Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T01:42:59.243Z Has data issue: false hasContentIssue false
  • English
  • Français

Passive flight in density-stratified fluids

Published online by Cambridge University Press:  03 December 2018

Try Lam ,
Lionel Vincent  and
Eva Kanso Open the ORCID record for Eva Kanso [Opens in a new window]
Try Lam
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
Lionel Vincent
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
Eva Kanso*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Leaves falling in air and marine larvae settling in water are examples of unsteady descents due to complex interactions between gravitational and aerodynamic forces. Understanding passive flight is relevant to many branches of engineering and science, ranging from estimating the behaviour of re-entry space vehicles to analysing the biomechanics of seed dispersion. The motion of regularly shaped objects falling freely in homogenous fluids is relatively well understood. However, less is known about how density stratification of the fluid medium affects passive flight. In this paper, we experimentally investigate the descent of heavy discs in stably stratified fluids for Froude numbers of order 1 and Reynolds numbers of order 1000. We specifically consider fluttering descents, where the disc oscillates as it falls. In comparison with pure water and homogeneous saltwater fluid, we find that density stratification significantly enhances the radial dispersion of the disc, while simultaneously decreasing the vertical descent speed, fluttering amplitude and inclination angle of the disc during descent. We explain the physical mechanisms underlying these observations in the context of a quasi-steady force and torque model. These findings could have significant impact on the design of unpowered vehicles and on the understanding of geological and biological transport where density and temperature variations may occur.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 200 - 223
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

van Aartrijk, M. & Clercx, H. J. H. 2010 The dynamics of small inertial particles in weakly stratified turbulence. J. Hydro-Environ. Res. 4 (2), 103–114.Google Scholar
van Aartrijk, M., Clercx, H. J. H. & Winters, K. B. 2008 Single-particle, particle-pair, and multiparticle dispersion of fluid particles in forced stably stratified turbulence. Phys. Fluids 20 (2), 025104.Google Scholar
Andersen, A., Pesavento, U. & Wang, Z. J. 2005a Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid Mech. 541, 65–90.Google Scholar
Andersen, A., Pesavento, U. & Wang, Z. J. 2005b Analysis of transitions between fluttering, tumbling and steady descent of falling cards. J. Fluid Mech. 541, 91–104.Google Scholar
Auguste, F., Magnaudet, J. & Fabre, D. 2013 Falling styles of disks. J. Fluid Mech. 719, 388–405.Google Scholar
Awotahegn, M. B., Oosterkamp, L. D. & Nystrøm, P. R. 2016 3D study of dropped object motion in sea water based on scale test. In ISOPE-I-16-474. International Society of Offshore and Polar Engineers.Google Scholar
Belmonte, A., Eisenberg, H. & Moses, E. 1998 From flutter to tumble: inertial drag and Froude similarity in falling paper. Phys. Rev. Lett. 81 (2), 345–348.Google Scholar
Biró, I., Gyure, B., Jánosi, I. M., Szabó, K. G. & Tél, T.2007 Oscillation and levitation of balls in continuously stratified fluids. arXiv:physics/0702208.Google Scholar
Blanchette, F. & Bush, J. W. M. 2005 Particle concentration evolution and sedimentation-induced instabilities in a stably stratified environment. Phys. Fluids 17 (7), 073302.Google Scholar
Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M. & Mykins, N. 2010 A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number. J. Fluid Mech. 664, 436–465.Google Scholar
