Integrated Regional Enstropy as a Measure of Kolmogorov Entropy

Abstract

Enstrophy in a fluid relates to the dissipation tendency in a fluid that has use in studying turbulent flows. It also corresponds to vorticity as kinetic energy does to velocity. Earlier work showed that the Integrated Regional Enstrophy (IRE) was related to the sum of the positive Lypunov Exponents. Lyapunov Exponents are the characteristic exponent(s) of a dynamic system or a measure of the divergence or convergence of system trajectories that are initially close.Relatively high values of IRE derived from an atmospheric flow field in the study of atmospheric blocking was identified with the onset or demise of blocking events, but also transitions of the large-scale flow in general. Kolmogorv Entropy (KolE) also known as metric entropy is related to the sum of the positive Lyapunov Exponents as well. This quantity can be thought of as a measure of predictability (higher values less predictability) and will be non-zero for a chaotic system. Thus, the measure of IRE is related to KolE as well. This study will show that relatively low (high) values of IRE derived from atmospheric flows correspond to more stable (transitioning) large-scale flow a greater (lesser) degree of predictability and KolE. The transition is least predictable and should be associated with higher IRE and KolE.