Cascade

From DispersiveWiki


A frequency cascade is a transfer of mass and energy from low frequencies to high (a low-to-high frequency cascade) or vice versa (a high-to-low frequency cascade). Cascades are a phenomenon that are only seen for nonlinear or variable-coefficient equations. In the former case, they are caused by the fact that the frequencies of the nonlinearity may be slightly different from the frequencies of the solution.

A runaway low-to-high frequency cascade can lead to blowup, or at least weak turbulence.

The Fourier truncation method and the I-method provide some tools with which to bound the strength of frequency cascades in a system.