Numerical Modeling of Fluid-Structure Interaction in Bio-Inspired Propulsion. (Modélisation numérique des problèmes d'interaction fluide-structure appliqué à la propulsion bio-inspiré)

Les animaux volants et flottants ont developpe des facons efficaces de produire l'ecoulement de fluide qui genere les forces desirees pour leur locomotion. Cette these est placee dans ce contexte interdisciplinaire et utilise des simulations numeriques pour etudier ces problemes d'interaction fluides-structure, et les applique au vol des insectes et a la nage des poissons. Basee sur les travaux existants sur les obstacles mobiles rigides, une methode numerique a ete developpee, permettant egalement la simulation des obstacles deformables et fournissant une polyvalence et precision accrues dans le cas des obstacles rigides. Nous appliquons cette methode d'abord aux insectes avec des ailes rigides, ou le corps et d'autres details, tels que les pattes et les antennes, peuvent etre inclus. Apres la presentation de tests de validation detaillee, nous procedons a l'etude d'un modele de bourdon dans un ecoulement turbulent pleinement developpe. Nos simulations montrent que les perturbations turbulentes affectent les insectes volants d'une maniere differente de celle des avions aux ailes fixees et concues par l'humain. Dans le cas de ces derniers, des perturbations en amont peuvent declencher des transitions dans la couche limite, tandis que les premiers ne presentent pas de changements systematiques dans les forces aerodynamiques. Nous concluons que les insectes se trouvent plutot confrontes a des problemes de controle dans un environnement turbulent qu'a une deterioration de la production de force. Lors de l‘etape suivante, nous concevons un modele solide, base sur une equation de barre monodimensionnelle, et nous passons a la simulation des systemes couples fluide–structure.

[1]  W. Wall,et al.  Truly monolithic algebraic multigrid for fluid–structure interaction , 2011 .

[2]  Silas Alben,et al.  Optimal flexibility of a flapping appendage in an inviscid fluid , 2008, Journal of Fluid Mechanics.

[3]  Eric Lamballais,et al.  A reference solution of the flow over a circular cylinder at Re = 40 , 2013, 1310.6641.

[4]  K. Senda,et al.  Aerodynamic forces and vortical structures in flapping butterfly's forward flight , 2013 .

[5]  Is the CFL Condition Sufficient? Some Remarks , 2013 .

[6]  John Young,et al.  Details of Insect Wing Design and Deformation Enhance Aerodynamic Function and Flight Efficiency , 2009, Science.

[7]  Hermann G. Matthies,et al.  Algorithms for strong coupling procedures , 2006 .

[8]  G. S. Patterson,et al.  Numerical Simulation of Three-Dimensional Homogeneous Isotropic Turbulence , 1972 .

[9]  F.S. Hover,et al.  Review of experimental work in biomimetic foils , 2004, IEEE Journal of Oceanic Engineering.

[10]  M. Uhlmann An immersed boundary method with direct forcing for the simulation of particulate flows , 2005, 1809.08170.

[11]  Y. Kaneda,et al.  Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation , 2009 .

[12]  Ramiro Godoy-Diana,et al.  Behind the performance of flapping flyers , 2010 .

[13]  Stefan Turek,et al.  Numerical Benchmarking of Fluid-Structure Interaction: A Comparison of Different Discretization and Solution Approaches , 2011 .

[14]  L. J. Pohlen,et al.  The influence of free-stream disturbances on low Reynolds number airfoil experiments , 1983 .

[15]  Kai Schneider,et al.  Decaying two-dimensional turbulence in a circular container. , 2005, Physical review letters.

[16]  Haecheon Choi,et al.  Sectional lift coefficient of a flapping wing in hovering motion , 2010 .

[17]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[18]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

[19]  Philippe Angot,et al.  A penalization method to take into account obstacles in incompressible viscous flows , 1999, Numerische Mathematik.

