A hybrid code which uses the spectral method for an incompressible fluid and the combined compact finite difference method for passive scalar is developed and applied to compute the spectrum of the passive scalar variance in turbulence at very high Schmidt numbers up to 1000. The accuracy and efficiency of the hybrid code are found to be very satisfactory when compared to the full spectral computation. The scalar spectrum in the viscous-convective range by direct numerical simulation is found

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... obey k −1 power law and to exponentially decay in the far diffusive range, and compared to Kraichnan's spectrum. It is argued that the exponential decay of the spectrum in the far diffusive range is due to the intermittency effect of the velocity field.