Observations and Modelling of Fronts and Frontogenesis

solution exist in the neighborhood of such a point. In order
to remove the singular solution, we impose the regularity
condition,
g(pf)(p3 - p2)[2h2v2 + h2v2 + (h1v1)I
- (f u2y)v2 + (f - u3y)v3 = 0. (25)
This may be derived either by power series solution of (16)
or by inspection of (24), requiring that v2 be bounded at
Y Y2-
The three conditions (20), (23), and (25), applied at
any juncture of two- and three-layer subdomains, close the
problem for the equations (16), with the boundary conditions
(17), when layer 2 vanishes in any portion of the domain.
III .2 . c Nondimensionalization
We nondimensionalize the equations by dimensional
quantities related to the forcing. In this subsection,
primes will denote nondimensional variables. Typical
dimensional values will be given in brackets. The basic
scales are the friction velocity u* [1 cm s] and the
heating Q* [75 W m2], in terms of which the forcing may be
written,
= pou*2r' [0.1 N m2], Q = Q*Q'.
The nondimensional variables and dimensional scales (with
0.5 (Davis et al., l981a, l981b), P0 = l0 kg m3,
g = 9.8 m 2, = i0 sfl-, specific heat of water at
(26a)