A mathematical framework for the design of scaled experiments featuring turbulence

Abstract Turbulence is a ubiquitous phenomenon that is prevalent in fluid flows and many practical engineering machines and equipment. It manifests in relatively low viscous fluids being the result of an excess of momentum in part of the flow, overcoming viscous forces, leading to an energy cascade. The phenomenon has been extensively investigated both theoretically and experimentally but nonetheless remains unresolved. The behaviour of turbulent flows and associated machinery change under scaling, which impedes experimental investigations performed at scale, making scaled models unrepresentative in many situations. This issue is the focus of this paper benefiting from the timely arrival of a new experimental scaling approach involving more than one scaled model. The new finite-similitude scaling theory systematically removes scale effects by means of additional similitude rules not available to dimensional analysis. This paper focuses on the application of a new scaling space $$\Omega _\beta $$ and the first- and second-order rules, but involving no more than two scaled experiments. The question addressed in the paper is whether it is possible, by means of an additional scaled experiment, to capture more accurately turbulent behaviour. It is demonstrated here through the analysis of disparate problems that, despite the considerable complexity involved, one additional scaled experiment is sufficient for good replication of experiments involving turbulence.