Testing the complexity and chaotic nature of wave-dominated turbulent flows

This study employs chaos theory concepts to investigate the complexity and chaotic nature of surface-generated waves in comparison to steady-flow state. The flows are generated through laboratory-flume experiments. Two separate tests are carried out: steady-flow test; and test with the addition of waves to the steady-flow under identical flow conditions. For wave addition, two-different frequencies of wave (i.e., 1.1 Hz and 2.1 Hz) are considered. Two chaos theory-based approaches are employed to determine the complexity and chaotic nature of wave-current dynamics: False nearest neighbour (FNN) method; and Lyapunov exponent method. An effort is also made to confirm and understand the results from these chaos-theory methods with the results from the wavelet and Shannon entropy methods. The results from the chaos-theory methods suggest optimistic evidence of the presence of chaotic behaviour in the combined wave-current cases. The results show that greater complexity is found at the near-bed region with aperiodic nature of the eddy scales and the complexity becomes less when moving towards the near-surface region. These results are well supported by the tests with wavelet and Shannon entropy methods. The results further reveal that the complexity for the steady-flow case is high and the complexity decreases with the addition of waves.