Wave Particle Turbulent Simulation of Spatially Developing Round Jets Using a Non Equilibrium Transport Model with a Mixing Length Characteristic Time Closure

Abstract: In this paper, the wave-particle turbulent simulation (WPTS), a recently developed multiscale, non-equilibrium turbulence modeling approach, is coupled with a turbulence characteristic-time closure derived from Prandtl mixing-length hypothesis and applied to spatially developing round jets. In WPTS, fluid elements in strongly turbulent regions are represented by Lagrangian particles that travel a finite distance before interacting with the background flow field represented in a wave-like (Eulerian) form. This mechanism bears conceptual similarity to the discrete fluid parcels invoked in the Prandtl mixing-length picture. WPTS differs from conventional mixing-length-based turbulence models in two key respects. First, particle evolution follows a non-equilibrium transport mechanism, rather than the equilibrium assumptions typically embedded in eddy-viscosity closures. Second, WPTS advances the wave and particle components in a coupled manner, with the particle fraction governed primarily by the modeled turbulence characteristic time, enabling laminar and turbulent regimes to be represented within a unified framework. Because spatially developing jets provide a canonical test case with well-established similarity behavior, they are used here for evaluation. Specifically, this work (1) develops a mixing-length-based characteristic-time model tailored to jet flows and (2) incorporates it into WPTS to assess predictive performance. The resulting WPTS framework accurately reproduces the jet similarity solution and other characteristic features at Reynolds numbers of 5,000 and 20,000, demonstrating the promise of WPTS as a practical tool for turbulence modeling and simulation.