Seasonal stratification and the spring bloom - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 176

Figure 6.3 The entrainment
velocity across the interface in
a grid-stirred tank experiment,
as a function of a measure of
the Richardson number. The
entrainment velocity has been
normalized to a measure of
the turbulent velocity
generated by the oscillating
grid. [Figure will use open
circles only for the case of
density controlled by salinity
changes.] Adapted from
Turner, 1973 , with permission
from Cambridge University
Press.

1

0.1

0.01

1 10 100

Richardson number

feedback in the growth of stratification also occurs in the full-scale shelf sea system so
that, once stratification is established, it tends to grow and is not easily destroyed by
episodes of enhanced stirring until the onset of cooling and convective mixing in the
autumn. We shall return to this interesting feedback aspect in Section 7.4 , but we
now turn to an analytical representation of the heating/stirring competition in its
simplest form that we can then apply to the real ocean.

6.1.2 Criterion for water column stratification (the energetics of mixing

by the tide alone)

We shall formulate the basic competition between the stratifying and stirring agen-
cies in terms of a stratification parameter

F (Simpson, 1981 ) defined as:

ð

0
h ð ^ ð

1
h

Jm 3 F ¼ z ÞÞ gzdz ½ ð 6 : 1 Þ

with the water column mean density

0
h ð

ð

kgm 3

^ ¼ z Þ dz ½ ð 6 : 2 Þ

Here r(z) is the density profile determined from temperature and salinity profiles.
The parameter

F , referred to as the potential energy anomaly, is a quantitative