Turbulence spectra in natural and forced convection

Abstract

Fourier spectra have been traditionally used to get insight into the flow structures of turbulence. In wall-bounded flows these are not reported usually in Kolmogorov units. In this paper the spectra are evaluated in these units to compare with the case of isotropic turbulence, to investigate at which distance from the wall flow isotropy is achieved. We have found that improvement of universality of the spectra in the near-wall region is achieved by evaluating the dissipative length scale from the total turbulence kinetic energy dissipation, rather than through the rate of isotropic dissipation as customary. The database of Lee and Moser [1] for flow in plane channel and of Pirozzoli et al. [2] for flow in a circular pipe have been considered. We have found similarities between pipe and channel flow up to a non-dimensional distance 0.2. Farther from the wall the spectra tend to become universal and similar to isotropic turbulence in channels, whereas the geometry of the circular pipe prevents universality. Large part of the paper is also focused on turbulent natural convection in rectangular enclosures. In that flow, comparison between velocity and temperature spectra allows to answer about possible differences in the slope of the inertial ranges. In this respect, the importance of the spectral bottleneck in the cascade of kinetic and thermal energy is stressed. The large amplitude of the bottleneck in the temperature spectra might be the cause for the k−4/3 spectral range observed at wall distances greater than the thermal boundary layer thickness, defined in terms of the maximum turbulent thermal energy production. Also in this flow evaluating the Kolmogorov length scale through the total dissipation yields better collapse of the spectral range with exponential decay on that of isotropic turbulence in the near-wall region. Flow visualisations and joint PDFs are used for deeper understanding of the complex physics of turbulent convection.