Fractal assessment of time series of density currents in flume

Density currents formed due to the difference in density, however small, with the surrounding fluid. In addition, even if this density difference exists in the layers of a fluid, this type of flow formed. These currents are a type of two-phase currents that have special and different characteristics compared to normal single-phase currents. Hydrological and hydraulic phenomena known as chaotic, non-linear, dependent and sensitive systems to the change of the initial conditions and the temporal and spatial scale of the study. For this reason, any processing of hydrological time series has a direct effect on the chaotic behavior and the way the system responds to hydrological models and network forecasting.

The experiments carried out in the hydraulic department of Shiraz University and a flume of 8 m length, 35 cm width and 60 cm height used. Flume has the ability to tilt. A source of 1000 liters containing thick sediment flow used. A number of 12 experiments conducted in such a way that the powder of passing rock classified from sieve No. 80 used as suspended sediment material to create a dense flow, which has a specific weight of 2650 kgm-3 and an average settling speed of 0.0106 mms-1 and an average diameter of particles. It is 0.0074 mm. The density of water is 998.7 kgm-3. Three channel slopes of 1, 2, and 3 percent and two density current inlet flow rates of 50 liters per minute and 90 liters per minute used. The density of the thick flow tank is 1005 kgm-3 and 1008 kgm-3, and the height opening under the sliding inlet valve is 1 cm. Fractal dimension is a decimal number that fractal objects are something between Euclidean and topological shapes. A fractal curve is a curve with an infinite self-similar component. This analysis based on the box counting method, which is a smart and simple method to implement. The fractal dimension obtained by calculating the number of non-overlapping boxes with the size required to cover the fractal curve.

A general study of fractal indices such as scale factor diagrams, generalized fractal dimension and singularity spectrum shown in Figure 5 for the time series of dense flow velocity in all models at a distance of m5 from the inlet valve. The highest fractal dimension with a rate of 1.459 related to test number 5 and the lowest fractal dimension related to test number 7 with a rate of 1.22. The highest range of α corresponds to test number 3 with a rate of 3.04 and the lowest corresponds to test number 12 with a rate of 0.087. The lower this range is from the rate of 3.04, the more its multifractal degree decreases and the trend of the system is more towards single fractal patterns. When the inlet flow rate changes from 50 liters per minute to 90 liters per minute, the fractal dimension of the speed time series decreases by 2.2%, and the amplitude and angle α decrease by 53.5% and increase by 3.9%, respectively, and the tendency of the system With the increase of the input flow rate, it tends towards single fractal. Also, in the technical spectrum charts, with the increase of the input flow rate from 50 liters per minute to 90 liters per minute, the technical spectrum chart tends from full symmetry to right symmetry, in other words, with Increasing the flow rate, the exact fractal diagram that created from self-similar elements tends towards a single fractal, which is sensitive to small changes in the flow rate caused by increasing the flow rate of this factor.

The generalized fractal dimension decreases with increasing flow rate and flow concentration, and it shows that the phenomenon is less sensitive to high concentrations and flow rates, and the flow behavior is dependent on the initial conditions. When the input density changes from 1005 kgm-3 to 1008 kgm-3, the fractal dimension of the velocity time series decreases by 4.2% and the amplitude and angle α decrease by 9.7% and increase by 9.8%, respectively. The rotation reduced by 6.7% and the Dq changes reduced by 1.5% and its graph is milder.