Comments on 'Contraction Rate and Its Relationship to Frontogenesis, the Lyapunov Exponent, Fluid Trapping, and Airstream Boundaries'

摘要

In Cohen and Schultz (2005, hereafter CS05), a new concept for kinematic diagnosis has been presented. Overall, I find their presentation fascinating and the ideas contained therein are both stimulating and of considerable value for kinematic applications. However, I found their derivation to be somewhat confusing. Some brief review of their derivation is necessary to set the stage for an alternative derivation that confirms their results. They considered the time evolution of the separation vector δr(t) = δx + iδy [their Eq.] between two fluid parcels, assuming that it could be represented for a small period of time (during which the linear form of the Taylor series expansion of the velocity field was valid) as their Eq.: δr(t) = δr(0) exp[(σ + iω)t]. In the first use of the complex representation, the real and imaginary parts correspond to the components of a vector. In the second use of the complex representation, the real and imaginary parts correspond to the growth rate and the frequency. Equating the real and imaginary parts of these two apparently different applications of complex representation was rather confusing to me. Hence, I chose to follow a different path and see if it would produce a corresponding result.