Subhasish Dey

Impact of phenomenological theory of turbulence on pragmatic approach to fluvial hydraulics

The phenomenological theory of turbulence (PTT) remains a long-standing and fascinating theory in turbulence research. In this review article, we highlight the state-of-the-science of the impact of the PTT on the pragmatic approach to fluvial hydraulics, explored over recent decades, discussing the salient and the subtle roles that the turbulence plays in governing many physical processes. To acquire a theoretical explanation of this pragmatic approach necessitates an intuitive thought that can bring together the background mechanisms of all the physical processes under one law—a thought that is capable of finding their inextricable links with the turbulent energy spectrum. We begin here with emphasizing the spectral and the co-spectral origin of the well-recognized laws of the wall, the resistance equation, and the turbulence intensities by portraying the typical momentum transfer mechanism of eddies in a turbulent flow. Next, we focus on the scaling laws of key fluvial processes derived from the perspective of the PTT, enlightening their physical insight and ability to judge how far the so-called empirical formulas can be used with confidence. The PTT has been able to disclose the origin of several primeval empirical formulas that have been used over many years without having any theoretical clarification and confirmation. Finally, we make an effort to describe some unsolved issues to be resolved as a future scope of research.The phenomenological theory of turbulence (PTT) remains a long-standing and fascinating theory in turbulence research. In this review article, we highlight the state-of-the-science of the impact of the PTT on the pragmatic approach to fluvial hydraulics, explored over recent decades, discussing the salient and the subtle roles that the turbulence plays in governing many physical processes. To acquire a theoretical explanation of this pragmatic approach necessitates an intuitive thought that can bring together the background mechanisms of all the physical processes under one law—a thought that is capable of finding their inextricable links with the turbulent energy spectrum. We begin here with emphasizing the spectral and the co-spectral origin of the well-recognized laws of the wall, the resistance equation, and the turbulence intensities by portraying the typical momentum transfer mechanism of eddies in a turbulent flow. Next, we focus on the scaling laws of key fluvial processes derived from the perspec...

Origin of the onset of meandering of a straight river

In this paper, to explore the origin of the onset of meandering of a straight river, we, first, analyse the linear stability of a straight river. We discover that the natural perturbation modes of a straight river maintain an equilibrium state by confining themselves to an onset wavenumber band that is dependent on the flow regimes, aspect ratio, relative roughness number and Shields number. Then, we put forward a phenomenological description of the onset of meandering of a straight river. Its mechanism is governed by turbulent flow, with counter-rotation of neighbouring large-scale or macro-turbulent eddies in succession to generate the processes of alternating erosion and deposition of sediment grains of the riverbed. This concept is explained by a theorem (universal scaling law) stemming from the phenomenology of a turbulent energy cascade to provide a quantitative insight into the criterion for the onset of meandering of a straight river. It is revealed from this universal scaling law that, at the onset of meandering of a river, the longitudinal riverbed slope is a unique function of the river width, flow discharge and sediment grain size. This unique functional relationship is corroborated by the data obtained from the measurements in natural and model rivers.

Review Article: Advances in modeling of bed particle entrainment sheared by turbulent flow

Bed particle entrainment by turbulent wall-shear flow is a key topic of interest in hydrodynamics because it plays a major role to govern the planetary morphodynamics. In this paper, the state-of-the-art review of the essential mechanisms governing the bed particle entrainment by turbulent wall-shear flow and their mathematical modeling is presented. The paper starts with the appraisal of the earlier multifaceted ideas in modeling the particle entrainment highlighting the rolling, sliding, and lifting modes of entrainment. Then, various modeling approaches of bed particle entrainment, such as deterministic, stochastic, and spatiotemporal approaches, are critically analyzed. The modeling criteria of particle entrainment are distinguished for hydraulically smooth, transitional, and rough flow regimes. In this context, the responses of particle size, particle exposure, and packing condition to the near-bed turbulent flow that shears the particles to entrain are discussed. From the modern experimental outcome...

