لایه مرزی استوکس - ویکی‌پدیا، دانشنامهٔ آزاد

${\displaystyle {\frac {\partial u}{\partial t}}=-{\frac {1}{\rho }}{\frac {\partial p}{\partial x}}+\nu {\frac {\partial ^{2}u}{\partial z^{2}}}}$

${\displaystyle \omega ={\frac {\partial u}{\partial z}}}$

${\displaystyle {\frac {\partial \omega }{\partial t}}=\nu {\frac {\partial ^{2}\omega }{\partial z^{2}}}}$

${\displaystyle u_{0}(t)=U_{0}\,\cos \left(\Omega \,t\right)}$

${\displaystyle u_{1}(0,t)=u_{0}(t)=U_{0}\,\cos \left(\Omega \,t\right)\quad {\text{ at }}\;z=0}$

${\displaystyle {\frac {\partial u_{1}}{\partial t}}=\nu {\frac {\partial ^{2}u_{1}}{\partial z^{2}}}}$

${\displaystyle u_{1}(z,t)=U_{0}\,{\text{e}}^{-\kappa \,z}\,\cos \left(\Omega \,t\,-\,\kappa \,z\right)\quad {\text{ with }}\;\kappa \,=\,{\sqrt {\frac {\Omega }{2\nu }}}.}$

${\displaystyle \delta ={\frac {2\pi }{\kappa }}=2\pi \,{\sqrt {\frac {2\nu }{\Omega }}}}$

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