High-performance fibers are key components for enhancing the mechanical properties of composite materials. The development of high strength nanofibers augurs the production of new nano-composites with outstanding features. However, the robust production of continuous glass nanofibers that can be feasible processed for efficiently manufacturing nanocomposites is still challenging. Recently, Cofiblas (Continuous Fiberizing by Laser melting and Supersonic dragging) was demonstrated as a technique capable of producing continuous glass nanofibers with unlimited length. Cofiblas process has some similarities with the widely known melt blowing technique for the production of polymeric fibers. In both techniques, the design of the gas nozzle is key to ensure the feasibility of the process since the turbulences of the gas jet may induce strong whipping of the filament.This paper gives novel experimental evidences on the correlation of the supersonic gas jet instabilities with the oscillation of the filament in the melt-blowing and Cofiblas processes, relating these oscillations with the presence of shock waves and unsteadiness in the flow, and gives valuable insight into the use of supersonic jets in the melt blowing process as an effective approach for the formation of nanofibers. A thin 3D-axisymmetric model in OpenFOAM® was put to test by comparing the performance of different solvers which were validated by flow visualization of the exit jet using digital holography (DH). In order to perform a realistic and thorough validation, we simulated the optical measurements of the flow from the CFD simulations of the mass density by Abel transform and numerical differentiation. The application of digital holography as the flow visualization technique makes possible both a precise validation of the density maps obtained from the Abel transformation of the 2D-alike results, and the analysis of the shockwave pattern in the air jet. Conversely, the numerical reconstruction of time-averaged holograms is employed to detect unsteadiness in the flow and to analyze the fiber oscillation, which is essential to assess the stability of the process. Lastly, the analysis and comparison of the vibration of the filament using the basic design and the optimized nozzle demonstrates a clear influence of the shock waves and flow unsteadiness in the stability of the filament.