Imaginary Mass Modes in Turbulence: A Fourier-Based Framework for Phase Transitions in Fluid Dynamics

This paper presents an independent theoretical proposal that extends the concept of imaginary mass particles into the framework of turbulent fluid dynamics. Building upon the previous works titled Imaginary Mass Particles and Superluminal Motion: A Theoretical Proposal (Zenodo record [10.5281/zenodo.15516114]) and Imaginary Mass Extensions in Relativistic Field Theories (v3) (Zenodo record [10.5281/zenodo.15511832]), this study develops a detailed mathematical formulation by introducing complex mass parameters $M_{\mathbf{k}} = m_{\mathbf{k}} + i \mu_{\mathbf{k}}$ into the Fourier decomposition of fluid velocity fields. The paper provides explicit derivations of the modified dispersion relations, damping rates, and triadic interaction terms in the nonlinear energy transfer equations. The critical transition velocity $v = \sqrt{2} c^*$ is reinterpreted within the context of turbulence, marking a phase boundary where imaginary mass modes may convert into real-mass modes. This framework proposes potential observable signatures in turbulent spectra and suggests broader implications for cosmological phenomena, including dark matter, dark energy, and multiverse phase transitions. This work stands as a mathematically strengthened and physically enriched extension of earlier concepts, aiming to bridge the gap between abstract theoretical models and potential physical realizations in complex fluid systems.