The direct resonance mechanism between vertical vorticity and vertical velocity is studied for plane Poiseuille flow. The resonance term, obtained from the initial-value problem, has been determined numerically for various initial disturbances. The amplitude, in wave-number space, is found to decay with time for all resonances. Because of its appearance in the Laplace-transform plane as a double pole, we show that a resonance term will have an initial amplitude which grows with Reynolds number, thus indicating that resonances will dominate the initial development of a disturbance at large Reynolds number.