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In this paper we examine the role of thermal mass in buffering the interior temperature of a naturally ventilated building from the diurnal fluctuations in the environment. First, we show that the effective thermal mass which is in good thermal contact with the air is limited by the diffusion distance into the thermal mass over one diurnal temperature cycle. We also show that this effective thermal mass may be modelled as an isothermal mass. Temperature fluctuations in the effective thermal mass are attenuated and phase-shifted from those of the interior air, and therefore heat is exchanged with the interior air. The evolution of the interior air temperature is then controlled by the relative magnitudes of (i) the time for the heat exchange between the effective thermal mass and the air; (ii) the time for the natural ventilation to replace the air in the space with air from the environment; and (iii) the period of the diurnal oscillations of the environment. Through analysis and numerical solution of the governing equations, we characterize a number of different limiting cases. If the ventilation rate is very small, then the thermal mass buffers the interior air temperature from fluctuations in the environment, creating a near-isothermal interior. If the ventilation rate increases, so that there are many air changes over the course of a day, but if there is little heat exchange between the thermal mass and interior air, then the interior air temperature locks on to the environment temperature. If there is rapid thermal equilibration of the thermal mass and interior air, and a high ventilation rate, then both the thermal mass and the interior air temperatures lock on to the environment temperature. However, in many buildings, the more usual case is that in which the time for thermal equilibration is comparable to the period of diurnal fluctuations, and in which ventilation rates are moderate. In this case, the fluctuations of the temperature of the thermal mass lag those of the interior air, which in turn lag those of the environment. We consider the implications of these results for the use of thermal mass in naturally ventilated buildings.

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This article investigates the molecular mixing caused by Rayleigh–Taylor (RT) instability of a gravitationally unstable density interface tilted at a small angle to the horizontal. The mixing is measured by the increase in background potential energy, and the mixing efficiency, or fraction of energy irreversibly lost to fluid motion doing work against gravity, is calculated. Laboratory experiments are carried out using saline and fresh water, and modeled with compressible numerical simulations, with a suitable choice of parameters and initial conditions. The experiments show that the high cumulative efficiency of mixing in RT instability at a horizontal interface is only slightly reduced by an interface tilt of up to 10°, despite the strong overturning that occurs. Instantaneous mixing efficiencies as high as 0.5–0.6 are measured, when RT instability is active, with lower values of about 0.35 during the subsequent overturning. The numerical simulations capture the most unstable scales and the overturning motion well, but generate more mixing than the experiments, with the instantaneous mixing efficiency remaining at 0.5 for most of the run. The difference may be due to restratification at small scales in the high Prandtl number experiments.

Abstract. This study investigates the baroclinic instability of a two-layer rotating fluid system. The instability is generated by releasing a cylinder of buoyant fluid at the surface of ambient fluid. The buoyant fluid is dyed so that its depth may be determined from its optical thickness. The system first adjusts until the horizontal density gradient is balanced by a flow along the front, and the adjusted state is then unstable to azimuthal waves. Contours of constant upper layer depth are examined, and the perturbation at each azimuthal wavenumber is determined. The initial wavenumber is well modelled by simple quasi-geostrophic theory. There is a clear high wavenumber cutoff, and a transfer of energy to larger scales with time.