Seasonal stratification and the spring bloom - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 177

Figure 6.4 The input of buoyancy due
to surface heating.

Heat

z

Δ Q

z =0

h 1

B

T ( z )

z = -h /2

z =- h

measure of stratification and represents the work required per unit volume to bring
about complete mixing of the water column. We can see this by splitting the integral
into its two components,

8
<

9
=

ð ð

0
h ^

0
h

1
h

F ¼ gzdz gzdz

: ;

ð 6 : 3 Þ

1
h f

:Þg ¼

PE
h

¼ PE ð mixed Þ PE ð strat ;

which are measures of the potential energy (PE) per unit area of the water column
before and after mixing.

is zero for a fully mixed column and becomes increasingly
positive as stratification increases.
Before proceeding further, we make two simplifying assumptions, namely (i) that
buoyancy input is only via surface heat exchange and (ii) that stirring is due only to
tidal flow. Both these restrictions will be removed later on, but for the moment they
provide valuable simplifications of the problem.
We start the analysis by asking how the input of buoyancy by heating will
change

F

Q [J m 2 ] entering the mixed
water column as solar radiation at the start of the seasonal heating cycle (soon after
the vernal equinox). As we saw in Section 2.2.1, this heat input will be absorbed close
to the surface in a thin layer, shown in Section Fig. 6.4 , which we represent as a mixed
layer of thickness h 1 . Within this layer the temperature will be increased by:

F . Consider an amount of heat per unit area D

Q
c p 0 h 1

½ C T ¼ ð 6 : 4 Þ

where c p is the specific heat capacity of seawater (4000 J kg 1

C 1 ). This rise in

temperature will reduce the density by:

r 0

Q
c p h 1 0 ¼

a Q

c p h 1 ;

¼ a r 0 T ¼ a ð 6 : 5 Þ