Abstract.
Gyrotactic algae are bottom heavy, motile cells whose swimming direction is determined by a balance between a buoyancy torque directing them upwards and fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic model for phytoplankton motility in flows. The essential attractiveness of this peculiar form of motility is the availability of a mechanistic description which, despite its simplicity, revealed predictive, rich in phenomenology, easily complemented to include the effects of shape, feedback on the fluid and stochasticity (e.g., in cell orientation). In this review we consider recent theoretical, numerical and experimental results to discuss how, depending on flow properties, gyrotaxis can produce inhomogeneous phytoplankton distributions on a wide range of scales, from millimeters to kilometers, in both laminar and turbulent flows. In particular, we focus on the phenomenon of gyrotactic trapping in nonlinear shear flows and in fractal clustering in turbulent flows. We shall demonstrate the usefulness of ideas and tools borrowed from dynamical systems theory in explaining and interpreting these phenomena.
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J.S. Guasto, R. Rusconi, R. Stocker, Annu. Rev. Fluid Mech. 44, 373 (2012)
R. Margalef, Oceanol. Acta 1, 493 (1978)
L. Rodolfi, G. Chini Zittelli, N. Bassi, G. Padovani, N. Biondi, G. Bonini, M.R. Tredici, Biotechnol. Bioeng. 102, 100 (2009)
O.A. Croze, G. Sardina, M. Ahmed, M.A. Bees, L. Brandt, J. R. Soc. Interface 10, 20121041 (2013)
Y. Duan, N. Gotoh, Q. Yan, Z. Du, A.M. Weinstein, T. Wang, S. Weinbaum, Proc. Natl. Acad. Sci. U.S.A. 105, 11418 (2008)
H.J. Kim, D. Huh, G. Hamilton, D.E. Ingber, Lab. Chip 12, 2165 (2012)
A.N. Ebrahimi, D. Or, Water Resour. Res. 50, 7406 (2014)
R. Rusconi, R. Stocker, Curr. Opin. Microbiol. 25, 1 (2015)
S. Chilukuri, C.H. Collins, P.T. Underhill, J. Phys.: Condens. Matter 26, 115101 (2014)
J. Locsei, T. Pedley, Bull. Math. Biol. 71, 1089 (2009)
R. Stocker, J.R. Seymour, Microbiol. Mol. Biol. Rev. 76, 792 (2012)
L. Karp-Boss, E. Boss, P. Jumars et al., Oceanogr. Mar. Biol. 34, 71 (1996)
B. Rothschild, T. Osborn, J. Plankton Res. 10, 465 (1988)
T. Kiørboe, B. MacKenzie, J. Plankton Res. 17, 2319 (1995)
S. Pigolotti, R. Benzi, P. Perlekar, M.H. Jensen, F. Toschi, D.R. Nelson, Theor. Popul. Biol. 84, 72 (2013)
T. Kiørboe, A Mechanistic Approach to Plankton Ecology (Princeton University Press, 2008)
W. Lampert, Funct. Ecol. 3, 21 (1989)
J.O. Kessler, Nature 313, 218 (1985)
T.J. Pedley, J.O. Kessler, Proc. R. Soc. B 231, 47 (1987)
T.J. Pedley, J.O. Kessler, Annu. Rev. Fluid Mech. 24, 313 (1992)
X. Garcia, S. Rafaï, P. Peyla, Phys. Rev. Lett. 110, 138106 (2013)
M. Martin, A. Barzyk, E. Bertin, P. Peyla, S. Rafai, Phys. Rev. E 93, 051101 (2016)
