Geoscience Reference
In-Depth Information
Chapter 3
Turbulence Basics
Abstract: When differential motion occurs between a sea ice cover and the up-
per ocean, momentum is exchanged across a turbulent boundary layer. If the heat
and mass balance at the ice-ocean interface dictates ice growth or ablation, the tur-
bulence will also transport heat and salt. This chapter introduces basic features of
turbulence in natural flows, by describing general characteristics of turbulence; how
it is measured in the somewhat unique under-ice environment; along with a dis-
cussion of how turbulent fluxes are estimated, including statistical significance and
assumptions underlying the connections between time-series covariances and en-
semble averages of turbulent fluctuation products. Simplified forms of the turbulent
kinetic energy and scalar variance equations are described, and related to spectral
characteristics including a length scale proportional to the inverse wave number at
the peak in the vertical velocity spectrum.
3.1 General Characteristics
There exists little consensus on a precise definition of fluid dynamical turbulence.
Hinze (1975) defines it thus: “Turbulent fluid motion is an irregular condition of
flow in which the various quantities show a random variation with time and space
coordinates, so that statistically distinct average values can be discerned.” Tennekes
and Lumley (1972) list pertinent characteristics of turbulent flow: (i) turbulence is
irregular (as in Hinze's definition); (ii) it is highly diffusive, which causes rapid
mixing and increases transfer rates; (iii) it occurs at high Reynolds number,
1
as
instabilities from interaction of viscous and inertial forces manifest themselves; (iv)
it is both highly rotational and three dimensional; (v) it is essentially dissipative,
meaning that work must be done to maintain viscous losses to internal energy of the
flow; and (vi) turbulence at high Reynolds number is a characteristic of the flow,
rather than the particular fluid.
1
Re
=
UL
/
ν
,where
U
and
L
are characteristic velocity and length scales in the flow and
ν
is
kinematic molecular viscosity.
