Abstract: The essential concept of many scientific investigations in computational and experimental fluid dynamics is to present an objective and quantitative representation of flow behavior. A thorough understanding of all key processes also lays the groundwork for the incorporation of fundamental fluid effects into technical applications and fluid-based devices. Experiments and numerical computations are the two pillars upon which this process relies. Almost all current techniques in quantitative fluid dynamics rely on a model equation, most often, say, the linearized Navier-Stokes equations and their variants. This model is implemented in the algorithms as a matrix-vector mul-application, which is critical for maintaining orthogonality or adding robustness to the corresponding approach. However, only the measured data are available in physical experiments. To reach the same level of quantitative description of fluid processes, popular algorithms must be adjusted to curtail their reliance on models and limit their input to data exclusively. In this context, we shall visit from elementary level to modern computational algorithm to accommodate the snapshot based process to understand the model reduction and explore the role of eigenmodes.
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