A local analysis of the axisymmetric Navier-Stokes flow near a saddle point and no-slip flat boundary

P. Y. Hsu, H. Notsu, T. Yoneda

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Tornadoes are one type of violent flow phenomenon and occur in many places in the world. There are many research methods that aim to reduce the loss of human lives and material damage caused by tornadoes. One effective method is numerical simulation such as that in Ishihara et al. (J. Wind Engng Ind. Aerodyn., vol. 99, 2011, pp. 239-248). The swirling structure of the Navier-Stokes flow is significant for both the mathematical analysis and numerical simulations of tornadoes. In this paper, we try to clarify the swirling structure. More precisely, we performed numerical computations on axisymmetric Navier-Stokes flows with a no-slip flat boundary. We compared a hyperbolic flow with swirl and one without swirl, and observed that the following phenomenon occurs only in the swirl case: the distance between the point with the maximum magnitude of velocity and the -axis changed drastically at a specific time (which we call the turning point). Besides, an 'increasing velocity phenomenon' occurred near the boundary, and the maximum value of was obtained near the axis of symmetry and the boundary when the time was close to the turning point in the swirl case.

Original languageEnglish
Pages (from-to)444-459
Number of pages16
JournalJournal of Fluid Mechanics
Volume794
DOIs
Publication statusPublished - 2016 May 10
Externally publishedYes

Fingerprint

tornadoes
Tornadoes
Stokes flow
saddle points
slip
swirling
applications of mathematics
Computer simulation
simulation
damage
symmetry

Keywords

  • mathematical foundations
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

A local analysis of the axisymmetric Navier-Stokes flow near a saddle point and no-slip flat boundary. / Hsu, P. Y.; Notsu, H.; Yoneda, T.

In: Journal of Fluid Mechanics, Vol. 794, 10.05.2016, p. 444-459.

Research output: Contribution to journalArticle

@article{7b78b8bd233f425993ff9af65c6e534d,
title = "A local analysis of the axisymmetric Navier-Stokes flow near a saddle point and no-slip flat boundary",
abstract = "Tornadoes are one type of violent flow phenomenon and occur in many places in the world. There are many research methods that aim to reduce the loss of human lives and material damage caused by tornadoes. One effective method is numerical simulation such as that in Ishihara et al. (J. Wind Engng Ind. Aerodyn., vol. 99, 2011, pp. 239-248). The swirling structure of the Navier-Stokes flow is significant for both the mathematical analysis and numerical simulations of tornadoes. In this paper, we try to clarify the swirling structure. More precisely, we performed numerical computations on axisymmetric Navier-Stokes flows with a no-slip flat boundary. We compared a hyperbolic flow with swirl and one without swirl, and observed that the following phenomenon occurs only in the swirl case: the distance between the point with the maximum magnitude of velocity and the -axis changed drastically at a specific time (which we call the turning point). Besides, an 'increasing velocity phenomenon' occurred near the boundary, and the maximum value of was obtained near the axis of symmetry and the boundary when the time was close to the turning point in the swirl case.",
keywords = "mathematical foundations, Navier-Stokes equations",
author = "Hsu, {P. Y.} and H. Notsu and T. Yoneda",
year = "2016",
month = "5",
day = "10",
doi = "10.1017/jfm.2016.174",
language = "English",
volume = "794",
pages = "444--459",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - A local analysis of the axisymmetric Navier-Stokes flow near a saddle point and no-slip flat boundary

AU - Hsu, P. Y.

AU - Notsu, H.

AU - Yoneda, T.

PY - 2016/5/10

Y1 - 2016/5/10

N2 - Tornadoes are one type of violent flow phenomenon and occur in many places in the world. There are many research methods that aim to reduce the loss of human lives and material damage caused by tornadoes. One effective method is numerical simulation such as that in Ishihara et al. (J. Wind Engng Ind. Aerodyn., vol. 99, 2011, pp. 239-248). The swirling structure of the Navier-Stokes flow is significant for both the mathematical analysis and numerical simulations of tornadoes. In this paper, we try to clarify the swirling structure. More precisely, we performed numerical computations on axisymmetric Navier-Stokes flows with a no-slip flat boundary. We compared a hyperbolic flow with swirl and one without swirl, and observed that the following phenomenon occurs only in the swirl case: the distance between the point with the maximum magnitude of velocity and the -axis changed drastically at a specific time (which we call the turning point). Besides, an 'increasing velocity phenomenon' occurred near the boundary, and the maximum value of was obtained near the axis of symmetry and the boundary when the time was close to the turning point in the swirl case.

AB - Tornadoes are one type of violent flow phenomenon and occur in many places in the world. There are many research methods that aim to reduce the loss of human lives and material damage caused by tornadoes. One effective method is numerical simulation such as that in Ishihara et al. (J. Wind Engng Ind. Aerodyn., vol. 99, 2011, pp. 239-248). The swirling structure of the Navier-Stokes flow is significant for both the mathematical analysis and numerical simulations of tornadoes. In this paper, we try to clarify the swirling structure. More precisely, we performed numerical computations on axisymmetric Navier-Stokes flows with a no-slip flat boundary. We compared a hyperbolic flow with swirl and one without swirl, and observed that the following phenomenon occurs only in the swirl case: the distance between the point with the maximum magnitude of velocity and the -axis changed drastically at a specific time (which we call the turning point). Besides, an 'increasing velocity phenomenon' occurred near the boundary, and the maximum value of was obtained near the axis of symmetry and the boundary when the time was close to the turning point in the swirl case.

KW - mathematical foundations

KW - Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=84962654533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962654533&partnerID=8YFLogxK

U2 - 10.1017/jfm.2016.174

DO - 10.1017/jfm.2016.174

M3 - Article

AN - SCOPUS:84962654533

VL - 794

SP - 444

EP - 459

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -