The role of scaling laws in upscaling

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Modeling Turbulent Flows in Porous Media (2020, background): “In quasi-ergodic spatial fields (cf. Christakos 2000, von Neumann 1932, Wood 2008, Yaglom 2012), by definition volume averages can bemade to be as close to the probabilistic average desired by making the volume sufficiently large.”
Velocity and stress jump conditions between a porous medium and a fluid (2013, unknown): “[24,25]).”
Pore‐scale simulation of mixing‐induced calcium carbonate precipitation and dissolution in a microfluidic pore network (2012, background): “Pore scale or microscale models are typically used to gain fundamental insights into physical behavior so that more accurate and robust upscaled constitutive models can be developed for the continuum scale [Whitaker, 1999; Wood, 2009; Kim et al., 2011].”