Nonlinear, Nonlocal and Fractional Turbulence: Alternative Recipes for the Modeling of Turbulence
暫譯: 非線性、非局部及分數湍流：湍流建模的替代方法

流體動力學專家一致認為，湍流是非線性和非局部的。由於存在直接的對應關係，非局部性也暗示了分數性。分數動力學是與分形（幾何）系統相關的物理學，並由分數微積分來描述。迄今為止，已經發表了許多對湍流的線性和局部理論的批評。非線性已經相當成熟，但目前只有極少數的一般非局部概念，且尚未有具體的非局部湍流流動解決方案。

本書呈現了基於非局部閉合的基本湍流問題的首個解析和數值解決方案。考量因素包括異常擴散（Lévy飛行）、分形幾何（分形-β、雙分形和多分形模型）以及分數動力學。範例包括一個新的「壁面定律」以及Kraichnan的能量-渦度譜的概括，這與非廣延和非平衡熱力學（Tsallis熱力學）及實驗相一致。此外，所提出的湍流理論揭示了與其他物理系統中的相變類似的臨界和協同現象，例如，二元流體、順磁-鐵磁材料等；湍流的兩個相識別層流條紋和富含渦度的相干結構。

本書除了針對流體專家外，還適合物理學、應用數學和數值數學的研究者，他們希望獲得有關湍流的解析和數值處理中涉及的替代方法的知識。

Peter W. Egolf made an apprenticeship as a heating designer and studied at the University of Applied Sciences of Central Switzerland heating and air conditioning. After working in an industrial R&D laboratory, he studied physics at the Swiss Federal Institute of Technology (ETH Zurich). In 1984 he obtained his diploma in Dynamical Meteorology. Then he entered a R&D division at Gebrüder Sulzer AG in Winterthur, where he invented and investigated industrial air conditioning systems. At an advanced age he had the opportunity to make a PhD in a Noble Laureate 'family' in low-temperature physics (superfluidity). In 1989 Egolf introduced the Lagrange-Hamilton description of the free surface of quantum fluid He II. In 1990 he obtained his PhD at ETHZ with an innovation award. In the late 1980's he invented the Difference-Quotient Turbulence Model (DQTM). From 1990 on a ten years' employment at the Swiss Federal Institute for Materials Testing and Research followed in the field ofenergy and buildings. In 1994 he entered the field of research on ice slurries. In 1998 Egolf created the International Working Party on Ice Slurries of the International Institute of Refrigeration (IIR) and was its first President. From 2000-2018 he was the head of the Theory and Numerics Division (SIT) of the Thermal Sciences Institute at the University of Applied Sciences of Western Switzerland. He initiated a second International Working Party of the IIR (on Magnetic Refrigeration), and for ten years he was serving as its President. Furthermore, he was awarded the first prices of the Swiss Technology Awards 1996 and 2006. Today, Peter W. Egolf is retired, however, he is still involved in the study of fundamental research on fractional turbulence and nonextensive thermodynamics of turbulence. He was a main organizer of eight international conferences. Egolf invented or co-invented a new melting/freezing model, an innovative storage device for ice slurries, a translucent solar thermal wall, an innovative decentralized air-conditioning system, a high-frequency magnetic refrigerator, a new hyper-thermia cancer treatment method with rotating nanowires, etc. You will find more information on his biography in numerous editions of Who'sWho in the World, Who's Who in Science and Engineering and Who'sWho in America.

Kolumban Hutter received a diploma in civil engineering in 1964 from ETH Zurich and a M. Sc. & Ph. Degree in Theoretical and Applied Mechanics from Cornell University, Ithaca, New York in 1973. He has held the position of Professor of Mechanics at Darmstadt University of Technology, Germany from 1987-2006. Presently he is a guest scientist at the Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich and was from 2006-2009 a part time researcher at Academia Sinica, Taiwan. His research interests are in geophysical mechanics with applications in the dynamics of glaciers and ice sheets, the mechanics ofgranular materials, avalanching flows of snow, debris and mud, physical limnology and the foundations of continuum mechanics and thermodynamics. Kolumban Hutter is author and co-author of more than 400 papers (more than 300 peer reviewed) and has written or edited more than 20 books, among these areTheoretical Glaciology, Continuum Methods of Physical Modeling (with K. Jöhnk) Avalanche Dynamics (with S. P. Pudasaini) Solid-Fluid Mixtures of Frictional Materials in Geophysical and Geotechnical Context (with L. Schneider), Physics of Lakes (with Profs Y. Wang and I.Chubarenko, 3 volumes), Fluid & Thermodynamics (with Prof Y. Wang, 2 volumes) all published by Springer-Verlag.He has also served as scientific editor of the Journal of Glaciology for 14 years and was the founder and Editor-in-Chief of Continuum Mechanics and Thermodynamics for 17 years. He is also the Founder and (now past) Editor-in-Chief of the Series "Advances in Geophysical and Environmental Mechanics" published by Springer Verlag. Kolumban Hutter was awarded the Max-Planck Prize of the Max-Planck Society and the Alexander von Humboldt Foundation (Germany) in 1994, the Alexander von Humboldt Prize of the Foundation of Polish Science in 1998, and the Seligman Crystal of the International Glaciological Society in 2003. He lives retired in Zurich, Switzerland

