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so i have a question concerning navier-stokes equations in a boundary layer, which, as a refresher, is [tex] \frac {D \vec{V}}{Dt} = - \nabla P + \nu \nabla^2 \vec{V}[/tex] where we know the x-component of [itex] \nabla^2 \vec{V}[/itex] may be re-wrote as [itex] \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}[/itex] (i dismiss the [itex]z[/itex] component due to two dimensions). define the vertical displacement as [itex] \delta[/itex] and the horizontal length scale as [itex] L [/itex]

okay, now for the question: we know [itex]\frac{\partial^2 u}{\partial x^2}[/itex] disappears, as it is not of much importance via order of magnitude. my question is, in boundary layer analysis, is this true from the fact that [itex]\delta < L \implies \delta^2 << L^2[/itex] and thus the [itex]\frac{\partial^2 u}{\partial x^2}[/itex] component can be thought of as insignificant (from the large denominator) compared to the [itex]\frac{\partial^2 u}{\partial y^2}[/itex] component?

if so, when we leave the boundary layer are we going to assume that the double partial over x is still insignificant, or are we allowed to assume this (assuming same flow and geometry, just outside the BL)

thanks!!

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# Navier-stokes simplifications

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