvj, Ω, and the latitude θ before the hurricane is mature using the
fact that the Coriolis and pressure accelerations sum to zero and the fact that, by definition,
the nonlinear, inertial forces in an immature hurricane are much smaller than the Coriolis
and pressure forces.
3. Find the approximate velocity of a mature hurricane by setting the magnitude of the Coriolis
and inertial (nonlinear) accelerations in the horizontal plane equal to each other.
4. Find ∆P and jvj for a mature hurricane by requiring that the Coriolis, Centrifugal and
Pressure accelerations sum to zero in the horizontal directions.
5. Estimate ∆P and jvj for hurricane Dorian. And compare these estimations to the actual
measurements.
2 Solution:
2.1
Based on the assumptions in the problem statement, we have
v ≡ jvjφ^ (1)
and
Ω = Ω[(^rsinφ + φ^cosφ)cosθ + z^0sinθ]; (2)
so, the Coriolis acceleration is
acoriolis ≡ 2v × Ω = 2V φ^ × Ω [(^r sinφ + φ^ cosφ)cosθ + z^0 sinθ] (3)
= 2V Ω (sinθ ^r − cosθ sinφ z^0); (4)
where we define jvj = V for convenience.
12.2
If we assume that the hurricane is axisymmetric, then
@P
@φ = 0: (5)
Therefore, the acceleration due to the air pressure is
a
p ≡
−rp
ρ
≡ −
1 ρ
(^r @P
@r + z^0 @z @P0 ):
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