Basis function multifield bispectral deconvolution analysis

Abstract

A different procedure for calculating linear and nonlinear coefficients of model systems for fully developed turbulence is derived. This procedure can be applied to systems with multiple interacting fields; in the single-field case the linear coefficients consist of mode frequencies and growth rates. This method differs from previous methods in the use of a limited set of functions or basis set from which the nonlinear terms in the turbulence equation are approximated in a series expansion. The algorithm is derived from this assumption using a least squares approach. This approach has been tested on simulations of fully developed two-dimensional turbulence and compared to previous methods. It is able to reconstruct coefficients with several significant figures precision and offers excellent noise rejection capabilities, and is moreover able to operate using tiny data sets compared to those required by previous methods. © 2005 American Institute of Physics.