Convection driven by differential heating at a horizontal boundary

Abstract

We report laboratory and numerical experiments with the convective circulation that develops in a long channel driven by heating and cooling through opposite halves of the horizontal base. The problem is similar to that posed by Stommel (Proc. Natl Acad. Sci. vol. 48, 1962, p. 766) and Rossby (Deep-Sea Res. vol. 12, 1965, p. 9; Tellus vol. 50, 1998, p. 242), where flow forced by a linear temperature variation along the ocean surface or the base of a tank presented a demonstration of the smallness of sinking regions in the meridional overturning circulation of the oceans. In contrast to the previous experiments, we use small aspect ratio, larger Rayleigh numbers, piecewise uniform boundary conditions and an imposed input heat flux. The flow is characterized by a vigorous overturning circulation cell filling the box length and depth. A stable thermocline forms above the cooled base and is advected over the heated part of the base, where it is eroded from below by small-scale three-dimensional convection, forming a ‘convective mixed layer’. At the endwall, the convective mixing is overshadowed by a narrow but turbulent plume rising through the full depth of the box. The return flow along the top of the box is turbulent with large slowly migrating eddies, and occupies approximately a third of the total depth. Theoretical scaling laws give temperature differences, thermocline thickness and velocities that are in good agreement with the experimental data and two-dimensional numerical solutions. The measured and computed density structure is largely similar to the thermocline and abyssal stratification in the oceans.

Down-slope cascading modulated by day/night variations of solar heating

“…Such horizontal temperature differences and the associated water exchange arise regularly in the day/night, synoptic and seasonal rhythms along all the coastal slopes of natural basins (Horsch and Stefan, 1988;Farrow and Patterson, 1993;Sturman et al, 1999;Fer et al, 2002;Farrow, 2004;Lei and Patterson, 2006) and, in fact, form natural background for all other processes. This kind of water exchange can be considered and described principally as a sort of horizontal convection, since it is driven by the difference in temperature (or heat flux) at a horizontal boundary (e.g., Farrow, 2004;Mullarney et al, 2004;Hughes and Griffith, 2008). Generally, it works in the following way: when, as a result of solar heating and/or heat-exchange with the atmosphere, water in the littoral region becomes denser than the open lake water -it cascades down-slope in lake pelagial, when it becomes less dense -it flows off-shore in the upper layers, replaced by an on-shore flow beneath.…”

Onset of Unsteady Horizontal Convection in Rectangular Tank atPr= 1

“…Paparella and Young [1] found Ra c ≈ 2 × 10 8 at P r = 1 in their simulations, which is significantly smaller than others' results [2,3,4,5,6,7,8]. For example, Rossby (1965), Wang and Huang (2005) found the flow is steady and stable for Ra < 5 × 10 8 in their experiments [3,5].…”

“…There is a critical Rayleigh number Ra c , and the steady flow is unstable and becomes unsteady when Ra > Ra c . The unsteady flow in horizontal convection was first found by numerical simulation [1], then was observed in the experiment at Ra > 10 12 [2]. This unsteady flow is proved to be non-turbulent even as Ra → ∞, though the flow field seems to be chaotic [1].…”

“…As the abyssal ocean circulation plays an important role in climate change, the horizontal convection has intensively been explored in recent years [1,2,3]. It can be set to motion by any small temperature gradient, unlike the Rayleigh-Bénard convection.…”

“…This unsteady flow is proved to be non-turbulent even as Ra → ∞, though the flow field seems to be chaotic [1]. The investigation on the unsteady horizontal convection flow is relatively less, except for [1,2,4]. However, they have mainly focused on how the turbulent plume maintains a stable stratified circulation.…”