Regions of freshwater influence (ROFIs) - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 281

Density C urre n ts

Ebb

Saltier Fresher

Initially mixed
at HW

Stable density
profile develops
during ebb tide

Flood

Saltier Fresher

Initially
stratified
at LW

Instability and
convective mixing
approaching HW

Mixed profile
before HW

Figure 9.8 Straining of the density profile in a ROFI regime where the tide is in the form of
a standing wave. (a) During ebb flow shear in the tidal current moves lighter water over denser
thus promoting stratification. (b) In the following flood flow, the current shear is reversed
and stratification is reduced. Tidal and wind mixing during ebb tides can mean that flood
currents 'over strain' the density profile, leading to instability and convective mixing.

We can analyse the contribution of tidal straining to the evolution of stratification
by using Equation ( 9.18 ) with a tidal velocity profile of the form:

bz 0 2 u ðÞ¼^ u ð a Þ ð 9 : 23 Þ

which, with 0.425, is a

good approximation to observed profiles of tidal flow (Bowden and Fairbairn , 1952 ).
On substituting, we have:

u the depth-mean current and the constants a ^ ¼ 1.15 and b ¼

St ¼

ð ð

0
1 ð

0
1 ð

@
@

gh @
@

u @
@

z 0 dz 0 ¼ bz 0 2 z 0 dz 0

u ^ u Þ gh ^ a 1 Þ

t x x

ð 9 : 24 Þ

u @
@

b

4 ð

a 1 Þ

u @
@

¼ gh ^ ¼ 0 : 031gh ^

x : x 2

This is the source term which produces the observed periodic component of stratifi-
cation. The condition for SIPS to occur is that the average positive contribution of
@F

/ @ t on the ebb should exceed the effects of tidal mixing, i.e.

u 3 M2 2

031ghu 2 @
@

4
3

ek b 0 ^

0 : > ð 9 : 25 Þ

x h

which reduces to:

2 2

0 @

1 2

3

ek b u M2

h

^ u M2

h

^

10 5

x >

: : ð : Þ

2 2 9 26

@ 0 : 031g