[20]  T. Weis-Fogh Quick estimates of flight fitness in hovering animals , 1973 .

[21]  Masateru Maeda,et al.  A Free-Flight Simulation of Insect Flapping Flight , 2010 .

[22]  V. Brummelen Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction , 2009 .

[23]  Philippe Angot,et al.  A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles , 2011, J. Comput. Phys..

[24]  W. Wall,et al.  Fixed-point fluid–structure interaction solvers with dynamic relaxation , 2008 .

[25]  E. Ramm,et al.  Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows , 2007 .

[26]  Petros Koumoutsakos,et al.  C-start: optimal start of larval fish , 2012, Journal of Fluid Mechanics.

[27]  Joakim Becker,et al.  A second order backward difference method with variable steps for a parabolic problem , 1998 .

[28]  Hao Liu,et al.  Integrated modeling of insect flight: From morphology, kinematics to aerodynamics , 2009, J. Comput. Phys..

[29]  Jörn Sesterhenn,et al.  Optimal distribution of porous media to reduce trailing edge noise , 2013 .

[30]  Z. Jane Wang,et al.  DISSECTING INSECT FLIGHT , 2005 .

[31]  Z. J. Wang,et al.  Active and passive stabilization of body pitch in insect flight , 2013, Journal of The Royal Society Interface.

[32]  Michael Schäfer,et al.  Experimental and numerical study on a laminar fluid-structure interaction reference test case , 2011 .

[33]  Sophie Papst,et al.  Computational Methods For Fluid Dynamics , 2016 .

[34]  J. Steindorf,et al.  Partitionierte Verfahren für Probleme der Fluid-Struktur Wechselwirkung , 2002 .

[35]  Jörn Sesterhenn,et al.  A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes , 2000 .

[36]  D. Dinkler,et al.  A monolithic approach to fluid–structure interaction using space–time finite elements , 2004 .

[37]  B. Tobalske,et al.  Lift production in the hovering hummingbird , 2009, Proceedings of the Royal Society B: Biological Sciences.

[38]  Masateru Maeda,et al.  Ground Effect in Fruit Fly Hovering: A Three-Dimensional Computational Study , 2013 .

[39]  Y. Kaneda,et al.  High Resolution DNS of Incompressible Homogeneous Forced Turbulence —Time Dependence of the Statistics— , 2003 .

[40]  T. Wick Fluid-structure interactions using different mesh motion techniques , 2011 .

[41]  Marcel Lesieur,et al.  Large-Eddy Simulations of Turbulence , 2005 .

[42]  S. N. Fry,et al.  The aerodynamics of hovering flight in Drosophila , 2005, Journal of Experimental Biology.

[43]  Kai Schneider,et al.  Simulation of confined magnetohydrodynamic flows using a pseudo-spectral method with volume penalization , 2012 .

[44]  Sebastien Honore Roland Michelin Falling, flapping, flying, swimming,... : high-Re fluid-solid interactions with vortex shedding , 2009 .

[45]  Carlos E. S. Cesnik,et al.  Effects of flexibility on the aerodynamic performance of flapping wings , 2011, Journal of Fluid Mechanics.

[46]  Angelo Iollo,et al.  Modeling and simulation of fish-like swimming , 2010, J. Comput. Phys..

[47]  C. Eloy,et al.  Skin friction on a flapping plate in uniform flow , 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[48]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[49]  Miguel Angel Fernández,et al.  Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit , 2011 .

[50]  Kai Schneider,et al.  Numerical simulation of the transient flow behaviour in chemical reactors using a penalisation method , 2005 .

[51]  F. Sotiropoulos,et al.  Immersed boundary methods for simulating fluid-structure interaction , 2014 .

[52]  Mao Sun,et al.  Unsteady aerodynamic forces of a flapping wing , 2004, Journal of Experimental Biology.

[53]  Rajat Mittal,et al.  Hawkmoth flight stability in turbulent vortex streets , 2013, Journal of Experimental Biology.

[54]  A. Vincent,et al.  The spatial structure and statistical properties of homogeneous turbulence , 1991, Journal of Fluid Mechanics.

[55]  Lixi Huang,et al.  Flutter of Cantilevered Plates in Axial Flow , 1995 .

[56]  L. Machiels Predictability of Small-Scale Motion in Isotropic Fluid Turbulence , 1997 .

[57]  Fabio Nobile,et al.  Fluid-structure partitioned procedures based on Robin transmission conditions , 2008, J. Comput. Phys..

[58]  M. Lighthill Large-amplitude elongated-body theory of fish locomotion , 1971, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[59]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[60]  T. Daniel,et al.  The Journal of Experimental Biology 206, 2979-2987 © 2003 The Company of Biologists Ltd , 2022 .

[61]  Kai Schneider,et al.  Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming , 2015 .

[62]  F. Lehmann,et al.  Elastic deformation and energy loss of flapping fly wings , 2011, Journal of Experimental Biology.

[63]  Dmitry Pekurovsky,et al.  P3DFFT: A Framework for Parallel Computations of Fourier Transforms in Three Dimensions , 2012, SIAM J. Sci. Comput..

[64]  Oleg V. Vasilyev,et al.  A Brinkman penalization method for compressible flows in complex geometries , 2007, J. Comput. Phys..

[65]  Toshiaki Hisada,et al.  Fluid–structure interaction analysis of the two-dimensional flag-in-wind problem by an interface-tracking ALE finite element method , 2007 .

[66]  Hao Liu,et al.  Recent progress in flapping wing aerodynamics and aeroelasticity , 2010 .

[67]  C. Peskin,et al.  Flexible clap and fling in tiny insect flight , 2009, Journal of Experimental Biology.

[68]  C. Peskin,et al.  A computational fluid dynamics of `clap and fling' in the smallest insects , 2005, Journal of Experimental Biology.

[69]  Sarah Miriam Iams,et al.  Characterizing Mosquito Flight Using Measurement and Simulation , 2014 .

[70]  David Jerison The World According to Wavelets : The Story of a Mathematical Technique in the Making Reviewed by David Jerison , 1999 .

[71]  Dmitry Kolomenskiy,et al.  Numerical simulation of fluid-structure interaction with the volume penalization method , 2015, J. Comput. Phys..

[72]  Gordon J. Berman,et al.  Energy-minimizing kinematics in hovering insect flight , 2007, Journal of Fluid Mechanics.

[73]  K. Breuer,et al.  Aeromechanics in aeroecology: flight biology in the aerosphere. , 2007, Integrative and comparative biology.

[74]  Xiaolei Yang,et al.  A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations , 2009, J. Comput. Phys..

[75]  C. Peskin Numerical analysis of blood flow in the heart , 1977 .

[76]  J S Humbert,et al.  Kinematic strategies for mitigating gust perturbations in insects , 2013, Bioinspiration & biomimetics.

[77]  M. Dickinson,et al.  A linear systems analysis of the yaw dynamics of a dynamically scaled insect model , 2010, Journal of Experimental Biology.

[78]  Elias Balaras,et al.  A strongly coupled, embedded-boundary method for fluid–structure interactions of elastically mounted rigid bodies , 2008 .

[79]  Martin Skote,et al.  Dragonfly (Sympetrum flaveolum) flight: Kinematic measurement and modelling , 2013 .

[80]  C. Ellington The novel aerodynamics of insect flight: applications to micro-air vehicles. , 1999, The Journal of experimental biology.

[81]  Peter A. Dewey,et al.  Scaling laws for the thrust production of flexible pitching panels , 2013, Journal of Fluid Mechanics.

[82]  Jun Zhang,et al.  Heavy flags undergo spontaneous oscillations in flowing water. , 2005, Physical review letters.

