in which the constant 0.014 contains a dimension of C. Multiply both sides of eq 76 by ρ, cp, and
z and divide by ∆T, the difference in temperature between the measurement height and the surface
(which was not measured in this study because there is no proven and reliable technique to measure
the snow surface temperature). The following equation is obtained:
0.014
Nu =
RePr ,
(80)
∆T
where Nu is the Nusselt number defined as Hz/k∆T, Re is the Reynolds number u ρz /, and Pr is the
Prandtl number, cp/k. The essential purposes in expressing the results in terms of the dimension-
less Nusselt, Reynolds, and Prandtl numbers is to include the effect of air temperature on the
variation of physical properties of air such as viscosity , density ρ, specific heat cp, and thermal
conductivity k. Although eq 80 is dimensionless, it is not in typical dimensionless form because it
contains the term ∆T (which was introduced to define the Nusselt number and was not measured
during the test). However, as shown in Table 4, the correlation coefficients are rather high,
demonstrating that quantities such as u*, σw′ , σ u′ , and w′ T ′ are strongly dependent on u2m alone.
Although the tests were conducted over nearly a one-year period, the values of ∆T appear to vary
within a small range, and subsequently a more or less identical correlation will be produced if the
data ∆T is available and is used to evaluate the Nusselt number, where H is the heat flux, u is the
mean horizontal wind speed, and z is the measurement height.
Since the value of Pr for the temperature range from 240 to 300 K can be approximated by
Pr = 0.97 0.0009T,
(81)
where T is air temperature in Kelvin (K), substituting eq 81 into eq 80 we have
0.014
Re (0.97 - 0.0009 T ) .
Nu =
(82)
∆T
As long as the mean wind speed u is known, along with the temperature at height z, even without
the data on ∆T, heat flux H can be calculated from eq 82 because ∆T is also used in defining the
Nusselt number Nu (i.e., Hz/k∆T), so we do not need to know the value of ∆T to calculate H from eq
82.
For an average temperature of 273.1 K during the winter months, eq 82 can be further
simplified as
0.010
Nu =
Re .
(83)
∆T
On the other hand (Table 4), for the period from May to August 1991, and by assuming an average
air temperature of 293 K, an expression of
0.028
Nu =
(84)
Re
∆T
can be derived. The value of ∆T does not come into the process to calculate heat flux H in either eq
82 or 84, so for the same value of Re values of H are about three times greater during the summer
season than during the winter. For the whole year (May 1991April 1992) based on the data shown
in Table 4, the value of Nu can be expressed by
0.024
Re (0.97 - 0.0009 T ) .
Nu =
(85)
∆T
Therefore, as long as the mean horizontal wind speed and the air temperature at the height of the
sonic measurement are determined, the value of Re can be calculated and subsequently the heat
flux H can be determined.
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