Observations and Modelling of Fronts and Frontogenesis

to remove the inertio-gravity waves. The momentum and
continuity equations are, in the surface mixed layer (layer
1),
ult + Viuly - fv1 TZ/P0 = (TX re)/pOhl, (la)
fu1 = /POi (lb)
Plz = - gp(y,t),
vly + wlz = 0,
and in the interior layers (layers 2 and 3),
(ic)
(ld)
uit + ViUiy fv 0, (2a)
fui Piy/P0 (2b)
Pjz = gpj. (2c)
Viy + = 0, i=2,3. (2d)
Here (ui,vi,wi) are the (x,y,z) components of velocity and Pj
is density in layer i, i = 1,2,3, p is pressure, h1 is the
depth of the mixed layer, P0 is a constant reference density,
f is the Coriolis parameter, and g is the acceleration of
gravity. Subscripts x, y, and z denote partial
differentiation. The upper layer density p is allowed to
vary with y and t, while the interior layer densities are
constant. The angle brackets around the upper layer pressure
gradient denotes a vertical average through the mixed layer.
This allows the neglect of the vertical shear that is
associated with horizontal density gradients through the
thermal wind relation. (This procedure can be justified as
in de Szoeke and Richman (1984) by an expansion in orthogonal
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