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.

我们考虑流体的流动，其响应特性由于速度梯度对称部分的范数的值而变化，在低于临界值时表现为欧拉流体，在高于临界值时表现为纳维-斯托克斯流体，规范是由外部刺激决定的。我们表明，这种流体在流过钝体时会形成边界层，这些边界层实际上与普朗特提出的经典边界层理论中遇到的边界层相同。与纳维-斯托克斯理论背景下作为近似值出现的经典边界层理论不同，这里边界层的发展是由于本构关系响应特性的变化。我们研究这种流体流过机翼的流动，并将其与纳维-斯托克斯方程的解进行比较。我们发现这两种情况的速度场和涡度场的结果非常一致。