English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the local balance of momentum for weak solutions of incompressibleEuler equations obtained from the zero-viscosity limit in the presence of solidboundaries, taking as an example flow around a finite, smooth body. We showthat both viscous skin friction and wall pressure exist in the inviscid limitas distributions on the body surface. We define a nonlinear spatial flux ofmomentum toward the wall for the Euler solution, and show that wall frictionand pressure are obtained from this momentum flux in the limit of vanishingdistance to the wall, for the wall-parallel and wall-normal components,respectively. We show furthermore that the skin friction describing anomalousmomentum transfer to the wall will vanish if velocity and pressure are boundedin a neighborhood of the wall and if also the essential supremum of wall-normalvelocity within a small distance of the wall vanishes with this distance (aprecise form of the non-flow-through condition). In the latter case, all of thelimiting drag arises from pressure forces acting on the body and the pressureat the body surface can be obtained as the limit approaching the wall of theinterior pressure for the Euler solution. As one application of this result, weshow that Lighthill's theory of vorticity generation at the wall is valid forthe Euler solutions obtained in the inviscid limit. Further, in a companionwork, we show that the Josephson-Anderson relation for the drag, recentlyderived for strong Navier-Stokes solutions, is valid for weak Euler solutionsobtained in their inviscid limit.

Inertial Momentum Dissipation for Viscosity Solutions of Euler Equations. I. Flow Around a Smooth Body