Chrust, M., Bouchet, G. & Dušek, J. 2013 Numerical simulation of the dynamics of freely falling discs. Phys. Fluids 25 (4), 044102.Google Scholar
Doostmohammadi, A., Dabiri, S. & Ardekani, A. M. 2014 A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid. J. Fluid Mech. 750, 5–32.Google Scholar
Economidou, M. & Hunt, G. R. 2009 Density stratified environments: the double-tank method. Expl Fluids 46 (3), 453–466.Google Scholar
Field, S. B., Klaus, M., Moore, M. G. & Nori, F. 1997 Chaotic dynamics of falling disks. Nature 388 (6639), 252–254.Google Scholar
Fortuin, J. M. H. 1960 Theory and application of two supplementary methods of constructing density gradient columns. J. Polym. Sci. 44 (144), 505–515.Google Scholar
Ganzevles, S. P. M., van Nuland, F. S. W., Maas, L. R. M. & Toussaint, H. M. 2009 Swimming obstructed by dead-water. Naturwissenschaften 96 (4), 449–456.Google Scholar
Gee, E., Western, A. & Swearer, S. 2016 Dispersal in stratified environments a biophysical modelling study of black bream larvae in a salt-wedge estuary. In Paper 26649 in Proceedings of the 11th International Symposium on Ecohydraulics, Melbourne, Australia, 7–12 February. The University of Melbourne.Google Scholar
Hanazaki, H., Kashimoto, K. & Okamura, T. 2009 Jets generated by a sphere moving vertically in a stratified fluid. J. Fluid Mech. 638, 173–197.Google Scholar
Heisinger, L., Newton, P. & Kanso, E. 2014 Coins falling in water. J. Fluid Mech. 742, 243–253.Google Scholar
Hill, D. F. 2002 General density gradients in general domains: the ‘two-tank’ method revisited. Expl Fluids 32 (4), 434–440.Google Scholar
Hoerner, S. F. 1965 Fluid-dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance. Hoerner Fluid Dynamics.Google Scholar
Hu, R. & Wang, L. 2014 Motion transitions of falling plates via quasisteady aerodynamics. Phys. Rev. E 90, 013020.Google Scholar
Hurlen, E. C.2006 The motions and wave fields produced by an ellipse moving through a stratified fluid. PhD thesis, University of California, San Diego.Google Scholar
Jin, C. & Xu, K. 2008 Numerical study of the unsteady aerodynamics of freely falling plates. Commun. Comput. Phys. 3 (4), 834–851.Google Scholar
Jones, M. A. & Shelley, M. J. 2005 Falling cards. J. Fluid Mech. 540, 393–425.Google Scholar
Kuznetsov, S. P. 2015 Plate falling in a fluid: regular and chaotic dynamics of finite-dimensional models. Regular Chaotic Dyn. 20 (3), 345–382.Google Scholar
Lee, C., Su, Z., Zhong, H., Chen, S., Zhou, M. & Wu, J. 2013 Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral. J. Fluid Mech. 732, 77–104.Google Scholar
Lin, E. I. H.1982 A review of the salt-gradient solar pond technology. JPL Publ. 81-116. Jet Propulsion Laboratory.Google Scholar
Lin, Q., Boyer, D. L. & Fernando, H. J. S. 1992a Turbulent wakes of linearly stratified flow past a sphere. Phys. Fluids A 4 (8), 1687–1696.Google Scholar
Lin, Q., Lindberg, W. R., Boyer, D. L. & Fernando, H. J. S. 1992b Stratified flow past a sphere. J. Fluid Mech. 240, 315–354.Google Scholar
Lofquist, K. E. B. & Purtell, L. P. 1984 Drag on a sphere moving horizontally through a stratified liquid. J. Fluid Mech. 148, 271–284.Google Scholar
Maas, L. R. M. & van Haren, H. 2006 Worden mooi-weer verdrinkingen door dood-water veroorzaakt. Meteorologica 15, 211–216.Google Scholar
MacIntyre, S., Romero, J. R., Silsbe, G. M. & Emery, B. M. 2014 Stratification and horizontal exchange in Lake Victoria, East Africa. Limnol. Oceanogr. 59 (6), 1805–1838.Google Scholar
Majed, A. & Cooper, P. 2013 High fidelity sink trajectory nonlinear simulations for dropped subsea objects. In ISOPE-I-13-310. International Society of Offshore and Polar Engineers.Google Scholar