G.J. Thorn, R.N. Bearon, Phys. Fluids 22, 041902 (2010)
M.A. Bees, O.A. Croze, Proc. R. Soc. Lond. A 466, 2057 (2010)
R. Bearon, M. Bees, O. Croze, Phys. Fluids 24, 121902 (2012)
F. De Lillo, M. Cencini, W. Durham, M. Barry, R. Stocker, E. Climent, G. Boffetta, Phys. Rev. Lett. 112, 044502 (2014)
M. Cencini, M. Franchino, F. Santamaria, G. Boffetta, J. Theor. Biol. 399, 62 (2016)
W.M. Durham, J.O. Kessler, R. Stocker, Science 323, 1067 (2009)
W.M. Durham, R. Stocker, Annu. Rev. Mar. Sci. 4, 177 (2012)
F. Santamaria, F. De Lillo, M. Cencini, G. Boffetta, Phys. Fluids 26, 111901 (2014)
W. Durham, E. Climent, R. Stocker, Phys. Rev. Lett. 106, 238102 (2011)
W.M. Durham, E. Climent, M. Barry, F. De Lillo, G. Boffetta, M. Cencini, R. Stocker, Nat. Commun. 4, 2148 (2013)
I. Fouxon, A. Leshansky, Phys. Rev. E 92, 013017 (2015)
K. Gustavsson, F. Berglund, P. Jonsson, B. Mehlig, Phys. Rev. Lett. 116, 108104 (2016)
C. Zhan, G. Sardina, E. Lushi, L. Brandt, J. Fluid Mech. 739, 22 (2014)
E. Ott, Chaos in Dynamical Systems (Cambridge University Press, 1993)
T. Pedley, N. Hill, J. Kessler, J. Fluid Mech. 195, 223 (1988)
S. Ghorai, N. Hill, Phys. Fluids 19, 054107 (2007)
S. Rafaï, L. Jibuti, P. Peyla, Phys. Rev. Lett. 104, 098102 (2010)
G.B. Jeffery, Proc. R. Soc. Lond. A 102, 161 (1922)
A. Zöttl, H. Stark, Phys. Rev. Lett. 108, 218104 (2012)
A. Zöttl, H. Stark, Eur. Phys. J. E 36, 4 (2013)
R. Rusconi, J.S. Guasto, R. Stocker, Nat. Phys. 10, 212 (2014)
R. Bearon, A. Hazel, J. Fluid Mech. 771, R3 (2015)
N. Khurana, J. Blawzdziewicz, N.T. Ouellette, Phys. Rev. Lett. 106, 198104 (2011)
J.R. Taylor, R. Stocker, Science 338, 675 (2012)
Marcos, H.C. Fu, T.R. Powers, R. Stocker, Proc. Natl. Acad. Sci. U.S.A. 109, 4780 (2012)
A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Phys. Rev. Lett. 101, 038102 (2008)
T. Kaya, H. Koser, Biophys. J. 102, 1514 (2012)
C. Torney, Z. Neufeld, Phys. Rev. Lett. 99, 078101 (2007)
C. Torney, Z. Neufeld, Phys. Rev. Lett. 101, 078105 (2008)
J.S. Guasto, K.A. Johnson, J.P. Gollub, Phys. Rev. Lett. 105, 168102 (2010)
T. Pedley, J. Kessler, J. Fluid Mech. 212, 155 (1990)
N. Hill, D. Häder, J. Theor. Biol. 186, 503 (1997)
I. Frankel, H. Brenner, J. Fluid Mech. 204, 97 (1989)
R. Bearon, A. Hazel, G. Thorn, J. Fluid Mech. 680, 602 (2011)
M. Dekshenieks, P. Donaghay, J. Sullivan, J. Rines, T. Osborn, M. Twardowski, Mar. Ecol. Prog. Ser. 223, 61 (2001)
O.M. Cheriton, M.A. McManus, D.V. Holliday, C.F. Greenlaw, P.L. Donaghay, T.J. Cowles, Estuaries Coast 30, 575 (2007)
J.H. Churnside, P.L. Donaghay, ICES J. Mar. Sci. 66, 778 (2009)
J.V. Steinbuck, M.T. Stacey, M.A. McManus, O.M. Cheriton, J.P. Ryan, Limnol. Oceanogr. 54, 1353 (2009)
J. Ryan, D. Greenfield, R. Marin III, C. Preston, B. Roman, S. Jensen, D. Pargett, J. Birch, C. Mikulski, G. Doucette et al., Limnol. Oceanogr. 56, 1255 (2011)
