Communications in Mathematical Sciences
Volume 21 (2023)
Numerical evidence of exponential mixing by alternating shear flows
Pages: 529 – 541
We performed a numerical study of the efficiency of mixing by alternating horizontal and vertical shear “wedge” flows on the two-dimensional torus. Our results suggest that except in cases where each individual flow is applied for only a short time, these flows produce exponentially fast mixing. The observed mixing rates are higher when the individual flow times are shorter (but not too short), and randomizing either the flow times or phase shifts of the flows does not appear to enhance mixing (again when the flow times are not too short). In fact, the latter surprisingly seems to inhibit it slightly.
exponential mixing on the torus, alternating shear flows
2010 Mathematics Subject Classification
L.T.C. acknowledges partial support by NSF grant DMS-1913144.
F.R. and K.Y.J.W. were supported in part by Division of Physical Sciences Undergraduate Summer Research Awards and TRELS Awards from UC San Diego.
A.Z. acknowledges partial support by NSF grant DMS-1900943 and by a Simons Fellowship.
Received 5 November 2021
Received revised 3 June 2022
Accepted 13 June 2022
Published 1 February 2023