Response to forcing: the governing equations and some basic solutions - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 89

Problems

....................................................................................................................
3.1. A cubic metre of near-surface water in the core of a steady current at latitude
33 N is moving to the northeast (045 T) at a speed of 1.75 ms 1 .
Determine:

(i) The Coriolis parameter in this latitude
(ii) The magnitude and direction of the Coriolis force acting on the water particle
(iii) The magnitude and direction of the slope of the sea surface assuming the
current is in geostrophic balance.

3.2. Explain how the horizontal components of the Coriolis force are balanced in
inertial oscillations and show that the period of these oscillations T f is equal to
2

/f where f is the Coriolis parameter. Estimate T f and the scale of the inertial
circle at latitude 32 S if the current speed is 0.27 ms 1 .

p

3.3. (i) A steady wind blows over the open ocean remote from land boundaries at
latitude 55 N. If the wind stress is 0.5 Pa and directed to the east, what will
be the magnitude and direction of the vertically integrated transport?
Explain which forces are involved and any assumptions you make.
(ii) If a wind of this magnitude is switched on abruptly, what will be the form of
the motion in the approach to a steady state? What other 'forces' are
involved in the transient motion?

(HINT: Check your answer to part (i) and investigate the transient response of
part (ii) by using the Ekman3 option at the website.)

3.4. A rectangular gulf of length 900 km, breadth 150 km and depth 60 metres
co-oscillates with the adjacent ocean. If the amplitude of the M 2 constituent at
the ocean boundary is 1.2 metres, estimate:

(i) The range at the head of the gulf.
(ii) The position of the nodes in the gulf.
(iii) The maximum level difference across the gulf if it is situated in latitude 35 S.

Describe the tidal regime in the gulf and make a schematic plot of the co-tidal
and co-range lines.

3.5. How does energy dissipation by bottom friction influence the position of amphi-
dromes in the shelf seas? Estimate the ratio of reflected and incident amplitudes of
the two Kelvin waves in a rectangular gulf of depth 46 metres at latitude 57 Nif
the single amphidrome in the gulf is displaced by 47 km from the axis of the gulf.