Maxwell, J. C. 1990 The Scientific Letters and Papers of James Clerk Maxwell: 1846–1862. Cambridge University Press.Google Scholar
Mercier, M. J., Vasseur, R. & Dauxois, T. 2011 Resurrecting dead-water phenomenon. Nonlinear Process. Geophys. 18 (2), 193–208.Google Scholar
Merzkirch, W. 1987 Flow Visualization. Academic Press.Google Scholar
Michelin, S. & Smith, S. G. L. 2009 An unsteady point vortex method for coupled fluid–solid problems. Theor. Comput. Fluid Dyn. 23 (2), 127–153.Google Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213, 70–76.Google Scholar
Pesavento, U. & Wang, Z. J. 2004 Falling paper: Navier–Stokes solutions, model of fluid forces, and center of mass elevation. Phys. Rev. Lett. 93 (14), 144501.Google Scholar
Pineda, J., Hare, J. A. & Sponaugle, S. 2007 Larval transport and dispersal in the coastal ocean and consequences for population connectivity. Oceanography 20 (3), 22–39.Google Scholar
Pounds, P., Potie, T., Kendoul, F., Singh, S., Jurdak, R. & Roberts, J. 2016 Automatic distribution of disposable self-deploying sensor modules. In Springer Tracts in Advanced Robotics, pp. 535–543. Springer.Google Scholar
Pullin, D. I. & Wang, Z. J. 2004 Unsteady forces on an accelerating plate and application to hovering insect flight. J. Fluid Mech. 509, 1–21.Google Scholar
Settles, G. S. 2012 Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media. Springer.Google Scholar
Spedding, G. R. 2002 Vertical structure in stratified wakes with high initial Froude number. J. Fluid Mech. 454, 71–112.Google Scholar
Staquet, C. 2005 Internal gravity waves in geophysical fluids. CISM Int. Cent. Mech. Sci. 479, 75–132.Google Scholar
Stringham, G. E., Simons, D. B. & Guy, H. P. 1969 The Behavior of Large Particles Falling in Quiescent Liquids. US Gov. Printing Office.Google Scholar
Tanabe, Y. & Kaneko, K. 1994 Behavior of a falling paper. Phys. Rev. Lett. 73 (10), 1372–1375.Google Scholar
Torres, C. R., Hanazaki, H., Ochoa, J., Castillo, J. & Van Woert, M. 2000 Flow past a sphere moving vertically in a stratified diffusive fluid. J. Fluid Mech. 417, 211–236.Google Scholar
Torres, C. R., Ochoa, J., Castillo, J. & Hanazaki, H. 1999 Numerical simulation of flow past a sphere in vertical motion within a stratified fluid. J. Comput. Appl. Math. 103 (1), 67–76.Google Scholar
Valdes, S., Urza, I., Pounds, P. & Singh, S. 2012 Samara: low-cost deployment for environmental sensing using passive autorotation. In Robotics: Science and Systems Workshop on Robotics for Environmental Monitoring. MIT Press.Google Scholar
Vincent, L., Shambaugh, W. S. & Kanso, E. 2016 Holes stabilize freely falling coins. J. Fluid Mech. 801, 250–259.Google Scholar
Wang, Z. J., Birch, J. M. & Dickinson, M. H. 2004 Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations versus robotic wing experiments. J. Expl Biol. 207 (3), 449–460.Google Scholar
Willmarth, W. W., Hawk, N. E. & Harvey, R. L. 1964 Steady and unsteady motions and wakes of freely falling disks. Phys. Fluids 7 (2), 197–208.Google Scholar
Yasseri, S. 2014 Experiment of free-falling cylinders in water. Underwat. Technol. 32 (3), 177–191.Google Scholar
Yick, K. Y., Torres, C. R., Peacock, T. & Stocker, R. 2009 Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. J. Fluid Mech. 632, 49–68.Google Scholar
Zhao, H. & Peterson, P. F. 2010 An overview of modeling methods for thermal mixing and stratification in large enclosures for reactor safety analysis. In NUTHOS PN8P0079. Elsevier.Google Scholar
Zhong, H., Lee, C., Su, Z., Chen, S., Zhou, M. & Wu, J. 2013 Experimental investigation of freely falling thin disks. Part 1. The flow structures and Reynolds number effects on the zigzag motion. J. Fluid Mech. 716, 228–250.Google Scholar