Scaling behavior of electromagnetic wake fields induced by underwater vehicles based on the hydrodynamic similarity

Abstract

When underwater vehicles navigate through the ambient geomagnetic field, the motion of ionized seawater in their wake generates electromagnetic signals, which have significant applications in underwater target detection and tracking. However, obtaining accurate electromagnetic wake signatures requires solving the complex coupling of fluid dynamics, ion transport, and electromagnetic fields, making full-scale simulations and analyses computationally challenging. In this study, we derive the scaling relationship for electromagnetic wake signatures across different scales of underwater vehicles based on hydrodynamic similarity principles and wake magnetic field equations. Numerical validation is conducted using large eddy simulation, and the effects of scale on wake dynamics and wake-induced magnetic fields are analyzed. The results indicate that, across different scaling ratios, the velocity field in the near-field region—specifically near the vehicle’s bow and immediately behind the propeller—exhibits high similarity. However, notable discrepancies emerge in the far-field region. A quantitative analysis reveals that as the scaling ratio increases, the error in magnetic field conversion gradually grows. In the near-field region behind the propeller, the conversion error remains below 5% and 6% for scaling ratios of λ = 2 and λ = 24, respectively. In contrast, in the far-field region, the error is less than 6% for λ = 2 but increases significantly to approximately 20% for λ = 24. This increase in conversion error is primarily attributed to nonlinear effects, including the scale-dependent evolution of turbulent structures, electromagnetic coupling, and dissipation mechanisms. This study clarifies the impact of scale effects on wake-induced magnetic fields and highlights the limitations of idealized similarity assumptions. The findings provide a theoretical foundation for the extrapolation of model-scale simulation results to full-scale applications, advancing the development of electromagnetic detection technologies for underwater vehicles.