Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System
المؤلفون المشاركون
Hadjinicolaou, Maria
Protopapas, Eleftherios
المصدر
Mathematical Problems in Engineering
العدد
المجلد 2016، العدد 2016 (31 ديسمبر/كانون الأول 2016)، ص ص. 1-6، 6ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2016-05-16
دولة النشر
مصر
عدد الصفحات
6
التخصصات الرئيسية
الملخص EN
When studying axisymmetric particle fluid flows, a scalar function, ψ , is usually employed, which is called a stream function.
It serves as a velocity potential and it can be used for the derivation of significant hydrodynamic quantities.
The governing equation is a fourth-order partial differential equation; namely, E 4 ψ = 0 , where E 2 is the Stokes irrotational operator and E 4 = E 2 ∘ E 2 is the Stokes bistream operator.
As it is already known, E 2 ψ = 0 in some axisymmetric coordinate systems, such as the cylindrical, spherical, and spheroidal ones, separates variables, while in the inverted prolate spheroidal coordinate system, this equation accepts R -separable solutions, as it was shown recently by the authors.
Notably, the kernel space of the operator E 4 does not decompose in a similar way, since it accepts separable solutions in cylindrical and spherical system of coordinates, while E 4 ψ = 0 semiseparates variables in the spheroidal coordinate systems and it R -semiseparates variables in the inverted prolate spheroidal coordinates.
In addition to these results, we show in the present work that in the inverted oblate spheroidal coordinates, the equation E ′ 2 ψ = 0 also R -separates variables and we derive the eigenfunctions of the Stokes operator in this particular coordinate system.
Furthermore, we demonstrate that the equation E ′ 4 ψ = 0 R -semiseparates variables.
Since the generalized eigenfunctions of E ′ 2 cannot be obtained in a closed form, we present a methodology through which we can derive the complete set of the generalized eigenfunctions of E ′ 2 in the modified inverted oblate spheroidal coordinate system.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Hadjinicolaou, Maria& Protopapas, Eleftherios. 2016. Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1112798
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Hadjinicolaou, Maria& Protopapas, Eleftherios. Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System. Mathematical Problems in Engineering No. 2016 (2016), pp.1-6.
https://search.emarefa.net/detail/BIM-1112798
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Hadjinicolaou, Maria& Protopapas, Eleftherios. Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1112798
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1112798
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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