## Kinetic Energy Spectra

We have Seen that oceanic circulation consists of many types of motion, acting over a range of scales within space and time.

I low. then, might it be possible lo Lali.nl.itL- ihe total kinetic energy of the ocean?

At any one point in the ocean, at a given time, the observed current may be regarded as the combination of a numher of components - perhaps a local northward wind-driven current has been superimposed on an inertia current generated some distance away (rattier like the situation illustrated in Figure 3.8). and this is in a region with strong tidal currents. Perhaps all of these motions are occurring in the region of an established current system like the Gulf Stream, which shows fluctuations but is nevertheless a permanent feature of the oceanic circulation. Such a long-term, large-scale flow is referred 10 as the mean flow (or. sometimes, the "mean motion"), If (he vary ing components of the How (tides, jneriia currents, eddies and other periodic fluctuations in currents) are resolved mathematically into regular oscillations, the relationship between the fluctuating components and the mean flow might look something like Figure 3.29.

hgure 3 29 A highly schematic representation of how current velocity might vary with rime for various fluctuating component. Over a long period (e.g. from A lo B), the fluctuating molinns average out. leaving only the mean llow represented by the straight line. (Not shown are fluctuations resulting from aperiodic phenomena Sucn as passage of a storm or large-scale eddy through the area in question - see Section 3 5.2.)

The kinetic energy of a mass m moving with speed v is given by \mv2. The kinetic energy possessed by a parcel of water at any instant is therefore the sum of the energies of all the components contributing to its motion, as determined by the squares of their speeds. For any particular region of the ocean, the fluctuations contributing to the overall current flow may be analysed to produce a kinetic energy density spectrum. Perhaps surprisingly, the fluctuating components account for most of the total kinetic energy of the flow, with only a very small proportion being contained in the mean flow.

period {hours)