Refining turbulence models: Time decay dynamics and energy spectrum insights from the GOY shell model

This study investigates the time decay characteristics of the energy spectrum in homogeneous isotropic decaying turbulence using the GOY shell model and proposes novel LES and K-ε models based on these findings. The GOY shell model, which simplifies the Navier–Stokes equations in Fourier space, effectively captures nonlinear energy transfers between neighboring wavenumber bands and provides an efficient framework for describing the temporal evolution of turbulence. Focusing on the inertial subrange where Kolmogorov's − 5/3 power law is observed, the analysis reveals that the time decay of the energy spectrum is governed by dissipation rate and viscosity. Leveraging insights from the GOY model, we developed a new LES model where the eddy viscosity is proportional to the turbulent Reynolds number raised to the 2/5 power, significantly reducing sensitivity to empirical constants inherent in conventional Smagorinsky models. Similarly, we derived an improved K-ε model that incorporates viscosity explicitly, yielding a more accurate representation of the dissipation rate's temporal evolution. These models demonstrate excellent agreement with the GOY shell model's predictions and address the high-wavenumber over-dissipation issue encountered in traditional approaches. The proposed framework not only enhances the predictive accuracy of turbulence models but also provides a physically consistent basis for simulating a broader range of turbulent flows. This work represents a significant step toward advancing turbulence modeling and deepening our understanding of energy dissipation dynamics in decaying turbulence.