DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

smoothing effect of molecular thermal diffusivity
κT . In natural waters, χ is mostly estimated
by profilers that measure the temperature fluctuations
T ′ at a high rate (at least such, as to
resolve the structures to the Batchelor scale). If
small-scale turbulence is isotropic, the rate of
dissipation of temperature variance χ[K2s−1 ]
is estimated from the temperature gradient spectra
by χ = 6κT , where z is
the profiling direction. The vertical turbulent
diffusivity κt v can be estimated by the relation
κt v = χ[2(∂T/∂z)2 ] −1 , a procedure often referred
to as Osborn–Cox method (Osborn and
Cox, 1972). See Cox number.
dissipation of turbulent kinetic energy
The rate at which turbulent kinetic energy ɛ[W
kg−1 ] is transformed to heat by internal friction
caused by viscosity ν. Dissipation is given
by ɛ = 2ν
ij [0.5 · (∂ui/∂xj +∂uj/∂xi)] 2
(see strain rate). In natural waters, ɛ is mostly
estimated by profilers that measure one velocity
component u ′ in the direction perpendicular
to the motion of the measuring profiler (directionz).
For isotropic small-scale turbulence, the
above nine terms in the summation collapse to
the simple form ɛ= 7.5ν (
indicates the average over a length scale, chosen
typically 0.5 to several meters). An alternative
estimate can be determined by the inertial dissipation
method.
dissipation profiler Instrument for the measurement
of oceanic turbulence levels. It is
equipped with fast sampling airfoil probes and
thermistors to resolve velocity and temperature
fluctuations in the dissipation range. Generally,
these instruments are designed to either fall or
rise vertically in the water in order to produce a
profile of the turbulent activity in the water column.
For certain applications, the instruments
are towed horizontally.
dissipation range The range of length scales
or wavenumbers at which velocity fluctuations
in turbulent flows are damped out (dissipated)
by molecular viscosity. See Kolmogorov scale,
turbulent cascade.
dissipation rate Rate at which turbulent
kinetic energy ( tke) is removed from turbu-
© 2001 by CRC Press LLC
diurnal
lent flows at length scales defined by the Kolmogorov
scale. The dissipation rate enters the
turbulent kinetic energy equation as the term
ɛ= 2νeijeij
whereν is the viscosity andeij is the fluctuating
strain rate tensor defined by
eij ≡ 1
∂ui
+
2 ∂xj
∂uj
∂xi
whereui andxi are the velocity and position, respectively,
for the spatial directions i= 1, 2, 3.
In oceanic turbulence studies,ɛ can be estimated
from measurements of velocity gradients. Under
the assumption of isotropic and steady turbulence,
ɛ is estimated from
ɛ= 15
2 ν
∂u2
∂x1
2
where x1 is the direction along which the measurement
device measures the perpendicular turbulent
velocity fluctuations u2. See also airfoil
probe.
dissolved organic matter See colored dissolved
organic matter.
distance indicator See standard candle.
distance modulus The distance to an object
can be derived by comparing its apparent magnitude
(m) and absolute magnitude M, where
M is defined to be the flux of the star at a standard
distance of (10pc2 ). Using the standard
definition for magnitude, we have
L/4πR2 m − M =−2.5 log
L/4π(10pc2
)
where R is the distance to the star and L is the
star’s intrinsic brightness (luminosity). This reduces
to
m − M = 5 log(R) − 5 .
diurnal Due to the daily variation of the solar
radiation received at the Earth’s surface, meteorological
quantities, such as temperature, pressure,
atmospheric pollution, wind speed and direction,
etc. have daily variations. Diurnal variation
is a periodic variation and does not contain