Energy Spectra for Decaying 2D Turbulence in a Bounded Domain

New results are presented for the energy spectra of decaying 2D turbulence in a square container with no-slip walls for integral-scale Reynolds numbers up to 20 000. The one-dimensional energy spectra measured close to the walls reveal a $k^{-5\mathrm{}/3}$ inertial range, instead of a $k^{-3\mathrm{}}$ direct enstrophy cascade, due to the production of small-scale vorticity near no-slip boundaries. During the intermediate decay stage a $k^{-3\mathrm{}}$ spectrum starts to emerge and the change in location of the injection scale of small-scale vorticity is explained in terms of an average boundary-layer thickness.