TURBULENT DIFFUSION OF HEAT AND
MOMENTUM IN THE OCEAN
CARL H. GIBSON AND Luis A. VEGA
Dcpurtmrnr oj .4pplied Muchunics und Engineering Sciences
a d the Scripps Insrirurion of Oceanography
Uniiwsiry of' Caltfornia. Sun Diugo. Lu Jolla, Caljfornia 92037. U.S.A.
AND
ROBERT BRUCE WILLIAMS
Naro Soc'lmir ASW Research Center. La Spesia, Italy
I . INTRODUCTION
Radiation from the sun is absorbed in the upper surface of the oceans,
changing the density of the nearby water and air in such a way that atmospheric turbujence is generated and oceanic turbulence is suppressed.
Viscous dissipation rates differ by three orders of magnitude for distances a
meter above and below the surface and four or five orders of magnitude for a
hundred meters. Nevertheless, turbulent diffusion is crucial to many oceanic
transport processes. This is suggested by the fact that the time constant L?/D
for the molecular diffusion of oxygen (D - lo-' cml/scc) through a meter
of water is several decades, yet life abounds throughout oceans many kilometers deep.
Because oceanic turbulence is so weak, and because background noise,
platform motion, and general inaccessibility is so strong, very few direct
measurements of turbulence or turbulent mixing in the m a n exist. The problem is illustrated by Table I, which lists typical values of viscous dissipation E
and thermal dissipation encountered in laboratory. atmosphere, and ocean
experiments. E values encountered in water tunnel studies are w e n orders of
magnitude larger than those one would like to be abk to measure in the
ocean. The viscous scale in the Ocean is nearly sixty times as large for this
reason, but this only brings the Kolmogoroff length up to 3 mm, which is
still very small for oceanographic current meters.
Temperature signal levels are equally difficult to detect in the Ocean and
occur at even smaller scales since the Prandtl number Pr = v/D * 10 for
temperature and the diffusive length is ( V ~ / E ) ' ' * P ~ - ' ' ~
(htchelor, 1959).
Because millimeter spatial resolution is needed at towing speeds of order
100 cm/sec, frequency response of the temperature sensor to a kilohertz is
needed to resolve the temperature fine structure fully.
Small scale, high frequency response insulatcd hot film anemometer
353
MOMENTUM IN THE OCEAN
CARL H. GIBSON AND Luis A. VEGA
Dcpurtmrnr oj .4pplied Muchunics und Engineering Sciences
a d the Scripps Insrirurion of Oceanography
Uniiwsiry of' Caltfornia. Sun Diugo. Lu Jolla, Caljfornia 92037. U.S.A.
AND
ROBERT BRUCE WILLIAMS
Naro Soc'lmir ASW Research Center. La Spesia, Italy
I . INTRODUCTION
Radiation from the sun is absorbed in the upper surface of the oceans,
changing the density of the nearby water and air in such a way that atmospheric turbujence is generated and oceanic turbulence is suppressed.
Viscous dissipation rates differ by three orders of magnitude for distances a
meter above and below the surface and four or five orders of magnitude for a
hundred meters. Nevertheless, turbulent diffusion is crucial to many oceanic
transport processes. This is suggested by the fact that the time constant L?/D
for the molecular diffusion of oxygen (D - lo-' cml/scc) through a meter
of water is several decades, yet life abounds throughout oceans many kilometers deep.
Because oceanic turbulence is so weak, and because background noise,
platform motion, and general inaccessibility is so strong, very few direct
measurements of turbulence or turbulent mixing in the m a n exist. The problem is illustrated by Table I, which lists typical values of viscous dissipation E
and thermal dissipation encountered in laboratory. atmosphere, and ocean
experiments. E values encountered in water tunnel studies are w e n orders of
magnitude larger than those one would like to be abk to measure in the
ocean. The viscous scale in the Ocean is nearly sixty times as large for this
reason, but this only brings the Kolmogoroff length up to 3 mm, which is
still very small for oceanographic current meters.
Temperature signal levels are equally difficult to detect in the Ocean and
occur at even smaller scales since the Prandtl number Pr = v/D * 10 for
temperature and the diffusive length is ( V ~ / E ) ' ' * P ~ - ' ' ~
(htchelor, 1959).
Because millimeter spatial resolution is needed at towing speeds of order
100 cm/sec, frequency response of the temperature sensor to a kilohertz is
needed to resolve the temperature fine structure fully.
Small scale, high frequency response insulatcd hot film anemometer
353