TY - JOUR

T1 - Bifurcation study of three-dimensional solutions of the curved square-duct flow

AU - Watanabe, Takeshi

AU - Yanase, Shinichiro

PY - 2013/7

Y1 - 2013/7

N2 - Steady, periodic and traveling-wave solutions of the flow through a curved square duct are obtained numerically, and their linear stability to two- and three-dimensional disturbances is investigated. It is found that a steady traveling-wave (STW) solution bifurcates from the symmetric steady solution branch and is linearly stable in the intermediate range between low and high pressure gradient regions. Two stable periodic traveling-wave (PTW) solutions are also found, which have oscillating components with different symmetry. One keeps the same symmetry as the STW solution and the other breaks it. They seem to bifurcate from the STW solution branch via Hopf bifurcation although their solution branches are not obtained exactly. It is strongly suggested that a two-dimensional time-periodic (2DP) solution is created via heteroclinic bifurcation, not from local bifurcation. 2DP solution is always linearly unstable against threedimensional disturbances though it has linearly stable region to two-dimensional disturbances.

AB - Steady, periodic and traveling-wave solutions of the flow through a curved square duct are obtained numerically, and their linear stability to two- and three-dimensional disturbances is investigated. It is found that a steady traveling-wave (STW) solution bifurcates from the symmetric steady solution branch and is linearly stable in the intermediate range between low and high pressure gradient regions. Two stable periodic traveling-wave (PTW) solutions are also found, which have oscillating components with different symmetry. One keeps the same symmetry as the STW solution and the other breaks it. They seem to bifurcate from the STW solution branch via Hopf bifurcation although their solution branches are not obtained exactly. It is strongly suggested that a two-dimensional time-periodic (2DP) solution is created via heteroclinic bifurcation, not from local bifurcation. 2DP solution is always linearly unstable against threedimensional disturbances though it has linearly stable region to two-dimensional disturbances.

KW - Bifurcation

KW - Curved square duct

KW - Navier-Stokes equation

KW - Traveling-wave solution

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U2 - 10.7566/JPSJ.82.074402

DO - 10.7566/JPSJ.82.074402

M3 - Article

AN - SCOPUS:84879828886

SN - 0031-9015

VL - 82

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

IS - 7

M1 - 074402

ER -