https://hal-insu.archives-ouvertes.fr/insu-00788726Bolster, DiogoDiogoBolsterCEEES - Department of Civil and Environmental Engineering and Earth Science [Notre Dame] - UND - University of Notre Dame [Indiana]Dentz, MarcoMarcoDentzIDAEA - Institute of Environmental Assessment and Water Research - CSIC - Consejo Superior de Investigaciones Científicas [Madrid]Le Borgne, TanguyTanguyLe BorgneGR - Géosciences Rennes - UR - Université de Rennes - INSU - CNRS - Institut national des sciences de l'Univers - OSUR - Observatoire des Sciences de l'Univers de Rennes - UR - Université de Rennes - INSU - CNRS - Institut national des sciences de l'Univers - UR2 - Université de Rennes 2 - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - CNRS - Centre National de la Recherche ScientifiqueHypermixing in linear shear flowHAL CCSD2011[SDU.STU] Sciences of the Universe [physics]/Earth SciencesDubigeon, Isabelle2013-02-15 10:12:402023-03-13 11:17:172013-02-15 15:05:02enJournal articleshttps://hal-insu.archives-ouvertes.fr/insu-00788726/document10.1029/2011WR010737application/pdf1[1] In this technical note we study mixing in a two‐dimensional linear shear flow. We derive analytical expressions for the concentration field for an arbitrary initial condition in an unbounded two‐dimensional shear flow. We focus on the solution for a point initial condition and study the evolution of (1) the second centered moments as a measure for the plume dispersion, (2) the dilution index as a measure of the mixing state, and (3) the scalar dissipation rate as a measure for the rate of mixing. It has previously been shown that the solute spreading grows with the cube of time and thus is hyperdispersive. Herein we demonstrate that the dilution index increases quadratically with time in contrast to a homogeneous medium, for which it increases linearly. Similarly, the scalar dissipation rate decays as t−3, while for a homogeneous medium it decreases more slowly as t−2. Mixing is much stronger than in a homogeneous medium, and therefore we term the observed behavior hypermixing.