[83]  K R I S H N A N M A H E S H, S A N J I V,et al.  The influence of entropy fluctuations on the interaction of turbulence with a shock wave , 2022 .

[84]  R. Peyret Spectral Methods for Incompressible Viscous Flow , 2002 .

[85]  Petros Koumoutsakos,et al.  Iterative Brinkman penalization for remeshed vortex methods , 2015, J. Comput. Phys..

[86]  C. Peskin The immersed boundary method , 2002, Acta Numerica.

[87]  Stephen Childress Natural locomotion in fluids and on surfaces : swimming, flying, and sliding , 2012 .

[88]  Mao Sun,et al.  Effects of wing deformation on aerodynamic forces in hovering hoverflies , 2010, Journal of Experimental Biology.

[89]  Rosa Donat,et al.  A high-resolution penalization method for large Mach number flows in the presence of obstacles , 2009 .

[90]  M. Belliard,et al.  Penalized direct forcing and projection schemes for Navier-Stokes , 2010 .

[91]  Michael P. Païdoussis,et al.  Cantilevered flexible plates in axial flow: Energy transfer and the concept of flutter-mill , 2009 .

[92]  Mandyam V. Srinivasan,et al.  Vision and air flow combine to streamline flying honeybees , 2013, Scientific Reports.

[93]  Ramiro Godoy-Diana,et al.  Vortex-induced drag and the role of aspect ratio in undulatory swimmers , 2014 .

[94]  R. Rogallo Numerical experiments in homogeneous turbulence , 1981 .

[95]  Lisandro Dalcin,et al.  Strong coupling strategy for fluid–structure interaction problems in supersonic regime via fixed point iteration , 2009 .

[96]  Toshiyuki Nakata,et al.  A fluid-structure interaction model of insect flight with flexible wings , 2012, J. Comput. Phys..

[97]  Takaji Inamuro,et al.  Lift and thrust generation by a butterfly-like flapping wing–body model: immersed boundary–lattice Boltzmann simulations , 2015, Journal of Fluid Mechanics.

[98]  Steven G. Johnson,et al.  The Design and Implementation of FFTW3 , 2005, Proceedings of the IEEE.

[99]  A. S. Monin,et al.  Statistical Fluid Mechanics: The Mechanics of Turbulence , 1998 .

[100]  C. Ellington,et al.  Foraging costs in bumblebees: field conditions cause large individual differences , 1999, Insectes Sociaux.

[101]  Kai Schneider,et al.  A numerical study of vortex-induced drag of elastic swimmer models , 2014 .

[102]  Marie Farge,et al.  Wavelets: Application to Turbulence , 2006 .

[103]  Gilles Carbou,et al.  Boundary layer for a penalization method for viscous incompressible flow , 2003, Advances in Differential Equations.

[104]  Michiel van de Panne,et al.  Flexible muscle-based locomotion for bipedal creatures , 2013, ACM Trans. Graph..

[105]  Roger C. Hardie,et al.  Visual transduction in Drosophila , 2001, Nature.

[106]  Michael H. Dickinson,et al.  Flies Evade Looming Targets by Executing Rapid Visually Directed Banked Turns , 2014, Science.

[107]  Alexis Weinreb,et al.  Four-Winged Flapping Flyer in Forward Flight , 2014, 1501.00050.

[108]  Jie Shen,et al.  An overview of projection methods for incompressible flows , 2006 .

[109]  C. Ellington Limitations on Animal Flight Performance , 1991 .

[110]  Jérôme Casas,et al.  Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces , 2013, Journal of Experimental Biology.

[111]  M. Triantafyllou,et al.  Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion , 1993 .

[112]  B. Balachandran,et al.  Influence of flexibility on the aerodynamic performance of a hovering wing , 2009, Journal of Experimental Biology.

[113]  Christophe Eloy,et al.  Aeroelastic instability of a flexible plate in a uniform flow , 2008 .

