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Numerical simulations demonstrate theoretical predictions that gravity waves with short periods (similar to 4-8 min) in the mesosphere and lower thermosphere may force secondary acoustic waves, with harmonic periods (similar to 2-4 minutes), that can reach detectable amplitudes in the thermosphere and ionosphere. The mechanism is through their vertical fluxes of vertical momentum, which lead to forcing as they are disrupted by varying stratification or instability. This is shown likely to occur where horizontally or radially opposing gravity waves interact at large amplitudes, such as above large convective sources, and after overturning. Evanescence and reflection of the waves can lead to further enhancements of the vertical fluxes and the potential for forcing. Results thus identify one of likely several mechanisms for the nonlinear conversion from gravity waves to acoustic waves, to elucidate an unappreciated source of vertical coupling.