Laboratory modeling of the structure of a thermal bar and related circulation in a basin with a sloping bottom

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

“…above the effective slope), a spectacular flow separation feature from the bottom boundary (Sturman et al, 1999) appears to be an intrinsic property of the flow: maximum flow velocities are significantly lifted up from the bottom (to ~0.1-0.15 of the local depth; Chubarenko and Demchenko, 2008;Chubarenko, 2010). This feature provides insight into the physical nature of the flow.…”

“…Analysis of the present numerical solutions suggests that the size of this region scales with the mixing depth, so that the horizontal extent of the cell is about ¼-⅓ of the length of the effective slope (e.g., of the (horizontal) distance from the shore to the point at the bottom, where the base of the upper convectively mixing layer meets the slope). Most probably, this is related to the depth of maximum of mean on-shore transport from the deeper lake part, which is formed at the level of approximately ¼-⅓ of the depth of the UML (Chubarenko and Demchenko, 2008;Chubarenko, 2010). In fact, the existence of such a specific circulation cell on the top is a common feature of all convective problems in triangular enclosures, and has been explained in various situations by several different reasons: by mathematical discontinuity in theory (Chubarenko and Hutter, 2005); by the influence of water heat conduction (rather than convection, working in the main sloping region) in laboratory experiments (Farrow, 2004); by shallowness and subsequent plane circulation in 3D numerical modelling (Chubarenko and Demchenko, 2010); and by wave-breaking or river inflow in field data.…”

“…For simplicity, we consider water at a temperature T above that of maximum density, so that cooling from the surface produces denser water in the shallows (autumnal situation). The results are also applicable to waters at T<Tmd, but then the cascades are generated by surface heating (early spring situation) (Chubarenko and Demchenko, 2008;Chubarenko, 2010).…”

“…Physically, the cooling from the surface of the basin with a sloping bottom (when water temperature, T, is above that of maximum density, Tmd) generates a flow, which is a combination of vertical convective cells (forced by negative buoyancy flux through the surface) and horizontal exchange, consisting of a down-slope density undercurrent and horizontal compensating flow in the upper layers, which are driven by horizontal pressure gradients (Carmack and Farmer, 1982;Farrow and Patterson, 1993;Farrow, 2004;Chubarenko and Demchenko, 2008;Chubarenko, 2010). These two different processes -vertical convection and horizontal exchange -develop with different celerity and are, to a certain extent, independent of one another.…”

“…As for the length scale, a number of spatial dimensions were used in different studies and geometries, including the following: the length of the laboratory tank (e.g., studies in laboratory tanks with horizontal bottom: Rossby, 1965;Mullarney et al, 2004;Hughes and Griffith, 2008); the length of the portion of the bottom that is heated/cooled (forcing plate) or the thickness of the turbulent boundary layer above this forcing plate (Sturman et al, 1999); and the water depth (Horsch et al, 1994;Farrow, 2004;Lei and Patterson, 2006). Studies with sloping bottom (Horsch et al, 1994;Sturman et al, 1999;Farrow, 2004;Chubarenko and Demchenko, 2008;Chubarenko, 2010) have demonstrated the complexity of the arising horizontal convective exchange, which, however, has many common features with Rossby's exchange flows. For example: i) horizontal temperature/density gradient as the driver; ii) characteristic always unsteady behaviour of the quasi-steady exchange; and iii) its 2-layered structure with the maximum speed of currents, observed at intermediate depths rather than at the boundaries (Sturman et al, 1999;Farrow, 2004;Chubarenko, 2010).…”