[114]  John Murtis,et al.  Odor Plumes and How Insects Use Them , 1992 .

[115]  R. Dudley,et al.  Mechanics of Forward Flight in Bumblebees: I. Kinematics and Morphology , 1990 .

[116]  M. Dickinson,et al.  Rotational accelerations stabilize leading edge vortices on revolving fly wings , 2009, Journal of Experimental Biology.

[117]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[118]  A. Alexeev,et al.  Free swimming of an elastic plate plunging at low Reynolds number , 2014 .

[119]  F. Lehmann,et al.  The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings , 2004, Journal of Experimental Biology.

[120]  A. Biewener,et al.  Hummingbird flight stability and control in freestream turbulent winds , 2015, The Journal of Experimental Biology.

[121]  S. Combes,et al.  Turbulence-driven instabilities limit insect flight performance , 2009, Proceedings of the National Academy of Sciences.

[122]  Kai Schneider,et al.  Numerical Modelling of Flexible Heaving Foils , 2013 .

[123]  Javier Jiménez,et al.  The structure of intense vorticity in isotropic turbulence , 1993, Journal of Fluid Mechanics.

[124]  Beverley J. Glover,et al.  Vortex shedding model of a flapping flag , 2008, Journal of Fluid Mechanics.

[125]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[126]  S. Michelin,et al.  Resonance and propulsion performance of a heaving flexible wing , 2009, 0906.2804.

[127]  F. Lehmann,et al.  The aerodynamic benefit of wing–wing interaction depends on stroke trajectory in flapping insect wings , 2007, Journal of Experimental Biology.

[128]  R. Ramamurti,et al.  A three-dimensional computational study of the aerodynamic mechanisms of insect flight. , 2002, The Journal of experimental biology.

[129]  Kai Schneider,et al.  The Lighthill–Weis-Fogh clap–fling–sweep mechanism revisited , 2011, Journal of Fluid Mechanics.

[130]  Mao Sun,et al.  Dynamic flight stability of a bumblebee in forward flight , 2008 .

[131]  Jean-Frédéric Gerbeau,et al.  A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows , 2003 .

[132]  Fabio Nobile,et al.  Added-mass effect in the design of partitioned algorithms for fluid-structure problems , 2005 .

[133]  S. Combes,et al.  Rolling with the flow: bumblebees flying in unsteady wakes , 2013, Journal of Experimental Biology.

[134]  Toshiyuki Nakata,et al.  Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach , 2012, Proceedings of the Royal Society B: Biological Sciences.

[135]  R. Mittal,et al.  Hawkmoth flight performance in tornado-like whirlwind vortices , 2014, Bioinspiration & biomimetics.

[136]  Kai Schneider,et al.  Numerical simulation of the transient flow behaviour in tube bundles using a volume penalization method , 2005 .

[137]  C. Eloy Optimal Strouhal number for swimming animals , 2011, 1102.0223.

[138]  Kai Schneider,et al.  Two-dimensional simulation of the fluttering instability using a pseudospectral method with volume penalization , 2013 .

[139]  M. Belliard,et al.  A SECOND ORDER PENALIZED DIRECT FORCING FOR HYBRID CARTESIAN/IMMERSED BOUNDARY FLOW SIMULATIONS , 2014 .

[140]  R. B. Srygley,et al.  Unconventional lift-generating mechanisms in free-flying butterflies , 2002, Nature.

[141]  Fritz-Olaf Lehmann,et al.  Experimental quantification and numerical simulation of unsteady flow conditions during free flight maneuvers of insects , 2012 .

[142]  Kai Schneider,et al.  The effect of toroidicity on reversed field pinch dynamics , 2014 .

[143]  M. Reeuwijk,et al.  Robust and accurate open boundary conditions for incompressible turbulent jets and plumes , 2013 .

