The Euler and Navier-Stokes equations form the cornerstone of fluid dynamics, governing the motion of fluids under a wide range of conditions. The Euler equations describe inviscid flows where ...

Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense. The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous ...

The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...

Tests of a proposed friction-factor equation have shown it to be accurate for calculating pressure loss in turbulent flow for a pipeline transporting a non-Newtonian fluid, such as most crude oils and ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...