On Lamb wave propagation from small surface explosions in the atmospheric boundary layer Page: 4 of 6

                                
On Lamb Wave Propagation From Small Surface Explosions in the
Atmospheric Boundary Layer.
Douglas O.ReVelle, Sergey N.Kulichkov2
'Atmospheric and Climate Sciences Group Los Alamos National Laboratory
2 A.M.Obukhov Institute of Atmospheric Physics Russian Academy of Sciences,
3 Pyzevsky,Moscow 109017,Russia, Tel: 7(095) 953-4876; Fax: 7(095) 953-1652.,
e-mail: snk@omega.ifaran.ru; root@iaph.msk.su
1.Abstract
The problem of Lamb waves propagation from small explosions in the atmospheric boundary layer are
discussed. The results of Lamb waves registrations from surface explosions with yields varied from 3 tons
up to a few hundred tons (TNT equivalent) are presented . The source-receiver distances varied from 20
km up to 310 km. The most of the explosions were conducted during the evening and early morning hours
when strong near-surface temperature and wind inversions existed. The corresponding profiles of
effective sound velocity are presented.
Some of the explosions had been realized with 15 minutes intervals between them when morning inversion
being destroyed. Corresponding transformation of Lamb waves was observed.
The Korteveg-de Vrize equation to explain experimental data on Lamb waves propagation along earth
surface is used.
2. Introduction and Overview
It's well known that the principal energy-bearing mode in the theory of the earth atmosphere oscillation is
fundamental mode representing passage of the acoustic-gravity wave along the surface, constituting an
analog of the two-dimensional Lamb wave for real atmospheric stratification. The general theory of lamb
wave propagation in the atmosphere had been developed in Garent (1969), Pierce and Posey (1971),
ReVelle and Whitaker (1996), Kulichkov (1987). The dispersion law for the fundamental mode (zero-
order normal wave) has the form
k(w) = do (1+ a &) + O(e) ); a = S (qH)'n/c'y ;q= [ (c2(H)- c2()) Mc2(6)J  (1)
w - angular frequency; k - wave number; c - effective sound velocity.
To develop (1) it had been supposed that vertical wave number is small quantity of the order of ,
compared with the horizontal wave number (Pierce and Posey,1971). The dispersion law (1) coincides
with the well known dispersion law for waves described by the linear Korteweg-de Vries equation.
Lamb waves with wavelengths of several hundred kilometers propagating over super long
distances in the atmosphere equivalent to several passages around the earth have been observed after
volcanic eruptions or large nuclear explosions. In these cases the values of c and a in (1) characterize
irregularities of stratification of temperature (sound velocity) and wind velocity averaged through whole
atmosphere and along all wave trajectory in the atmosphere (Garent,1969; Pierce and Posey ,1971).
3.Lamb waves from small surface explosions
Infrasound wave lengths from small surface explosions are order of dozens and several hundreds of meters
that corresponds to vertical scales of temperature and wind irregularities in the atmospheric boundary
layer. In this case fundamental mode is effective generated in the surface waveguide formed by inversion
of temperature and wind velocity when (Chunchuzov,1986)
to= 2 qw k H <1
(2)
fi = 3/16[c/(qn2H)J >fo
H - vertical scale of the surface inversion;fr -first characteristic frequency of the waveguide;
fo - central frequency of the spectrum of the initial acoustic pulse near explosion.
The existence of a general dispersion law (1) leads to general propagation laws for infrasonic perturbation
independently of the stratification profile of the surface wave-guide.