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.