Entropic balance theory and variational field Lagrangian formalism: Tornadogenesis

Abstract

The entropic balance theory has been applied with outstanding results to explain many important aspects of tornadic phenomena. The theory was originally developed in variational (probabilistic) field Lagrangian formalism, or in short, variational formalism, with Lagrangian density and action appropriate for supercell-storm and tornadic phenomena. The variational formalism is broadly used in in modern physics, not only in classical mechanics, with Lagrangian density and action designed for each physical problem properly. The Clebsch transformation (equation) was derived in the classical variational formalism but has not been used because of the unobservable and nonmeteorological Lagrange multiplier. The entropic balance condition is thus developed from the Clebsch transformation, changing the unobservable nonmeteorological Lagrange multiplier to observable meteorological rotational flow velocity with entropy and making it applicable to tornadic phenomena. Theoretical details of the entropic balance are presented such as the entropic right-hand rule, entropic dipole, source and sink, overshooting mechanism of hydrometeors against westerlies and the existence of single and multiple vortices and their relation to tornadogenesis. These results are in reasonable agreement with the many observations and data analysis publications. The Clebsch transformation and entropic balance are the new balance conditions, different from the known other balance conditions such as hydrostatic, (quasi-)geostrophic, cyclostrophic, Boussinesq, and anelastic balance. The variations in calculus of variations and in the classical variational formalism are hypothetical. However, this article suggests that the hypothetical variations could be physical, relating to quantum variations and their interaction with the classical systems. © 2014 American Meteorological Society.