Pathways to Turbulence

in Strongly-Stratified Flows

James J. Riley

University of Washington, Seattle



Important issues in stable, strongly-stratified flows, often occurring in the atmosphere and oceans,

are when and how ‘classical’ 3D turbulence appears, and the properties of the resulting turbulence.

(Strongly stratified flows will be defined in terms of a local internal Froude number being small.) For

example, in the oceans at horizontal scales above a few meters, buoyancy often exerts a dominant

influence on the flows. One pathway to classical 3D turbulence in a strongly stratified flow is

through the generation and breakdown of propagating internal waves. In this seminar, another,

possibly more general, pathway is proposed, that of ‘stratified turbulence’.

The term stratified turbulence was introduced by Lilly (1983) to describe the dynamics of flows

dominated by stable density stratification. Such flows can consist of internal waves, but also of

quasi-horizontal, meandering motions; they possess potential vorticity, and are strongly nonlinear.

In examining laboratory and numerical simulations of these flows, a key aspect is whether an

activity parameter, defined by F2R, is large enough that small-scale, classical 3D turbulence can

be sustained. Here F and R are Froude and Reynolds numbers defined in terms of a velocity scale

and horizontal length scale characterizing the energy-containing motions.

To address these flows very high resolution direct numerical simulations are utilized. The flows

are initiated at low Froude number but with the Reynolds number as large as possible in order

to maintain a high activity parameter. It is found that strong, vertical shearing of the horizontal

motions develops, resulting in intermittent, smaller-scale turbulence, and in a strong energy cascade

of horizontal kinetic energy and potential energy to small scales. This appears to result in an

inertial subrange in the horizontal, but not in the vertical. The subrange is characterized by the

dissipation rates of kinetic and potential energy. The results are shown to be consistent with

previously unexplained oceanographic and atmospheric field data.