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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In a manner exactly analogous to that leading to (16), making<br />
careful use <strong>of</strong> (A6), an equation for the ageostrophic<br />
velocities may be obtained:<br />
g(p<strong>of</strong>Y1(p3 pB)[(h3v3) vBh3TjI + (f u3y)(vB - v3)<br />
g(p0f)[(p3 PB) We] y<br />
This may be rewritten as<br />
re(z) [ Q + (PB p)w(z)Jy)<br />
g(pf)((p3 PB)(h3v3)yy + [(P3 PB)e]y<br />
g(pfY1-(p3 pB)vBh3 (f U3y)(V - v3)<br />
- (poh1)(rX(z) Te(z)<br />
(A9)<br />
[- Q + (PB - p)w(z)]y). (AlO)<br />
Then (AlO) may be integrated across the interval (y2 6'Y2 +<br />
6), in which the transition layer between the two homogeneous<br />
parts <strong>of</strong> the composite layer meet the surface <strong>of</strong> layer 3, <strong>and</strong><br />
the width 26 <strong>of</strong> this region allowed to approach zero. If we<br />
assume that h3 is twice differentiable at y2(t), none <strong>of</strong> the<br />
terms on the right h<strong>and</strong> side <strong>of</strong> (AlO) will be singular in the<br />
limit as 5 0, so their integral across this region will<br />
vanish in that limit. Since layer 1 consists primarily <strong>of</strong><br />
fluid that has been entrained from layer 2, the variation in<br />
PB is very small. If it is neglected altogether, the left<br />
h<strong>and</strong> side <strong>of</strong> (AlO) may be integrated exactly across the<br />
transition region. The result is (23c).
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