[144]  Michael Schäfer,et al.  Efficiency and accuracy of fluid-structure interaction simulations using an implicit partitioned approach , 2008 .

[145]  John Guckenheimer,et al.  Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles , 2010, Proceedings of the National Academy of Sciences.

[146]  C. Ellington The Aerodynamics of Hovering Insect Flight. VI. Lift and Power Requirements , 1984 .

[147]  Mao Sun,et al.  Control of flight forces and moments by flapping wings of model bumblebee , 2008 .

[148]  Kai Schneider,et al.  Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint , 2012, Numerische Mathematik.

[149]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

[150]  John E. Sader,et al.  Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order , 2007 .

[151]  R. Sani,et al.  Résumé and remarks on the open boundary condition minisymposium , 1994 .

[152]  Nikolaus A. Adams,et al.  A windowing method for periodic inflow/outflow boundary treatment of non-periodic flows , 2005 .

[153]  K. Schneider,et al.  Aerodynamic Ground Effect in Fruitfly Sized Insect Takeoff , 2015, PloS one.

[154]  S. N. Fry,et al.  The Aerodynamics of Free-Flight Maneuvers in Drosophila , 2003, Science.

[155]  Dmitry Kolomenskiy,et al.  A Fourier spectral method for the Navier-Stokes equations with volume penalization for moving solid obstacles , 2009, J. Comput. Phys..

[156]  R. Dudley,et al.  Mechanics of Forward Flight in Bumblebees: II. QUASI-STEADY LIFT AND POWER REQUIREMENTS , 1990 .

[157]  Richard Pasquetti,et al.  A pseudo-penalization method for high Reynolds number unsteady flows , 2008 .

[158]  K. Kawachi,et al.  A Numerical Study of Insect Flight , 1998 .

[159]  Chunning Ji,et al.  A novel iterative direct-forcing immersed boundary method and its finite volume applications , 2012, J. Comput. Phys..

[160]  K. Bathe,et al.  A mesh adaptivity procedure for CFD and fluid-structure interactions , 2009 .

[161]  Fritz-Olaf Lehmann,et al.  Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl , 2008, Journal of The Royal Society Interface.

[162]  D. Yue,et al.  Flapping dynamics of a flag in a uniform stream , 2007, Journal of Fluid Mechanics.

[163]  J. Pinton,et al.  Velocity measurement of a settling sphere , 2000 .

[164]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[165]  J. Wyngaard Turbulence in the Atmosphere: Contents , 2010 .

[166]  T. Daniel,et al.  The Journal of Experimental Biology 206, 2989-2997 © 2003 The Company of Biologists Ltd , 2003 .

[167]  Kai Schneider,et al.  Two- and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects , 2010 .

[168]  R. Dudley,et al.  Into turbulent air: size-dependent effects of von Kármán vortex streets on hummingbird flight kinematics and energetics , 2014, Proceedings of the Royal Society B: Biological Sciences.

[169]  P. Moin,et al.  Large-eddy simulation of turbulent confined coannular jets , 1996, Journal of Fluid Mechanics.

[170]  Charbel Farhat,et al.  Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity , 2006 .

[171]  Mao Sun,et al.  Lateral dynamic flight stability of a model bumblebee in hovering and forward flight. , 2013, Journal of theoretical biology.

[172]  R. Dudley,et al.  Comparative Energetics of the Giant Hummingbird (Patagona gigas) , 2011, Physiological and Biochemical Zoology.

[173]  C. Ellington The Aerodynamics of Hovering Insect Flight. III. Kinematics , 1984 .

[174]  Kai Schneider,et al.  FluSI: A Novel Parallel Simulation Tool for Flapping Insect Flight Using a Fourier Method with Volume Penalization , 2015, SIAM J. Sci. Comput..

[175]  S. Turek,et al.  Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow , 2006 .

[176]  F. Lehmann,et al.  Bumblebee Flight in Heavy Turbulence. , 2015, Physical review letters.