Spectral analysis of flow and scalar primitive variables in near and far laminar wake of an elliptic cylinder

TL;DR

This study uses spectral analysis via FFT to investigate flow and scalar variables in the wake of an elliptic cylinder, revealing primary and secondary frequency structures and their physical origins in different wake regions.

Contribution

It provides new insights into the spectral characteristics of flow and scalar fields behind an elliptic cylinder, highlighting the physical sources of observed frequencies.

Findings

Primary frequency linked to saturated wake state

Secondary low frequency associated with transitional chaos

Scalar primarily transported by streamwise velocity and pressure

Abstract

We analyze the primitive variables of fluid flow and scalar fields through fast Fourier transform (FFT) in the near and far wake of an elliptic cylinder. Numerical simulation of flow and scalar fields behind an elliptic cylinder of axis ratio 0.4 at a Reynolds number of 130 is performed. The semi-major axis of the elliptic cylinder is kept perpendicular to the incoming flow, where the fluid flow is two-dimensional and the Prandtl number is 0.71. The scalar is injected into the flow field by means of heating the cylinder continuously. The simulation is run for a long time to show that the secondary vortex street is a time-dependent phenomenon. Three distinguishable flow and scalar regions are observed in the wake of the cylinder. This study reveals the presence of low-frequency structures besides the primary shedding structures in linear, transition and saturation regions of temporal wake development. We show that the spectral source of the primary frequency is the saturated state of the temporal wake development, while its physical source is the periodic arrangement of structures of primitive variables, which inhibits the transmutation of their wavelength. On the other hand, the secondary low frequency is embedded in the transitional developing stage of the wake and its physical source is the chaotic behaviour of the transition process, which aids in the transmutation of the wavelength of the structures. Our spectral analysis also reveals that the scalar is predominately carried by the streamwise velocity and the pressure throughout the wake.