Hybrid POD-FFT analysis of nonlinear evolving coherent structures of DNS wavepacket in laminar-turbulent transition

TL;DR

This paper introduces a hybrid POD-FFT method to analyze DNS data of wavepackets in laminar-turbulent transition, effectively identifying flow modes and their spectral content.

Contribution

A novel hybrid POD-FFT approach is developed to interpret flow modes in DNS data, revealing detailed subharmonic content and mode distinctions without prior physics knowledge.

Findings

Automatically identifies fundamental, subharmonic, and Klebanoff modes.

Separates subharmonic content into three distinct parts.

Provides explanation for positively detuned subharmonic modes.

Abstract

This paper concerns the study of direct numerical simulation (DNS) data of a wavepacket in laminar turbulent transition in a Blasius boundary layer. The decomposition of this wavepacket into a set of "modes" (a basis that spans an approximate solution space) can be achieved in a wide variety of ways. Two well-known tools are the fast Fourier transform (FFT) and the proper orthogonal decomposition (POD). To synergize the strengths of both methods, a hybrid POD-FFT is pioneered, using the FFT as a tool for interpreting the POD modes. The POD-FFT automatically identifies well-known fundamental, subharmonic and Klebanoff modes in the flow, even though it is blind to the underlying physics. Moreover, the POD-FFT further separates the subharmonic content of the wavepacket into three fairly distinct parts: a positively detuned mode resembling a Lambda-vortex, a Craik-type tuned mode and a Herbert-type positive-negative detuned mode pair, in decreasing order of energy. This distinction is less widely recognized, but it provides a possible explanation for the slightly positively detuned subharmonic mode often observed in previous experiments and simulations.