Turbulence characteristics in wall-wake flows downstream of wall-mounted and near-wall horizontal cylinders

Turbulent characteristics in wall-wake flows downstream of wall-mounted and near-wall cylinders are investigated. The distributions of the defect of streamwise velocity, Reynolds shear stress and turbulence intensities exhibit a certain degree of self-preserving characteristic when they are scaled by their respective peak defect values. For the velocity defect distributions, the vertical distances are scaled by the half-width of peak defect velocity. However, for the distributions of the defects of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the half-width of Reynolds shear stress defect. The peak defects of all the quantities reduce with longitudinal distance signifying the recovery of the upstream distributions of the individual quantities. The third-order correlations reveal that for the wall-mounted cylinder, a streamwise acceleration associated with a downward flux of streamwise Reynolds normal stress (SRNS) in the inner-layer of wall-wake composes sweeps and a streamwise deceleration associated with an upward flux of SRNS in the outer-layer forms ejections. On the other hand, for the near-wall cylinder, a streamwise deceleration associated with a downward flux of SRNS in the inner-layer of wall-wake flow and the gap flow produces the inward interaction events, while the outer-layer characteristic is similar to that of wall-mounted cylinder. The turbulent kinetic energy (TKE) budget in the wake flow demonstrates strong negative pressure energy diffusion in addition to a strong TKE dissipation and diffusion and that in the gap flow exhibits a minor positive peak of pressure energy diffusion and a minor negative peak of TKE diffusion.

Splitter plate as a flow-altering pier scour countermeasure

Results of an experimental study on the countermeasure of scour depth at circular piers are presented. Experiments were conducted for pier scour with and without a splitter plate under a steady, uniform clear-water flow condition. The results of pier scour without splitter plate were used as a reference. Different combinations of lengths and thicknesses of splitter plates were tested attaching each of them to a pier at the upstream vertical plane of symmetry. Two different median sediment sizes (d50xa0=xa00.96 and 1.8xa0mm) were considered as bed sediment. The experimental results show that the scour depth consistently decreases with an increase in splitter plate length, while the scour depth remains independent of splitter plate thickness. In addition, temporal evolution of scour depth at piers with and without a splitter plate is observed. The best combination is found to be with a splitter plate thickness of b/5 and a length of 2b. Here, b denotes the pier diameter. An empirical formula for the estimation of equilibrium scour depth at piers with splitter plates is obtained from a multiple linear regression analysis of the experimental data. The flow fields for various combinations of circular piers with and without splitter plate including plain bed and equilibrium scour conditions were measured by using an acoustic Doppler velocimeter. The turbulent flow fields for various configurations are investigated by plotting the velocity vectors and the turbulent kinetic energy contours on vertical and horizontal planes. The splitter plate attached to the pier deflects the approach flow and thus weakens the strength of the downflow and the horseshoe vortex, being instrumental in reducing the equilibrium scour depth at piers. The proposed method of pier scour countermeasure is easy to install and cost effective as well.

Hydrodynamics of sediment transport: grain scale to continuum scale

A theory of sediment transport, describing the entrainment phenomenon from the grain scale to the continuum scale, under a steady-uniform flow over a sediment bed is presented. The sediment grains, assumed as discrete spherical grains, are subjected to turbulent wall-shear flows. At the grain scale, the forces acting on a sediment grain resting over three compact spherical grains are analysed to determine the criteria for entrainment threshold in rolling, sliding and lifting modes taking into account the turbulence effects. Comparison of the theoretical results with the experimental data shows that the entrainment threshold lies within the sliding and lifting modes. Then, at the grain scale, using the log-normal probability density function for the near-bed instantaneous horizontal velocity, the entrainment probabilities in rolling, sliding and lifting modes for a given grain size are derived. The rolling and sliding probabilities increase with an increase in Shields function and after attaining their individual maximum values, they reduce, whereas the lifting probability increases with Shields function. The maximum value of entrainment probability in rolling mode is close to the threshold Shields function in rough flow, whereas the entrainment probability in lifting mode initiates from the value of the threshold Shields function. In a continuum scale, the bedload flux is derived by hypothesising the saltating mode of sediment transport incorporating the lifting probability obtained at the grain scale.