ERROR GROWTH IN A DECAYING 2-DIMENSIONAL TURBULENCE

Error growth in a two-dimensional turbulence is investigated by solving numerically the Navier-Stokes equation and its linearized form, starting from a fully-developed turbulent field with Reynolds number up to about 105. The computation was done by the spectral method with 6822 effective modes. Both the energy and the squared stream function of the difference field, which stress the lower wavenumber part of the spectrum of the flow field, exhibit an exponential growth. The enstrophy and the palinstrophy, which stress the higher wavenumber part, on the other hand, grow faster than exponentially in an earlier stage and later grow exponentially. The growth rate is found to be independent of the norm and the Reynolds number in a certain time interval. The enstrophy spectrum of the difference field shows a power law k0. © 1990, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.