HR: 09:00h
AN: AE11B-03 INVITED [Abstracts]
TI: General Instability of Clouds With Respect to the Formation of Horizontal Space Charge Layers
AU: * Handel, P H
EM: handel@umsl.edu
AF: Physics Dept., Univ. MO, BH, St. Louis, MO 63121 United States
AB:
The origin of the multiple horizontal charge layers observed with balloons in the trailing stratiform region of mesoscale
convective systems is explained through energy considerations and stability calculations inspired by he author's polarization catastrophe theory of atmospheric electricity [1]. We prove a cloud instability with respect to formation of horizontal
polarization layers and space charge layers. Let n be the concentration of polarizable ice crystallites, each of them in the
local field Eloc =E +P/3e, where E is macroscopic electric field in the cloud, e is vac. permitt., and P =np the cloud
polarization, defined as the dipole moment per m3. Each crystallite has two charges +q and -q separated by the dipole length
x. The average contribution of the dipole moment dipole moment p of an ice crystallite of mass M to the polarization vector
is p=qx= AEloc=AF/q, where F is the force opposing the separation of the charges in the crystallite, A is polarizability. The work u' done to create the dipoles in the ice crystals per unit cloud volume is u'=n∫Fdx=(nqq/A)∫xdx=nqqxx/2A
=npp/2A =PP/2nA. This increases the energy of the cloud, just like the energy of a set of extended springs. On the other
hand, the cloud loses energy due to orientational polarization of the crystallites that tend to align themselves in a minimum energy direction in the local field u"=∫ElocdP=(E + P/3e)dP=∫PP/6e+∫EdP. The energy of the cloud is thus
u=u'-u"=(pp/2)[n/A- nn/3e]. E also contains a polarization caused (depolarization) component that is largely compensated by
the masking charges of ions attached to the regions where the divergence c(z) of P differs from zero, and will be neglected
as is usual in the polarization catastrophe theory for stationary clouds [1]. The cloud polarization P in u" is usually well
approximated [1] by the saturation polarization P=np, with p being the total dipole moment of each crystallite. Indeed, the
author's polarization catastrophe criterion [1] is mmn>2.5 10exp21 cm-3, where m is the average number of water molecules
in each crystallite. This criterion is satisfied in most clouds. However, our derivation is more general, and applicable for
any kind of polarization of the individual crystallite. Let us apply to all crystallites in the cloud a local field of small
virtual displacements in the z direction X'(z, t) = X(t)sin kz, with an arbitrarily small amplitude X(t). The whole cloud
that was assumed to be initially homogeneous [X(0)=0], with concentration n(z)=N assumed to be initially constant over the
whole cloud, from z=0 at the cloud base, to z =h at cloud top. Then, from the equation of continuity, we obtain in first
order the concentration perturbation for crystallites n' = -(d/dz)(XN), i.e, n(z,t) = N-NX(t)kcoskz. Substituting into the
expression U=(pp/2)∫[n/A-nn/3e]dz, of the cloud energy, its change U'=(pp/2)∫[-(NX/A)kcoskz+(2X/3e)kcoskz
-(XXkkNN/3e)cos2kz]dz. Integrating over z, we obtain, at least for k=2p'r/h with integer r and p'=3.14,
DE: 3329 Mesoscale meteorology
SC: Atmospheric and Space Electricity [AE]
MN: 2005 Joint Assembly