Analysis of localized damping effects in channel flows with arbitrary rough boundary. Issue 13 (3rd October 2019) - Ahn, Jaewook; Choi, Jung-Il; Kang, Kyungkeun; Kim, Jae-Myoung
Abstract: We justify a modified Navier–Stokes system that includes the damping effect for a channel flow with an arbitrary irregular boundary. The effects of rough walls are modeled by a localized damping term in the momentum equation. We prove the existence and uniqueness of a solution to the modified Navier–Stokes system in a smooth extended domain using the fixed-point theorem and Saint-Venant technique. The proposed damping term yields an o ( ε ) quadratic approximation of real flow for a sufficiently small flux, under the assumption of the almost periodicity of the roughness profile ω . We further obtain O ( ε 3 / 2 ) quadratic approximation of real flows by the damping model with a quasi-periodic function ω and the diophantine condition. Consequently, we confirm that the localized damping effect can provide an effective model to predict channel flows with an arbitrary irregular surface.