Four independent stream functions which satisfied the boundary conditions were presumed for an agitated vessel. Differential equations for the stream functions, which were derived from the Navier Stokes equation, were solved numerically. An analysis of the cross-correlation of the velocity components showed that the low frequency fluctuations in the flow corresponded to large-scale flow patterns over the entire vessel. The correspondence was also observed experimentally. The period of the low frequency motion was about 34 times that of the external input stream function, which agreed with the value of 20-30 times the blade passage frequency that was found experimentally. The increase in the number of the stream functions from 3 to 4 contributed to describing the characteristics of the local phenomena in the flow rather than to changing the dynamics, as was shown bp the results of the frequency analysis and the mutual correlation function. It was confirmed that this deterministic analysis with the small number of variables was very effective to predict the dynamic behavior for the low frequency fluctuations in an agitated vessel.