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.

翻译：我们考虑一种流体的流动，其响应特性因速度梯度对称部分范数的变化而改变：当范数低于临界值时，流体表现为欧拉流体；当范数达到或超过临界值时，则表现为纳维-斯托克斯流体，该范数由外部刺激决定。研究表明，此类流体在流经钝体时发展的边界层，与普朗特经典边界层理论所描述的边界层几乎完全相同。不同于经典边界层理论作为纳维-斯托克斯理论框架下的近似结果，此处边界层的产生源于本构关系响应特性的变化。我们研究了此类流体流经翼型的流动，并将其与纳维-斯托克斯方程的解进行对比。发现两种情形下的速度场和涡量场结果高度吻合。