1
$\begingroup$

Consider an incompressible viscous fluid of kinematic viscosity $ν$ , dynamic viscosity $µ$ and density $ρ$ . A viscous boundary layer is located over a solid surface at $y = 0$ and $x > 0$. The flow in the boundary layer must match with the constant inviscid bulk velocity $U$. The steady two-dimensional boundary-layer equations are $$\frac{∂ u}{ ∂ x} + \frac{∂ v}{ ∂ y} = 0$$ $$ρ \bigg( u \frac{∂ u }{∂ x} +v \frac{∂ u }{∂ y} \bigg)= µ \frac{∂ ^2u }{∂ y^2}$$ where $u(x,y)$ is the horizontal velocity and $v(x,y)$ the vertical velocity.

(i) State the boundary conditions on $u$ and $v$ along $y = 0$ and $x > 0$.

(ii) State the far-field condition on $u$ as $y→∞$.


It says "The flow in the boundary layer must match with the constant inviscid bulk velocity $U$" so does this mean that the resultant of the $u$ and $v$ velocity components should be equal to $U$?

Then for (i) $u(x,y=0)=v(x,y=0)=U/\sqrt2$?

For (ii), is the far field condition just $u \rightarrow 0$ as $y \rightarrow \infty$?

$\endgroup$
  • $\begingroup$ I think the far field condition is $u\rightarrow U$. $\endgroup$ – David May 11 '16 at 6:10
-1
$\begingroup$

'It says "The flow in the boundary layer must match with the constant inviscid bulk velocity U'

It means that as you approach the boundary from within the boundary layer, the velocity must approach the bulk velocity U. It does NOT mean that the velocity within the boundary layer is constant.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.