Recent developments in scientific deep learning [e.g.~1] have demonstrated the ability to learn complex, fluid-mechanical dynamics. However, such methods require large amounts of training data. Especially for multiscale flows, their generation can be very time consuming. For this reason, approximations that can provide data of sufficient accuracy at lower numerical costs than classical CFD approaches are of interest. The deviation-propagation formalism [2] linearizes the Navier-Stokes equations around reference time series and treats deviations from these series as small perturbations. In first order, their evolution is governed by a linear propagator that can be computed from the Navier-Stokes equations. Predictions of how a flow field evolves are made by determining its nearest neighbor within the reference series, convoluting the propagator with the deviation, and adding it to the evolved reference state. This way, the nonlinear dynamics is split into a purely data-driven nearest neighbor part (corresponding to the method of analogues) and a data-assisted, physics-informed, linear propagator. While the propagator can be obtained from the Navier-Stokes equations, its calculation is time consuming and memory demands are very large. Hence, further approximations are necessary. A physics-inspired, Gaussian assumption [3] allows one to compute it with little overhead to the generation of the reference time series, and to integrate it into CFD frameworks easily. The scope of the method is demonstrated for the case for turbulent vortex shedding behind a cylinder. Various boundary conditions induce deviations from the reference series. Results are analyzed on a step-by-step basis for the short-term evolution and via their moments and correlations to assess the statistical long-term behavior. Good to very good agreement with detailed CFD simulations is found at a fraction of their runtime. Hence, the method is suitable for fast calculations on their own and for efficient data generation for subsequent machine learning tasks. [1] Alkin B. et al., NeuralDEM for real time simulations of industrial particular flows, Comm. Phys. 8.1, 440, 2025 [2] Lichtenegger, T., Data-assisted, physics-informed propagators for recurrent flows, Phys. Rev. Fluids 9.2, 024401, 2024 [3] Lichtenegger, T., An efficient, moments-based approximation for deviation propagators of recurrent flows, Phys. Fluids, 37.12, 2025