M.T. Barry, R. Rusconi, J.S. Guasto, R. Stocker, J. R. Soc. Interface 12, 20150791 (2015)
G.I. Sivashinsky, Physica D 17, 243 (1985)
Z.S. She, Phys. Lett. A 124, 161 (1987)
V. Borue, S.A. Orszag, J. Fluid Mech. 306, 293 (1996)
S. Musacchio, G. Boffetta, Phys. Rev. E 89, 023004 (2014)
Z. Wang, L. Goodman, Cont. Shelf Res. 30, 104 (2010)
J.M. Sullivan, M.A. McManus, O.M. Cheriton, K.J. Benoit-Bird, L. Goodman, Z. Wang, J.P. Ryan, M. Stacey, D. Van Holliday, C. Greenlaw, M.A. Moline, M. McFarland, Cont. Shelf Res. 30, 1 (2010)
S.A. Thorpe, An Introduction to Ocean Turbulence (Cambridge University Press, 2007)
S. Redner, A Guide to First Passage Processes (Cambridge University Press, 2001)
A. Martin, Prog. Oceanogr. 57, 125 (2003)
D.L. Mackas, K.L. Denman, M.R. Abbott, Bull. Mar. Sci. 37, 652 (1985)
E. Malkiel, O. Alquaddoomi, J. Katz, Meas. Sci. Technol. 10, 1142 (1999)
S.M. Gallager, H. Yamazaki, C.S. Davis, Mar. Ecol. Prog. Ser. 267, 27 (2004)
M.R. Maxey, J.J. Riley, Phys. Fluids 26, 883 (1983)
K.D. Squires, J.K. Eaton, Phys. Fluids A 3, 1169 (1991)
E. Calzavarini, M. Kerscher, D. Lohse, F. Toschi, J. Fluid Mech. 607, 13 (2008)
J. Bec et al., Phys. Rev. Lett. 98, 84502 (2007)
U. Frisch, Turbulence: The Legacy of AN Kolmogorov (Cambridge University Press, 1995)
E.L. Harvey, S. Menden-Deuer, T.A. Rynearson, Front. Microbiol. 6, 1277 (2015)
J. Bec, Phys. Fluids 15, L81 (2003)
K.J. Falconer, The Geometry of Fractal Sets, Vol. 85 (Cambridge University Press, 1986)
P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)
G. Paladin, A. Vulpiani, Phys. Rep. 156, 147 (1987)
M. Wilkinson, B. Mehlig, Europhys. Lett. 71, 186 (2005)
G. Falkovich, A. Fouxon, M. Stepanov, Nature 419, 151 (2002)
E. Balkovsky, G. Falkovich, A. Fouxon, Phys. Rev. Lett. 86, 2790 (2001)
I. Fouxon, Phys. Rev. Lett. 108, 134502 (2012)
M. Borgnino, G. Boffetta, F. De Lillo, M. Cencini, J. Fluid Mech. 856, R1 (2018)
A. La Porta et al., Nature 409, 1017 (2001)
J. Bec, A. Celani, M. Cencini, S. Musacchio, Phys. Fluids 17, 073301 (2005)
M. Borgnino, F. De Lillo, G. Boffetta, Phys. Rev. E 95, 023108 (2017)
A. Sengupta, F. Carrara, R. Stocker, Nature 543, 555 (2017)
L. Schmidt, I. Fouxon, D. Krug, M. van Reeuwijk, M. Holzner, Phys. Rev. E 93, 063110 (2016)
V. Shukla, R. Volk, M. Bourgoin, A. Pumir, New J. Phys. 19, 123030 (2017)
A. Chengala, M. Hondzo, J. Sheng, Phys. Rev. E 87, 052704 (2013)
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Cencini, M., Boffetta, G., Borgnino, M. et al. Gyrotactic phytoplankton in laminar and turbulent flows: A dynamical systems approach. Eur. Phys. J. E 42, 31 (2019). https://doi.org/10.1140/epje/i2019-11792-0
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DOI: https://doi.org/10.1140/epje/i2019-11792-0