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

Abstract

The behaviour of warm water discharge at a temperature \(T_{m}\) horizontally into a homogeneous body of cold fresh water at a temperature \(T=0\) was investigated by means of a numerical model through lock-exchange. Water density here was taken to be a quadratic function of temperature. 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. Such scenarios are evident in lakes, especially in holomictic lakes and warm discharge from thermoelectric power generating plants. Because the sudden increase in the water temperature after discharge will leads to "thermal shock" killing aquatic life that has become acclimatised to living in a stable temperate environment. The aim of this investigation is to better fathom and as well, gain more insight into such studies. Cabbeling process was key as whenever fluid of different temperature come in contact and as well as the development of Kelvin-Helmholtz instability in the interaction surface. The general behaviours here are dependent of lock volume, density difference and Reynolds number. We noticed that the collapsing velocity of the denser fluid within the first time frame was high, higher than every fluid movement elsewhere. Relations that describes the various regimes of flow were also drawn, and as well as those for the spreading distance \(L_{d c}\) of the density current. However, there are little variations in the scaling laws as compared to the earlier studied cases where density difference was by the means of salt water. But for those where density difference is as a result of temperature, we believe that these results are a good starting point to better fathom and as well, gain more insight into such studies. Lastly, the consideration of barrier position is key, being that the lock volume is also believed to be a factor. Researchers can also gain more knowledge in terms of the dynamics of such flows.

A Numerical Study of the behaviour on Lock Volume Variations in Lock-Exchange Density Current in Cold Fresh Water

“…Gravity current are natural behaviours that are frequently encountered in our environment and also in some man-made situations. These currents are likely to appear whenever a flow fluid with a particular density propagates into an ambient fluid with a different density, where the motion is required to be in the horizontal direction [1,2]. Density differences in such flows are as a result of changes in temperature, salinity or concentration of suspended particles [3].…”

“…In some cases, the water in such areas also contains more suspended sediment than the surrounding water. Thus, these currents are also known to be responsible for the transportation of sediments in reservoirs [ 2,3] . Gravity current can also be formed when the door of a heated room is opened for ventilation.…”

“…In this case, we can observed that cold air from outside flows into the room, displacing the less dense air on the floor inside. These currents can also be found in thunderstorm outflows, sea-breeze fronts, discharge of industrial waste water into rivers, lakes or oceans, volcanic clouds, etc., [1,2,3,21,22]. We can also view [4,5,6,7] for more examples of such flows.…”

“…Quite a number of literature has been given in this area of research and also examined theoretically, experimentally and numerically together with some mathematical relations and values that describes the propagation speed and spreading distance of such currents. Different regimes of flow are also identified that describe the flow behaviour [2,5,8,9]. Nevertheless, [10,11,12] have also considered density currents, using a simplified theoretical model that describes the evolution of the frontal head and a derivation of theoretical model for the initiation of a steady two-dimensional density current in a rectangular channel.…”

“…But then, in most of the configurations, the lockexchange method is used (see Fig. 1): as this enables such flow scenarios over the rough and smooth horizontal surfaces and as well as the inclined surfaces [2]. In such experimental cases, salt is mostly used to create the density difference in fresh water and example of such investigation with the lock-exchange configuration include [8, 9, 13 -18].…”