ME 106 Spring 2021 HW1 Solution February 2, 2021

1 Required: 1. Find the Coriolis acceleration component in 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 , |v|, 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 |v| for a mature hurricane by requiring that the Coriolis, Centrifugal and Pressure accelerations sum to zero in the horizontal directions. 5. Estimate ∆P and |v| for hurricane Dorian. And compare these estimations to the actual measurements.