Analysis of localized damping effects in channel flows with arbitrary rough boundary

Jaewook Ahn, Jung Il Choi, Kyungkeun Kang, Jae Myoung Kim

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1 Citation (Scopus)

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(ε3/2) quadratic approximation of real flows by the damping model with a quasi-periodic function (Formula presented.) 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.

Original languageEnglish
Pages (from-to)2359-2377
Number of pages19
JournalApplicable Analysis
Volume98
Issue number13
DOIs
Publication statusPublished - 2019 Oct 3

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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