Development of boundary layers in Euler fluids that on "activation'' respond like Navier-Stokes fluids

TL;DR

This paper introduces a fluid model that switches between Euler and Navier-Stokes behaviors based on flow stimuli, resulting in boundary layer development similar to classical theory but driven by constitutive response changes.

Contribution

It presents a novel fluid model where boundary layers form due to response characteristic changes, not just classical viscous effects, and validates it against Navier-Stokes solutions.

Findings

Boundary layers develop similarly to classical theory.

Flow solutions match Navier-Stokes results for airfoil case.

Model captures transition from Euler to Navier-Stokes behavior.

Abstract

We consider the flow of a fluid whose response characteristics change due the value of the norm of the symmetric part of the velocity gradient, behaving as an Euler fluid below a critical value and as a Navier-Stokes fluid at and above the critical value, the norm being determined by the external stimuli. We show that such a fluid, while flowing past a bluff body, develops boundary layers which are practically identical to those that one encounters within the context of the classical boundary layer theory propounded by Prandtl. Unlike the classical boundary layer theory that arises as an approximation within the context of the Navier-Stokes theory, here the development of boundary layers is due to a change in the response characteristics of the constitutive relation. We study the flow of such a fluid past an airfoil and compare the same against the solution of the Navier-Stokes equations. We find that the results are in excellent agreement with regard to the velocity and vorticity fields for the two cases.