Space fractional kinetic model for different types of suspension profiles in turbulent flows with a neural network-based estimation of fractional orders

A unified model of suspension concentration distribution in sediment mixed turbulent flows using generalized fractional advection-diffusion equation

“…Earlier, it is assumed that the jump of particles during turbulent motion is restricted to representative elementary volume (REV); whereas the findings of Chen et al (2013) from the time series data of the instantaneous Reynolds shear stress of Noguchi and Nezu (2009) show many remarkable extreme events that are related to the fact that particle jumps occur beyond the REV limits which are referred as non-local mixing. Chen et al (2013), Kundu (2018a)and Kundu and Sinha (2021) used space fractional ADE (FADE) to study the sediment distribution as the nonlocal movement of sediment particles during the flow and their results show that space fractional models (FADE) provide better estimation than the traditional ADE. Recently, Kundu and Sinha (2021) showed that using the space fractional kinetic model with the help of Riemann-Liouville fractional integral, different patterns (type-I and type-II) of suspension distribution can be obtained.…”

“…Chen et al (2013), Kundu (2018a)and Kundu and Sinha (2021) used space fractional ADE (FADE) to study the sediment distribution as the nonlocal movement of sediment particles during the flow and their results show that space fractional models (FADE) provide better estimation than the traditional ADE. Recently, Kundu and Sinha (2021) showed that using the space fractional kinetic model with the help of Riemann-Liouville fractional integral, different patterns (type-I and type-II) of suspension distribution can be obtained. It is to note here that several experimental observations (Hung et al 1980, Bouvard and Petkovic 1985, Wang and Ni 1990 showed that apart from the type-I profile, the type-II profile of concentration distribution also exists.…”

“…In natural revers, near the bed, the transportation mechanism is complex and affected by near bed velocity, turbulence characteristics and therefore modeling such behavior is thus more crucial and challenging for river engineers (Pu et al 2017, Padhi et al 2019, Pu 2021). Most of the aforementioned studies can predict the Type-I profiles only; whereas models of Wang and Ni (1990), Jacobson and Testik (2013)and Kundu and Sinha (2021) are applicable for both types of suspension distribution. Though several models have been proposed, the findings of Kundu and Sinha (2021) indicate that still a generalized fractional model can be achieved by generalizing the fractional differential operator in FADE.…”

“…Most of the aforementioned studies can predict the Type-I profiles only; whereas models of Wang and Ni (1990), Jacobson and Testik (2013)and Kundu and Sinha (2021) are applicable for both types of suspension distribution. Though several models have been proposed, the findings of Kundu and Sinha (2021) indicate that still a generalized fractional model can be achieved by generalizing the fractional differential operator in FADE. These aforementioned studies show that studying the behavior of turbulence using the non-local mixing theory is more appropriate than the traditional simple diffusion theory.…”

“…Several studies reported the application of FADE in turbulent flow to investigate the suspension concentration distribution (Chen et al 2013, Nie et al 2017, Kundu 2018a, 2018b, 2019a, 2019b, Kundu and Sinha 2021. Among them Nie et al (2017) investigated seven concentration distribution model including one fADE model of Chen et al (2013).…”