彼得·W·埃戈夫（Peter W. Egolf）曾擔任暖通設計師的學徒，並在瑞士中央應用科技大學學習暖氣和空調。在一家工業研發實驗室工作後，他在瑞士聯邦理工學院（ETH Zurich）學習物理學。1984年，他獲得動態氣象學的文憑。隨後，他進入位於溫特圖爾的Gebrüder Sulzer AG的研發部門，發明並研究工業空調系統。在較高年齡時，他有機會在一位諾貝爾獎得主的「家族」中攻讀低溫物理學（超流體）的博士學位。1989年，埃戈夫引入了量子流體He II自由表面的拉格朗日-哈密頓描述。1990年，他在ETHZ獲得博士學位並獲得創新獎。1980年代末，他發明了差商湍流模型（Difference-Quotient Turbulence Model, DQTM）。自1990年起，他在瑞士聯邦材料測試與研究所從事能源和建築領域的工作，任職十年。1994年，他進入冰漿研究領域。1998年，埃戈夫創建了國際制冷學會（IIR）冰漿國際工作組並擔任首任主席。2000年至2018年，他擔任瑞士西部應用科技大學熱科學研究所理論與數值部門（SIT）的負責人。他發起了IIR的第二個國際工作組（關於磁性制冷），並擔任其主席十年。此外，他還獲得了1996年和2006年瑞士科技獎的首獎。如今，彼得·W·埃戈夫已退休，但仍參與分數湍流和湍流的非廣延熱力學的基礎研究。他是八場國際會議的主要組織者。埃戈夫發明或共同發明了一種新的熔化/冷凍模型、一種創新的冰漿儲存裝置、一種半透明的太陽熱牆、一種創新的分散式空調系統、一種高頻磁性冰箱、一種使用旋轉納米線的新型高熱癌症治療方法等。您可以在《世界名人錄》（Who's Who in the World）、《科學與工程名人錄》（Who's Who in Science and Engineering）和《美國名人錄》（Who's Who in America）的多個版本中找到有關他的更多信息。

科倫班·胡特（Kolumban Hutter）於1964年在ETH Zurich獲得土木工程文憑，並於1973年在美國紐約州伊薩卡的康奈爾大學獲得理論與應用力學的碩士及博士學位。他於1987年至2006年擔任德國達姆施塔特科技大學的力學教授。目前，他是ETH Zurich水利學、氫氣學和冰川學實驗室的客座科學家，並於2006年至2009年在台灣中央研究院擔任兼職研究員。他的研究興趣包括地球物理力學，應用於冰川和冰蓋的動力學、顆粒材料的力學、雪、碎石和泥土的雪崩流動、物理湖沼學以及連續介質力學和熱力學的基礎。科倫班·胡特是400多篇論文的作者和合著者（其中300多篇經過同行評審），並撰寫或編輯了20多本書籍，其中包括《理論冰川學》（Theoretical Glaciology）、《物理建模的連續方法》（Continuum Methods of Physical Modeling，與K. Jöhnk合著）、《雪崩動力學》（Avalanche Dynamics，與S. P. Pudasaini合著）、《地球物理和岩土背景下的摩擦材料的固體-流體混合物》（Solid-Fluid Mixtures of Frictional Materials in Geophysical and Geotechnical Context，與L. Schneider合著）、《湖泊物理學》（Physics of Lakes，與Y. Wang和I. Chubarenko教授合著，三卷本）、《流體與熱力學》（Fluid & Thermodynamics，與Y. Wang教授合著，兩卷本），均由Springer-Verlag出版。他還擔任《冰川學期刊》（Journal of Glaciology）的科學編輯14年，並創辦並擔任《連續介質力學與熱力學》（Continuum Mechanics and Thermodynamics）的主編17年。他還是Springer Verlag出版的《地球物理與環境力學進展系列》（Advances in Geophysical and Environmental Mechanics）的創始人及（現已卸任）主編。科倫班·胡特於1994年獲得馬克斯·普朗克學會和亞歷山大·馮·洪堡基金會（德國）的馬克斯·普朗克獎，1998年獲得波蘭科學基金會的亞歷山大·馮·洪堡獎，2003年獲得國際冰川學會的塞利格曼水晶獎。他目前在瑞士蘇黎世退休生活。