Observations and Modelling of Fronts and Frontogenesis
Observations and Modelling of Fronts and Frontogenesis
Observations and Modelling of Fronts and Frontogenesis
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When (28) have been solved for the velocities vi, we<br />
time-step the evolution equations for the layer depths, upper<br />
layer density, <strong>and</strong> geostrophic velocities along<br />
characteristic curves in the respective layers. We then<br />
solve the boundary value problem for the vi with the new<br />
depths, density, <strong>and</strong> velocities. We repeat this process<br />
indefinitely. In a region where layer 2 vanishes, the<br />
nondimensional form <strong>of</strong> (l6c), which may be read <strong>of</strong>f from<br />
(28a) by replacing each subscript 2 with a subscript 3,<br />
replaces (28). The nondimensional matching conditions (20)<br />
<strong>and</strong> (23) are identical to the dimensional conditions, while<br />
the regularity condition (25) becomes,<br />
32{21'2y'2y + h2v2 + (h1v1)}<br />
- (1 u2y)v2 + (1 - u3y)v3 0. (29)<br />
The differential equations for the characteristic curves<br />
i(t,y) in layer i, i=l,2,3, are,<br />
d/dt vi, i(O,iO) iO' i=l,2,3. (30)<br />
Along the interior layer characteristic curves, the<br />
interior layer momentum equations (2a) satisfy,<br />
du(y,t)/dt = v(y,t), i = 2,3, (31)<br />
so the geostrophic interior velocities may be evaluated<br />
without any additional integration as,<br />
uj(t,t) = ujO(7iO) + (t,710) iO' i=2,3. (32)<br />
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