University:
Widener University
Course:
ESSC 103 | Intriduction To Earth Science
Academic year:

2023
Views:

215

Pages:

1
Author:

bravacooperages

Coriolis force lab The code simulates movement of a particle on a rotating ellipsoid under the inﬂuence of gravity and speciﬁed forces. The dynamical equations can be found from a Lagrangian (for conservative forces) λ 1 L = u2 − φg (x) − S(x) − V 2 2 where φg is the gravitational potential (NOT the geopotential which also includes centrifugal terms), λ is a Lagrangian multiplier and the constraint that the particle remain on the surface is 1 S(x) = (x2 + y 2 ) + Ez 2 − a2 = 0 E Here E is the ratio of the equatorial radius to the polar radius and a is the average radius related to the volume. V is the potential for the additional forces. Coriolis force lab problems: 1) Show that starting the particle with velocity u = Ω × x gives a stationary solution in the rotating frame. 2) Find the frequency of oscillations for perturbations around the stationary solution. How does this frequency depend on latitude? Amplitude? 3) Find the velocity which leads to a steady solution in the presence of a northward force. How does it depend on the force? 4) For a high or low pressure center force = ±0.1*center(x,[0.7;0;0.7],0.3,omega*t) ﬁnd the initial velocity which give smooth solutions, What is the period of the motion and how does it depend on the strength/ sign of the forcing?