Ultimate Image Singularities in Oblate Spheroidal Coordinates with Applications in Hydrodynamics

المنفردات الصورية النهائية في الإحداثيات الكروانية المفلطحة مع تطبيقات في الديناميكا المائية

Clicks: 309
ID: 116616
2020
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Abstract
This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamical applications. The theorem provides explicit relations that express the oblate spheroidal harmonics, given in terms of the fundamental solutions of the Laplace equation. Here, the theorem is employed to transform the underlying Green’s function into the relevant coordinate system and, consequently, to formulate the diffraction potential. The case considered refers to the axisymmetric placement of the spheroid, namely, symmetrical axis perpendicular to the free surface. The mathematical formulations have been implemented numerically providing exceptionally accurate computations, which manifests the consistency and robustness of the relevant formulas.
تستثمر هذه الدراسة مبرهنة توفيا ميلوه للمجسم شبه الكروي المفلطح مع تركيز خاص على التطبيقات الهيدروديناميكية. تقدم المبرهنة علاقات صريحة للتعبير عن التوافقيات شبه الكروية المفلطحة بدلالة الحلول الأساسية لمعادلة لابلاس. وتُوظَّف المبرهنة هنا لتحويل دالة غرين الأساسية إلى نظام الإحداثيات المناسب، ومن ثم صياغة جهد الحيود. وتتناول الحالة قيد الدراسة التموضع متناظر المحور للمجسم شبه الكروي، وتحديداً عندما يكون محور التناظر عمودياً على السطح الحر. وقد نُفِّذت الصياغات الرياضية عددياً لتقدم حسابات فائقة الدقة، مما يُبرز اتساق الصيغ المعنية وقوتها.
Reference Key
chatjigeorgiou2020journalultimate Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Ioannis K. Chatjigeorgiou;Eva Loukogeorgaki;Eirini Anastasiou;Nikos Mantadakis;Chatjigeorgiou, Ioannis K.;Loukogeorgaki, Eva;Anastasiou, Eirini;Mantadakis, Nikos;
Journal journal of marine science and engineering
Year 2020
DOI
10.3390/jmse8010032
URL
https://www.mdpi.com/2077-1312/8/1/32
Keywords
hydrodynamics sources image singularities miloh theorem oblate spheroids green’s function multipoles

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