Convective circulation in littoral water due to surface cooling

Abstract

Cooling of littoral waters of a lake under calm conditions creates a horizontal temperature gradient because surface heat loss is distributed over progressively larger depth by plunging sheets (thermals). Resulting convective circulation establishes an exchange flow between littoral and open waters. Numerical simulations illustrate the development ofthe flow from the formation ofthermals to the establishment of a horizontal circulation. Circulation flow rate was found to be proportional toW'/fl,2<n<3(Wisth R l'h e ay etg number) for W values in the range 104-1O8. A laboratory visualization experiment at %? -lo9 confirmed the main features of the simulation. To consider applications to vegetated littoral slopes, we interpreted the results with a formula accounting for the added resistance offered to the flow by the aquatic plants. An example showed that convective Icirculation can be a significant factor in renewing littoral waters.In coastal waters heat transfer through the water surface may, under favorable conditions, generate horizontal temperature gradients. An example is the spring thermocline which occurs when solar radiation heats nearshore shallow waters faster than open waters and creates an inclined density interface (Csanady 1982). On a much shorter time and length scale a phenomenon of similar nature may occur during nighttime cooling of littoral waters, or on a seasonal scale in midlatitude lakes during early fall. The phenomenon does not seem to have been documented in the literature, but unpublished data confirm its occurrence (J. Barko unpubl. data). A nearshore temperature gradient develops during cooling because shallow water cools faster than deeper water when both regions are subjected to the same surface rate of cooling. The result is that the shallow nearshore water becomes negatively buoyant, and a convective circulation (underflow) is set in motion (Fig.

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

“…In addition, in the field where time and space variations of heat-exchange conditions and bathymetry peculiarities are always the case, flow characteristics, such as instantaneous speed, thickness, or particular velocity profiles, are practically unpredictable, and one can only hope to gain an impression on the general structure of the exchange, and register some particular/instant flow patterns. The most extensive field studies of seasonal cascading (Horsch and Stefan, 1988;Farrow and Patterson, 1993;Sturman et al, 1999;Fer et al, 2002;Chubarenko and Demchenko, 2010) point exactly at the intermittent character of the flow, and the truly convective (irregularly changing) behaviour of the water-exchange pattern.…”

“…In this paper, we discuss some features of horizontal water exchange between shallow and deeper areas, arising in a day/night circle, owing to an alternative formation of differential coastal cooling and 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).…”

On contribution of horizontal and intra-layer convection to the formation of the Baltic Sea cold intermediate layer

“…The slugs moving down-slope are colder, than overlying waters, and of almost the same salinity (in deep areas sometimes just a few hundredth less). The thickness of the down-flow is variable (see upper panel of , and less than 0.43 d, predicted by numerical modelling of Horsh and Stefan (1988) for laboratory conditions.…”

“…Numerical and laboratory experiments (Horsh and Stefan, 1988) showed, that in a "quasi-steady state" the circulation flow-rate Q is proportional to Ra 1/n F , where 2<n<3; i.e., taking local depth d as the length scale, the flow-rate increases with the depth of the domain, Q∼d 1.33 ÷d 2 . The thickness of the underflow h is shown to be proportional to the local depth as well: h =0.43 d (numerical result of Horsh and Stefan, 1988).…”

“…The thickness of the underflow h is shown to be proportional to the local depth as well: h =0.43 d (numerical result of Horsh and Stefan, 1988). Sturman et al (1999) have complied results from numerical, laboratory and field (in lakes and side-arms) studies to obtain the expression…”