Bibliographic Details
| Title: |
SMALL SCALES IN INVISCID LIMITS OF STEADY FLUIDS. |
| Authors: |
GUO, YAN1 yan_guo@brown.edu, YANG, ZHUOLUN2 yang.8242@osu.edu |
| Source: |
SIAM Journal on Mathematical Analysis. 2025, Vol. 57 Issue 5, p5216-5242. 27p. |
| Subjects: |
Navier-Stokes equations, Inviscid flow, Shear flow, Euler, Leonhard, 1707-1783, Boundary layer (Aerodynamics), Incompressible flow |
| Abstract: |
In this article, we study the two-dimensional incompressible steady Navier-Stokes equation in a channel (- L, 0) × (- 1, 1) with the no-slip boundary condition on { Y = 土1 } and consider the inviscid limite ε→ 0. In the special case of Euler shear flow ( ue (Y), 0), we construct a steady Navier-Stokes solution for epsilon ε << 1, {uε ~ Ue+Up+O(√ε), &vε ~h(Y) exp{Xue(Y)/ε}+O√ε), where up represents the classical Prandtl layer profile, and h(Y) is an arbitrary smooth, compactly-supported function with small magnitude. While the classical Prandtl boundary layer up exhibits a small scale of order √ε in Y near Y = 土1 the profile we construct reveals an a small scale of Xue (Y) in the vertical velocity component. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
