Transitional regimes of penetrative convection in a plane layer

Abstract

Hydrodynamical regimes are described for penetrative convection in a twodimensional bounded plane layer of water at the temperature range close to the point of maximum density. Stress-free conditions on the horizontal and vertical boundaries of the domain are assumed. The point of maximum density is supposed to be located in the middle plane of the layer in conductive state. Steady and time-periodic solutions are found on large horizontal scales and the lengths of a spatial periodicity inside the layer are determined. Hydrodynamical peculiarities of time-periodic solution are described. In the domain equal to the periodicity cell corresponding to time-periodic solution, the sequence of hydrodynamical regimes with the increase of supercriticality is analyzed and the full sequence of bifurcations from conductive state to chaotic motion is described. The time-periodic solution loses the stability through the subcritical Neimark-Sacker bifurcation. First, the closed invariant curve has one stable period-2 cycle, so the bifurcation looks like period doubling. With a further increase of supercriticality the period-2 cycle transforms to a torus through the saddle-node bifurcation for maps. Then, loss of stability of quasiperiodic motion occurs through intermittency and chaotic mixing on the background of quasiperiodic solution. The window of quasiperiodicity was obtained in the interval of supercriticality corresponding to intermittent regimes, after which intermittency on the background of another quasiperiodic mode appears.

Penetrative convection of water in cavities cooled from below

“…Besides the papers related to infinite horizontal layers with either stress-free or rigid top and bottom boundaries [1][2][3][4][5][6], the studies carried out on penetrative convection of water near its density-inversion point in cavities laterally confined by solid walls, which can be of interest for cooling thermal energy storage applications, are relatively few. The first of them was performed experimentally by Townsend [7] who used a tank having an ice-covered square bottom of 30 cm × 30 cm, filled with distilled water to a depth of 15 cm, whose upper surface was maintained at about 25°C.…”

Correlations for Transient Thermal Convection of Water Near Its Density-Inversion Point in a Square Enclosure Heated From Below

“…Besides the studies executed on infinite horizontal layers considering either stress-free or rigid horizontal boundaries [1][2][3][4][5][6], the papers readily available in the open literature on thermal convection in enclosures filled with water near its density-inversion point are relatively few. Townsend [7] executed an experimental study using a tank whose bottom and top surfaces were kept at 0°C and 25°C, respectively.…”