Liquid fuel jet in Crossflow (LJIC) is significant to the aviation industry since it is a vital technique for atomization. The hydrodynamic instability mechanisms that drive a transverse jet’s primary breakup were investigated using modal and traveling wavelength analysis. This study highlights the primary breakup mechanisms for aviation fuel Jet-A. However, the techniques discussed are applicable to any liquid. Mathematical decomposition techniques are known as POD (Proper Orthogonal Decomposition), and MrDMD (Multi-Resolution Dynamic Mode Decomposition) are used together to identify dominant instability flow dynamics associated with the primary breakup mechanism. Implementation of the MrDMD method deconstructs the nonlinear dynamical systems into multiresolution time-scaled components that capture the intermittent coherent structures. The MrDMD, in conjunction with the POD method, is applied to data points taken across the entire spray breakup regimes, which are: enhanced capillary breakup, bag breakup, multimode breakup, and shear breakup. The dominant frequencies of both breakup regimes are extracted and identified. These coherent structures are classified with an associated time scale and Strouhal number. Characterization of the traveling column and surface wavelengths are conducted and associated with a known instability model. It is found that the Plateau-Rayleigh instability model predicts columns wavelengths similar to wavelengths found in dominant modes associated with a capillary breakup. Rayleigh Taylor’s instability model matches well with bag and multimode breakup. Small scale surface wavelengths associated with a shear breakup are correlated to a modified Rayleigh Taylor instability model founded by Wang et al. . Furthermore, an atomization model that predicts the Sauter Mean Diameter associated with the dominant small-scale surface traveling wavelengths is established.