TY - JOUR
T1 - Generalized analytic functions in axially symmetric oseen flows
AU - Zabarankin, M.
PY - 2010
Y1 - 2010
N2 - A class of generalized analytic functions arising from the Oseen equations in the axially symmetric case has been identified. For this class of functions, the generalized Cauchy integral formula has been obtained, and a series representation for the region exterior to a sphere has been constructed. The velocity field of the axially symmetric Oseen flow has been represented in terms of two generalized analytic functions, and it has been shown that for an exterior Oseen flow problem, those functions are uniquely determined, provided that they both vanish at infinity. Also the pressure and vorticity have been determined as the real and imaginary parts of the two functions representing the velocity field, and the drag exerted on a solid body of revolution in the axially symmetric Oseen flow has been expressed in terms of one of the involved generalized analytic functions. The problem of the axially symmetric Oseen flow past a solid body of revolution has been reduced to an integral equation based on the generalized Cauchy integral formula. The integral equation has been shown to have computational advantage over an integral equation based on the Oseenlets. The developed framework of generalized analytic functions has been illustrated in solving the problem of the Oseen flow past a solid sphere and solid bispheroids. For different Reynolds numbers, a minimum drag spheroid of fixed volume has been found.
AB - A class of generalized analytic functions arising from the Oseen equations in the axially symmetric case has been identified. For this class of functions, the generalized Cauchy integral formula has been obtained, and a series representation for the region exterior to a sphere has been constructed. The velocity field of the axially symmetric Oseen flow has been represented in terms of two generalized analytic functions, and it has been shown that for an exterior Oseen flow problem, those functions are uniquely determined, provided that they both vanish at infinity. Also the pressure and vorticity have been determined as the real and imaginary parts of the two functions representing the velocity field, and the drag exerted on a solid body of revolution in the axially symmetric Oseen flow has been expressed in terms of one of the involved generalized analytic functions. The problem of the axially symmetric Oseen flow past a solid body of revolution has been reduced to an integral equation based on the generalized Cauchy integral formula. The integral equation has been shown to have computational advantage over an integral equation based on the Oseenlets. The developed framework of generalized analytic functions has been illustrated in solving the problem of the Oseen flow past a solid sphere and solid bispheroids. For different Reynolds numbers, a minimum drag spheroid of fixed volume has been found.
KW - Drag
KW - Generalized analytic functions
KW - Generalized cauchy integral formula
KW - Integral equation
KW - Oseen flows
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U2 - 10.1137/090776937
DO - 10.1137/090776937
M3 - Article
AN - SCOPUS:77956260380
SN - 0036-1399
VL - 70
SP - 2473
EP - 2508
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 7
ER -