PREDICTION OF SUBSURFACE-DETONATION FALLOUT
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Specification of the Horizontal Wind Field for the Model
The horizontal wind field that transports the debris-disk centroids
during their fall to the earth’s surface may be specified in two ways in
the cratering fallout model:
1. Idealized Wind Hodograph. If H denotes height above surface
zero, then the horizontal wind, v,, at height H for a simple wind hodograph (see Fig. 5) is
A(p)
v,(H ) =v, (H,, )——
A(p_)
m)
— S(H,, — H)n
where y,(H,,) = steady-state wind at cloud-top level H,, (or it can be
specified as a function of time and space in either wind
component form or by means of a stream function)
A(p) = wind-shear component tangential to the horizontal wind
at cloud-top level and is evaluated from shot-time
winds in a diagnostic fallout calculation or from pre-
shot wind information for a predictive fallout calculation (it is held constant in time for the period of fallout
deposition)
A(p,,) = value of A(p) at cloud-top level (normally it is set equal
to 1)
S = wind-shear component normalto the horizontal wind at
cloud-top level (it is evaluated from shot-time winds or
preshot wind information, depending on the purpose of
the fallout calculation, and is held constant in time)
n= unit vector normalto v,(H,,) in a right-handed system
p = atmospheric pressure corresponding to H
. 2, Arbitrary Hodograph. The horizontal wind can be specified in
wind-component form for as fine a vertical interval as desired or for
which wind information exists.
Debris-disk Radius as a Function of Time
For estimation of the radius of a debris disk expanding by horizontal eddy diffusion during its fall to earth, it is proposed that the
disk radius as a function of time R,(t) be represented by
R,(t) = (Reg + 2Dt’)*
where t’
is the distance traveled by the disk centroid divided by the
mean horizontal wind speed in the layer through which the disk has
settled, R.) is the debris-disk radius at time of stabilization, and D
is the horizontal eddy-diffusion coefficient.? The diffusion coefficient
D is estimated as the Richardson’s diffusion coefficient 0.2 x f��, where