Waves, turbulent motions and mixing - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 105

energy from internal waves, generated mainly by stratified flow over topography,
assumes considerable importance as one of the few sources of energy available to drive
the vertical mixing and maintain biogeochemical fluxes through the thermocline.

4.3 Turbulence and mixing

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We turn now from the well-developed theory of wave motions to a less well under-
stood class of motions which play a crucial role in our later discussion of processes in
the shelf seas. Turbulence is the random fluctuation of flow and properties which
is widely observed to occur in moving fluids. We experience it in the gustiness of the
wind and see it in the eddies which are apparent in the swift flow of a river. It is
present for much of the time almost everywhere in the shelf seas and plays a key role
in the dynamics and in the mixing of water properties. It has long been recognized
that turbulence has its origin in the instability of larger scale motions which arise
through the non-linear nature of the equations of motion, but detailed understanding
of the processes of turbulence remains limited, with much of the theory being of
a semi-empirical nature.
In this section, we shall describe the nature of turbulence, its generation by stirring,
its dissipation through frictional stresses and the way it brings about dispersion and
mixing. The subject of turbulence is extensive and our coverage will, necessarily, be
selective, with a focus on those aspects which are relevant in the discussion of
processes in the shelf seas in later chapters. For a fuller account of some of the topics
discussed below and a more general view of turbulent processes in the ocean, the
reader is referred to the excellent volume by Thorpe (Thorpe, 2005 ).

4.3.1 The nature of turbulence and its relation to mixing

Marine turbulence is sometimes referred to as the 'disorganized motion of the ocean'.
Turbulence has a chaotic aspect, first described in the late nineteenth century by the
physicist Osborne Reynolds on the basis of studying the flow of water in pipes. At
sufficiently low flow speed U 0 in pipes of small diameter d, Reynolds found that dyed
fluid particles followed straight line paths parallel to the pipe wall in what is referred
to as 'laminar flow'. But as U 0 or d increased there came a point of abrupt transition
to a turbulent flow regime in which fluid particles no longer stayed on wall-parallel
streamlines but acquired random components of velocity both across and along the
pipe axis. Reynolds deduced that the switch between laminar and turbulent condi-
tions was controlled by the relative magnitude of inertial and viscous forces, which
he expressed in a non-dimensional number Re

¼

U 0 d/n where n is the kinematic
viscosity of the fluid (units m 2 s 1 ). For values of this Reynolds number of greater
than about 2000 the flow was turbulent and dye, introduced at a point into the flow,
was rapidly diffused across the pipe cross-section by turbulent flow components.
Here we are interested in the high Reynolds number flows we often find in the shelf
seas, and we want to be able to describe how the associated turbulence behaves, how