TR No. 22 
It has further been hypothesized (Kolmogoroff, 1941) that if 
there exists within the equilibrium range of wave numbers a range (the 
inertial subrange) where dissipation is negligible, then E(/X, t) is 
independent of Y and therefore of Ky 3 and consequently F(K/ky must 
be a constant, Therefore, within the inertial subrange, 
BR Se 
BORO RIE Ra (3) 
The necessary condition fcr the existence of an inertial subrange 
of wave numbers has been shown (Batchelor, 1) to be that condition in 
which the Reynolds number of the turbulence is large enough so that the 
Wave numbers corresponding to the maximum dissipation of energy and to 
the maximum energy are considerably separated on the wave number scale. 
This condition is satisfied (Grant, Stewart and Moilliet, 2) in large 
scale oceanographic flows, wherein the wave numbers corresponding to the 
Maximum energy are several orders of magnitude smaller than those cor- 
responding to the maximum dissipation of energy. (The wave numbers cor- 
responding to the maximum dissipation of energy are of the same order of 
Magnitude for oceanographic turbulence as for laboratory turbulence. ) 
Measurements of the turbulent velocity component parallel to the 
axis of a tidal current were made by Grant, Stewart and Moilliet (2) 
using a hot film anemometer mounted on the front of a heavy, towed body. 
The instrument was towed from the research vessel C. N. A. Ve OSHAWA at 
a depth of 15 meters in Discovery Passage, adjacent to Vancouver Island. 
One-dimensional energy spectra were derived from samples of the data 
using analog filtering techniques over the range of wave numbers from 
0.01 em™*+ to 35 em™1, ‘The spectra followed the -5/3 power law predicted 
by the Kolmogoroff hypothesis from wave numbers of around 0.01 em™t to 
emt, thus indicating the extensiveness and importance of the inertial 
subrange in oceanographic turbulence, Similar measurements have been made 
by Grant and Moilliet (3) of the turbulent velocity component perpendicular 
to the axis of a tidal cyrrent (Discovery Passage south of Cape Mudge). 
Although a calibration of the hot film anemometer was not obtained, the 
spectra were of the -5/3 power law form when represented on an arbitrary 
scale, The first set of measurements allowed the energy dissipation 
spectra to be calculated, from which values of € and hence the universal 
constant K could be determined. 
