This review paper addresses the structure of the mean flow and key turbulence quantities in free-surface flows with emergent vegetation. Emergent vegetation in open channel flow affects turbulence, flow patterns, flow resistance, sediment transport, and morphological changes. The last 15 years have witnessed significant advances in field, laboratory, and numerical investigations of turbulent flows within reaches of different types of emergent vegetation, such as rigid stems, flexible stems, with foliage or without foliage, and combinations of these. The influence of stem diameter, volume fraction, frontal area of stems, staggered and non-staggered arrangements of stems, and arrangement of stems in patches on mean flow and turbulence has been quantified in different research contexts using different instrumentation and numerical strategies. In this paper, a summary of key findings on emergent vegetation flows is offered, with particular emphasis on: (1) vertical structure of flow field, (2) velocity distribution, 2nd order moments, and distribution of turbulent kinetic energy (TKE) in horizontal plane, (3) horizontal structures which includes wake and shear flows and, (4) drag effect of emergent vegetation on the flow. It can be concluded that the drag coefficient of an emergent vegetation patch is proportional to the solid volume fraction and average drag of an individual vegetation stem is a linear function of the stem Reynolds number. The distribution of TKE in a horizontal plane demonstrates that the production of TKE is mostly associated with vortex shedding from individual stems. Production and dissipation of TKE are not in equilibrium, resulting in strong fluxes of TKE directed outward the near wake of each stem. In addition to Kelvin–Helmholtz and von Kármán vortices, the ejections and sweeps have profound influence on sediment dynamics in the emergent vegetated flows.

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The coronavirus disease 2019 (COVID-19) pandemic is the most rapidly evolving global emergency since March 2020 and one of the most exercised topics in all aspects of the world. So far there are numerous articles that have been published related to COVID-19 in various disciplines of science and social context. Since from the very beginning, researchers have been trying to address some fundamental questions like how long it will sustain when it will reach the peak point of spreading, what will be the population of infections, cure, or death in the future. To address such issues researchers have been used several mathematical models from the very beginning around the world. The goal of such predictions is to take strategic control of the disease. In most of the cases, the predictions have deviated from the real data. In this paper, a mathematical model has been used which is not explored earlier in the COVID-19 predictions. The contribution of the work is to present a variant of the linear regression model is the piece-wise linear regression, which performs relatively better compared to the other existing models. In our study, the COVID-19 data set of several states of India has been used.

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The present study investigates the turbulent hydrodynamics in an open channel flow with an emergent and sparse vegetation patch placed in the middle of the channel. The dimensions of the rigid vegetation patch are 81 cm long and 24 cm wide and it is prepared by a 7× 10 array of uniform acrylic cylinders by maintaining 9 cm and 4 cm spacing between centers of two consecutive cylinders along streamwise and lateral directions respectively. From the leading edge of the patch, the observed nature of time averaged flow velocities along streamwise, lateral and vertical directions is not consistent up to half length of the patch; however the velocity profiles develop a uniform behavior after that length. In the interior of the patch, the magnitude of vertical normal stress is small in comparison to the magnitudes of streamwise and lateral normal stresses. The magnitude of Reynolds shear stress profiles decreases with increasing downstream length from the leading edge of the vegetation patch and the trend continues even in the wake region downstream of the trailing edge. The increased magnitude of turbulent kinetic energy profiles is noticed from leading edge up to a certain length inside the patch; however its value decreases with further increasing downstream distance. A new mathematical model is proposed to predict time averaged streamwise velocity inside the sparse vegetation patch and the proposed model shows good agreement with the experimental data.

To control the spread of COVID-19, around the world, many countries imposed lockdowns. Numerous studies were reported on COVID-19 in different disciplines with various aspects. The doubling time is a mathematical technique to estimate the current rate of spread of the disease. Researchers used the doubling technique to address the COVID-19 pandemic situation. The larger doubling period represents a low spreading rate, whereas the smaller doubling period represents a high spreading rate. In other words, high infection implies the low doubling period and low infection implies the high doubling period. So, there is an inverse relationship between doubling time and the infection rate. But the real-life data does not follow such a rule properly in various domains. The data shows that after a certain time when the infection is high, the doubling period is also high, which misleads our general concept of doubling time. This chapter addressed this issue by investigating the real-time COVID-19 data. To overcome this limitation, a gradient smoothing technique has been proposed.

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