For the purpose of obtaining computational resources at ZIB, Berlin, we describe the outline of the research project 'small-scale instabilities and their effect upon the turbulent energy cascade'. The focus of the present document is the presentation of the pseudo-spectral direct simulation code, its parallel implementation and data structure. Some preliminary tests of the performance of the code (before optimization for the architecture of the CRAY T3E) are reported. Necessary resources for the envisaged simulations are estimated.