A theoretical investigation of raindrop oscillations
Feng, James Qingwu
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Permalink
https://hdl.handle.net/2142/20096
Description
Title
A theoretical investigation of raindrop oscillations
Author(s)
Feng, James Qingwu
Issue Date
1991
Doctoral Committee Chair(s)
Beard, Kenneth V.
Department of Study
Atmospheric Science
Discipline
Atmospheric Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Atmospheric Science
Language
eng
Abstract
Clouds and precipitation play very active roles in weather systems and influence our daily life significantly. A fundamental entity involved in the precipitation processes is the raindrop. As is common to liquid masses held together by surface tension, raindrops are easily distorted by external forces. Indeed, complicated time-varying raindrop shape deformations are observed by various means. These oscillation shapes affect the propagation of microwaves in communication links and backscattering of microwaves as detected by weather radars. In particular, knowledge about raindrop oscillations is needed for determining the rainfall rate using dual-polarization radar.
This thesis work is devoted to understanding the basic fluid dynamic behavior of raindrop oscillations by means of theoretically analyzing the solutions of simplified mathematical models. The present work involves two previously unexplored theoretical aspects of general drop dynamics: one focusing on the calculations of the oscillation characteristics of a drop influenced by various steady-state external fields, and the other concentrating on the analysis of nonlinear resonances exhibited by a drop subjected to a time-varying external excitation.
By means of the method of multiple-parameter perturbations developed in this work, the dynamics of a drop under the influences of various external fields can be analyzed systematically. Present solutions reveal a fine structure in the spectrum of drop oscillation characteristic frequencies, indicating removal of the linear mode degeneracy when the drop is oscillating in the absence of any external fields. This provides clues to understanding how the oscillatory mode selection occurs in laboratory experiments and nature.
With a simpler mathematical model where only one small parameter is involved in the perturbation scheme, various nonlinear resonances are studied for a drop under the time-varying external excitations. Typical secondary resonances (superharmonic, subharmonic and coupled resonances) are revealed in the second- and third-order perturbation solutions. The mechanisms of secondary resonances provide a consistent explanation to why raindrops are very likely to be oscillating in the environment with natural forces of various spatial and temporal structures.
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