Drag coefficients, June 1996
1. Bulk method
Neutral drag coefficients were calculated from the
TOGA-COARE
bulk algorithm using 1 Hz 30m data. This algorithm iterates to get
the Monin-Obokov length L, estimates the profile function, and derives
the transfer coefficients, u*, and u adjusted to a reference level (among
other variables.)
The drag coefficient vs winds adjusted to 10m
is shown here.
Above about 6 m/s, the drag coefficient increases with wind speed. Below,
it decreases with wind speed where flow is aeronautically smooth. The coefficient
has not been adjusted to neutral.
2. Direct method
Neutral drag coefficients were calculated from direct
fluxes from the 30m runs. The drag coefficient vs winds adjusted
to 10m is shown here.
The increase at low wind speeds is seen again. The proceedure outlined
in Enriqez
(1994) was followed to adjust the coefficient to neutral.
A linear fit to the data gives:
U10 < 6 m/s,
Cdn*1000 = -.26097*U10 + 2.4316
U10 >= 6 m/s, Cdn*1000
= .064986*U10 + .44053
The relation to U10 resembles open ocean measurements from Yelland
and Taylor (1996) and central California coastal measurements from
Enriqez
(1994), as can be seen in this comparison.
(The Enriquez (1994) value is quite similar to the Large and Pond (1981)
relation above 12 m/s.) Later I may discard points where sea-air
T diff and heat flux are not of same sign, as in Edson et al (1998).
3. Comparison
Comparison
of drag coefficients from the 2 methods. The coefficient
from the direct method depends more strongly on wind speed, and for speeds
greater than 6 m/s, better resembles the Enriquez (1992) calculation for
central California in summertime.
Difficulties with the direct method
The direct method is more scattered than the bulk algorithm, but gives
values closer to previous studies. It was found that choosing
segments where the plane did not change altitude more than 15 m or undergo
turns was crucical. Often only half a run could be used. The
averaging time was chosen by the frequency at which most ogives reached
an asymptotic value (120 seconds). Data south of Point Conception
was not included since winds changed drastically heading out of the Santa
Barbara Channel.
Is the change at 6 m/s due to a change in the wave state?
Bulk drag coefficients
Graphs of the drag coefficient calculated from the bulk algorithm are in
the table below.
The top graph shows the drag coefficeint vs speed adjusted to 10 m.
A linear fit to the data is shown in red and its equation given in the
title.
The bottom graph shows a map of the drag coefficient for the average
speed of the flight day. The slope of the drag dependence on U was
used to adjust the local winds to Uaverage, and calculate Cdn from that,
as in Enriquez
(1994). All data was from the lowrate 30m runs shown in
black on the bottom map.
Note that flights with low wind speeds (June 02 and 26) have a double
valued Cd for u10<5 m/s or so. Could this be due to higher
SST in low wind cases, causing Cd to increase due to unstable conditions?
Change of stress with height depends on layer stability
Unstable stress decreases linearly from the surface, while there is curvature
for stable cases as shown here
(from M. Tjenstrom and A.-S. Smedman, "The vertical turbulence structure
of the coastal MABL," JGR 93(C3), p. 4821.)
This was also seen by J. Zemba and C. A. Friehe, "The marine atmospheric
boundary layer jet during CODE", JGR 92(C2), 1489-1496 .
In the table below are stresses calculated from the level runs only.
They are directly calculated using the eddy correlation method. In
Tjenstrom and Smedman stresses are calculated from profiles, which I plan
to do later. Though less statistically reliable than the level run
fluxes, fluxes from sawtooth legs would allow the stress profiles to be
calculated. The blue lines show 0 and 1st order fits to the
data (not very good).
The data on this page is unpublished. If it is used please cite the
author Kathleen Edwards, the Center for Coastal Studies, and the Coastal
Waves group at Scripps Insitution of Oceanography.
Please send comments or questions to me at kate@coast.ucsd.edu
