Response to forcing: the governing equations and some basic solutions - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 86

large increase in wave height and tidal currents, by factors of 16 respect-

ively, as the tide crosses into the shallower water of the shelf while conserving energy;
and second, the possibility of further amplification governed by the proximity of the
geometry of a semi-enclosed shelf region to resonance with the tidal wave.

∼

2.5 and

∼

3.7 Tidally averaged residual circulation

...................................................................................
Having looked at the basic responses of the shelf seas to forcing by wind, tides and
density differences, we might ask at this point: what is the effect of the combined
responses in terms of the net movement of water particles? In other words, what is the
extent of the residual circulation? Most of the movement induced by tidal forcing
is oscillatory in nature and does not result in a significant net displacement when
the flow is averaged over a tidal cycle. Similarly, wind forcing is highly variable in
direction and so the net effect of wind-induced movements tends to be greatly
reduced by averaging over a period of months. On the other hand, horizontal density
gradients, if sustained, can drive significant geostrophically balanced residual flows.
In addition, energetic tidal motions can result in rectified currents through processes
involving the non-linear terms in the equations of motion.
Few shelf sea areas have been subjected to the intensive long-term study with
current meters needed to properly determine their residual circulation. Even where
measurements have been made, there can be difficulties in resolving small residual
flows in the presence of strong tidal flows. The alternative to direct current measure-
ment is to determine the residual currents on the basis of tracer distributions.
For example, Fig. 3.17 shows the distributions of Caesium Cs 137 , a radionuclide with
a half life of 30 years which is released from the Sellafield nuclear processing plant

on the northwest coast of England. The contours of this tracer indicate a residual
flow northward from the Irish Sea and passing around the north of Scotland and on
into the North Sea. This observed Cs 137 distribution has been used in conjunction
with a numerical model to infer the details of the residual flows (Prandle, 1984 ). With
the exception of a few relatively energetic flows at the shelf edge and along some
coasts where density gradients are large, the long-term average currents over much of
this area are found to be weak, typically

∼

2cms 1 . Such small flows are consistent
with the limited contribution of horizontal transport to the heat budget, which we
found in Section 2.2.4 . Together, these results provide a basis for the assumption,
which we shall make in later chapters, that vertical exchanges predominate over
horizontal fluxes in the control of water column structure. We will see in Chapter 8
that stronger residual flows can be associated with fronts in shelf seas; while still
much weaker than the tidal currents, these consistent residual currents can play an
important role in the transport of, for instance, fish larvae.
Consideration of these weak residual flows within the shelf sea interior also allows
us to lay to rest a commonly held misconception about circulation through the seas
off Western Europe. Low average flow rates imply long residence times for water
particles. For example, the time for a water particle to pass through the North Sea is

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