Energy Transfer into Cross-Waves by Wavemakers

In the long channels, the cross-waves derive their energy directly from wavemaker not only from basic flow. In the present talk we show how cross-waves are generated in long rectangular channels by wavemaker even without having to take into account the presence of any basic flow waves. Here we apply Lam\`e's method of superposition for the first time in such channel geometry. This method allows one to construct a simple mathematical model, which shows how the cross-waves can be generated directly by the wavemaker motion. This mathematical model of the resonant cross-wave excitation is the easiest way to study pattern formation on fluid free surface. Our experimental observations agree with the theoretical results.