Thermal convection with mixed thermal boundary conditions: effects of insulating lids at the top

Abstract

The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range 2.3 × 10 9 Ra F 1.8 × 10 11 and cylindrical cells in the range 1.4 × 10 10 Ra F 1.2 × 10 12 with the Prandtl number Pr fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading order level, the magnitude of temperature fluctuation in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function (PDF) in the bulk is essentially invariant with respect to both insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed Ra F , the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical one.

Mixed thermal conditions in convection: how do continents affect the mantle’s circulation?

“…The two latter numerical studies have shown that from a certain characteristic patch size, the effect on the flow dynamics becomes almost negligible in the turbulent regime. The three-dimensional work by Bakhuis et al (2017) also showed that the effect of the shape of these patches is small, something which at first glance contradicts Cooper et al (2013) and Wang et al (2017). Therefore, a cross-over between two regimes must exist, one where large adiabatic patches which significantly affect the flow topology and another where small adiabatic patches whose effect is only present very close to the plates must exist.…”

“…To help understand these issues, Wang et al (2017) performed an experimental study of Rayleigh-Bénard flow with mixed thermal boundary conditions, insulating a fraction of the top plate with adiabatic patches. They used two experimental set-ups: a rectangular tank and a cylindrical tank, in an attempt to make their results as general as possible.…”

“…This in line with the simulations of Cooper et al (2013), but contrasts with the approach by Ripesi et al (2014), whose largest patches are a tenth of the plate size, and only get smaller. Wang et al (2017) first focus on the heat transfer, finding that for both geometries the leading-order effect happens through the fraction of the boundary which is adiabatic, and through the arrangement of the patterns. The adiabatic area affects the scaling behaviour of the heat transport, and for higher Rayleigh numbers the difference between a perfectly conducting plate and the mixed boundary conditions grows.…”

“…When compared to previous studies, the work by Wang et al (2017) focuses on large adiabatic patches, as do the simulations of Cooper et al (2013), while the simulations of Ripesi et al (2014) in two dimensions, and their recent extension by Bakhuis et al (2017) to three dimensions, have all focused on patches which have characteristic dimensions smaller than the distance between plates. The two latter numerical studies have shown that from a certain characteristic patch size, the effect on the flow dynamics becomes almost negligible in the turbulent regime.…”

“…Sea ice comes in a wide range of topologies, and understanding how the fractures, leads and polynyas in ice affect the dynamics of oceanic and atmospheric circulation (Maykut 1982), and by extension global warming, is crucial in today's world where ice caps are disappearing. And while several studies for mixed temperature boundary conditions have been performed numerically either in two dimensions (Ripesi et al 2014) or for lower Rayleigh numbers (Cooper, Moresi & Lenardic 2013), no systematic analysis of the flow structure or heat transport in the turbulent regime was performed up to the work of Wang, Huang & Xia (2017).…”