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

Jaewook Ahn, Jung-il Choi, Kyungkeun Kang, Jae Myoung Kim

Research output: Contribution to journalArticle

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

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Channel Flow
Channel flow
Rough
Quadratic Approximation
Damping
Damping Term
Navier-Stokes System
Irregular
Arbitrary
Diophantine Condition
Almost Periodicity
Periodic Functions
Roughness
Justify
Fixed point theorem
Existence and Uniqueness
Momentum
Predict
Model
Surface roughness

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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.",
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Analysis of localized damping effects in channel flows with arbitrary rough boundary. / Ahn, Jaewook; Choi, Jung-il; Kang, Kyungkeun; Kim, Jae Myoung.

In: Applicable Analysis, Vol. 98, No. 13, 03.10.2019, p. 2359-2377.

Research output: Contribution to journalArticle

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