A phenomenon that the aviation industry deals with quite frequently is turbulence. While there are several variants to its meaning, each depending on their context, the variant taken in this paper is that it describes a wide range of vortical structures in various scales, ultimately resulting in a chaotic motion of fluid flows. In terms of a certain mathematical model in computational fluid dynamics, known as Large Eddy Simulations (LES), they are represented as eddy currents to be resolved using filtered Navier-Stokes equations [1]. Turbulent eddies will break down into smaller eddies and can be resolved directly. Through molecular viscosity, the smallest eddies will undergo heat dissipation, and such eddies can be resolved only after modelling. This transition is called an energy cascade [2]. Due to chaotic dynamics, the precise trajectory which an eddy can take during an energy cascade cannot be calculated but approximated based on chaos theory, specifically, the Lyapunov exponent [3]. The primary objective of this research is to incorporate orientational-sensitive properties into the Lyapunov exponent. The boundary conditions, the Reynolds’ number, and other appropriate control parameters of the flow must first be determined. The behavior of the flow field is based on the evolution of perturbations added and can be analyzed with Jacobian matrices. The novelty of this method is shown by using unit quaternions of hypercomplex numbers to represent Lyapunov vectors. The forecasted results of this research would allow the Lyapunov exponent to embody orientational-sensitive attributes by incorporating quaternionic algebra, Jacobian matrices, and Lyapunov vector analysis. Consequently, it would provide an alternative for additional smaller eddies to be resolved within LES and bring predictive analysis within the domain of fluid dynamics one step closer to being more accurate and complete.