Cumulative compressibility effects on slow reactive dynamics in turbulent flows

References

• Fisher , R. 1937 . The wave of advance of advantageous genes . Ann. Eugenics 7, (1997), pp. 335–369; A. Kolmogorov, I. Petrovsky and N. Piscunov, Etude de l equation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Moscow, Univ. Bull. Math. , 1 : 1
   Google Scholar
• Wakita , J.-i. , Komatsu , K. , Nakahara , A. , Matsuyama , T. and Matsushita , M. 1994 . Experimental Investigation on the Validity of Population Dynamics Approach to Bacterial Colony Formation . J. Phys. Soc. Jpn. , 63 : 1205 – 1211 . doi: 10.1143/JPSJ.63.1205
   Google Scholar
• D’Ovidio , F. , De Monte , S. , Alvain , S. , Dandonneau , Y. and Levy , M. 2010 . Fluid dynamical niches of phytoplankton types . Proc. Natl. Acad. Sci. , 107 : 18366 – 18370 . doi: 10.1073/pnas.1004620107
   PubMed Web of Science ®Google Scholar
• McKiver , W. J. and Neufeld , Z. 2009 . Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity . Phys. Rev. , E 79 : 061902 – 8 .
   Google Scholar
• Tzella , A. and Haynes , P. H. 2007 . Small-scale spatial structure in plankton distributions . Biogeosciences , 4 : 173 – 179 . doi: 10.5194/bg-4-173-2007
   Web of Science ®Google Scholar
• Toschi , F. and Bodenschatz , E. 2009 . Lagrangian Properties of Particles in Turbulence . Ann. Rev. Fluid. Mech. , 41 : 375 – 404 . doi: 10.1146/annurev.fluid.010908.165210
   Web of Science ®Google Scholar
• Bec , J. 2003 . Fractal clustering of inertial particles in random flows . Phys. Fluids , 15 : L81 – L84 . doi: 10.1063/1.1612500
   Web of Science ®Google Scholar
• Durham , W. M. , Climent , E. and Stocker , R. 2011 . Gyrotaxis in a Steady Vortical Flow . Phys. Rev. Lett., , 106 : 238102 – 4 . doi: 10.1103/PhysRevLett.106.238102
   PubMed Web of Science ®Google Scholar
• Torney , C. and Neufeld , Z. 2007 . Transport and Aggregation of Self-Propelled Particles in Fluid Flows . Phys. Rev. Lett. , 99 : 078101 – 4 . doi: 10.1103/PhysRevLett.99.078101
   Google Scholar
• Benzi , R. and Nelson , D. R. 2009 . Fisher equation with turbulence in one dimension . Physica , D 238 : 2003 – 2015 .
   Google Scholar
• Perlekar , P. , Benzi , R. , Nelson , D. R. and Toschi , F. 2011 . Population Dynamics At High Reynolds Number . Phys. Rev. Lett. 105 (2010), pp. 144501–4; Statistics of population dynamics in turbulence, J. Phys.: Conf. Ser. , 318 : 092025 – 8 .
   Google Scholar
• Benzi , R. , Jensen , M. H. , Nelson , D. R. , Perlekar , P. , Pigolotti , S. and Toschi , F. 2012 . Population dynamics in compressible flows . Eur. Phys. J. Special Topics , 204 : 57 – 73 . doi: 10.1140/epjst/e2012-01552-0
   Web of Science ®Google Scholar
• Durham , W. M. and Stocker , R. 2012 . Thin Phytoplankton Layers: Characteristics, Mechanisms, and Consequences . Annu. Rev. Mar. Sci., , 4 : 177 – 207 . doi: 10.1146/annurev-marine-120710-100957
   PubMed Web of Science ®Google Scholar
• Moore , L. , Goerrcke , R. and Chisholm , S. 1995 . Comparative physiology of Synechococcus and Prochlorococcus: influence of light and temperature on growth, pigments, fluorescence and absorptive properties . Mar. Ecol. Prog. Ser. , 116 : 259 – 275 . doi: 10.3354/meps116259
   Web of Science ®Google Scholar
• McKiver , W. and Neufeld , Z. 2009 . Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity . Phys. Rev. , E 79 : 061902 – 8 .
   Google Scholar
• Martin , A. 2003 . Phytoplankton patchiness: the role of lateral stirring and mixing . Prog. in Oceanography , 57 : 125 – 174 . doi: 10.1016/S0079-6611(03)00085-5
   Web of Science ®Google Scholar
• Benzi , R. and Biferale , L. 2009 . Fully Developed Turbulence and the Multifractal Conjecture . J. Stat. Phys. , 135 : 977 – 990 . doi: 10.1007/s10955-009-9738-9
   Web of Science ®Google Scholar
• Frisch , U. 1996 . Turbulence: The Legacy of A.N. Kolmogorov , Cambridge : Cambridge University Press .
   Google Scholar