Abstract
We study turbulent flows in pressure-driven planar channels with imposed unstable thermal stratification, using direct numerical simulations in a wide range of Reynolds and Rayleigh numbers and reaching flow conditions which are representative of fully developed turbulence. The combined effect of forced and free convection produces a peculiar pattern of quasi-streamwise rollers occupying the full channel thickness, with aspect ratio considerably higher than unity; it has been observed that they have an important redistributing effect on temperature and momentum, providing for a substantial fraction of the heat and momentum flux at bulk Richardson numbers larger than$0.01$. The mean values and the variances of the flow variables do not appear to follow Prandtl’s scaling in the free-convection regime, except for the temperature and vertical velocity fluctuations, which are more directly affected by wall-attached turbulent plumes. We find that the Monin–Obukhov theory nevertheless yields a useful representation of the main flow features. In particular, the widely used Businger–Dyer flux-profile relationships are found to provide a convenient way of approximately accounting for the bulk effects of friction and buoyancy, although the individual profiles may have wide scatter from the alleged trends. Significant deviations are found in direct numerical simulations with respect to the commonly used parametrization of the momentum flux in the light-wind regime, which may have important practical impact in wall models of atmospheric dynamics. Finally, for modelling purposes, we devise a set of empirical predictive formulae for the heat flux and friction coefficients, which are within approximately$10\,\%$standard deviation from the numerical results in a wide range of flow parameters.
Highlights
Mixed convection is the process whereby heat and momentum are transferred under the concurrent effect of shear and buoyancy, and it is at the heart of several physical phenomena of great practical importance, especially within the context of atmospheric dynamics
We have carried out direct numerical simulations of turbulent channel flows with unstable thermal stratification in a wide range of Reynolds and Rayleigh numbersvarying between the extreme cases of pure free and forced convection
It is worthwhile noting that this effect, absent in pure Rayleigh–Benard convection and in the turbulent channel flow, shows–up for a wide range of Richardson numbers, virtually in all situations where mixed convection is relevant
Summary
Mixed convection is the process whereby heat and momentum are transferred under the concurrent effect of shear and buoyancy, and it is at the heart of several physical phenomena of great practical importance, especially within the context of atmospheric dynamics. All the above numerical studies were carried out at rather low Reynolds and/or Rayleigh number, they are not necessarily representative of fully turbulent flow conditions of practical relevance, and they span a limited range of Richardson numbers, typically close to the case of pure forced convection. Lz = 4h may be regarded as a minimal spanwise box size to achieve healthy turbulence in channel flow simulations of mixed convection It is the main purpose of this study to establish a high–fidelity database for unstably buoyant channel flows which encompasses a wide range of Richardson numbers, at high enough values of Reynolds and Rayleigh number to be representative of fully developed turbulence.
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