Numerical Simulations of the Cabbeling Phenomenon in Surface Gravity Currents in Cold Fresh Water

Abstract

The behaviour of warm water discharge at a temperature higher then Tm horizontally into a homogeneous body of cold fresh water at a temperature lower then Tm was investigated by means of a numerical model. Water density here was taken to be a quadratic function of temperature. Thus cabbeling process was inevitable as positively buoyant water form surface current while penetrating the ambient water. The current halted as mixture became dense and sink. These results are very similar to the experimental study of warm discharge into cold water by Marmoush et al. [14] and Bukreev [22]. The results showed an initially sinking water at the point where the two water bodies meets within the first few time interval. Development of Rayleigh-Taylor instabilities was observed at the lower part of the surface current as lighter fluid penetrate further. The frontal head was found to being replenished by a surface flow of warm unadulterated water, but after much entrainment of ambient fluid and cabbeling then, this head halted and sink. On the floor, denser fluid advance in the same direction as the original surface current, with some degree of Kelvin-Helmholtz instability as it penetrates further. Relations were also drawn that describes the speed, the spread length of both surface current were obtained.
 Relation were also drawn that describes the final spread length of the surface current Lsm and the time taken to reach that final spread length Tsm as a function ϕin. This work as presented here is practical and relevant to many fields of study and also enhances policy making towards the protection of the aquatic ecosystems.

Density Current Simulations In Cold Fresh Water And Its Cabbeling phenomenon: A Comparative Analysis With Given Experimental Results

“…This also resulted in a very slow fluid motion being that the temperature of the denser fluid at this point had reduced drastically, so was not energetic enough to accelerate faster. The third phase is the phase where viscous effects overcome inertial effects and the current front velocity decreases more rapidly as t − 4 5 as also cited in [2]. In this present study, our result show a stepwise movement.…”

“…Density currents are a phenomenal behaviours that occur in many practical applications both in nature and man-made situations, and examples of such scenarios are given in [1,2,3,4] . These currents (flows) are mainly driven by difference in density between the flow fluid and the ambient fluid.…”

“…Researchers have also extensively studied these behaviours experimentally, theoretically and numeri-cally and have given some mathematical relations and values that describes the propagation speed and spreading distance of such currents and as well as identifying different regimes of flow [2,6,7]. However, earlier works on density currents can be found in [8,9,10].…”

“…Such scenarios are also evident in lakes, especially in holomictic lakes and warm discharge from thermoelectric power generating plants. We can see [2,7,16,17] for more insights and a more detailed literature review in other to minimise repetition. However, density currents flows through lockexchange whereby density variation is as a result of temperature difference had not received much attention as compared to that with saltwater that is widely used [6].…”

“…Recently, we have also considered a "Numerical Simulations of the Cabbeling phenomenon in Surface Gravity Currents in Cold Fresh Water" where we have extensively discussed the behaviour of such flows taken density as a quadratic function of temperature. Relations were also drawn that describes the propagation speed of the frontal head and as well as the distance traveled with respect to time [2]. The behaviour of the negatively buoyant plume as mixed fluid that have mixed up to the Tm was also key.…”