Sk Zeeshan Ali

Hydrodynamics of sediment threshold

A novel hydrodynamic model for the threshold of cohesionless sediment particle motion under a steady unidirectional streamflow is presented. The hydrodynamic forces (drag and lift) acting on a solitary sediment particle resting over a closely packed bed formed by the identical sediment particles are the primary motivating forces. The drag force comprises of the form drag and form induced drag. The lift force includes the Saffman lift, Magnus lift, centrifugal lift, and turbulent lift. The points of action of the force system are appropriately obtained, for the first time, from the basics of micro-mechanics. The sediment threshold is envisioned as the rolling mode, which is the plausible mode to initiate a particle motion on the bed. The moment balance of the force system on the solitary particle about the pivoting point of rolling yields the governing equation. The conditions of sediment threshold under the hydraulically smooth, transitional, and rough flow regimes are examined. The effects of velocity fluctuations are addressed by applying the statistical theory of turbulence. This study shows that for a hindrance coefficient of 0.3, the threshold curve (threshold Shields parameter versus shear Reynolds number) has an excellent agreement with the experimental data of uniform sediments. However, most of the experimental data are bounded by the upper and lower limiting threshold curves, corresponding to the hindrance coefficients of 0.2 and 0.4, respectively. The threshold curve of this study is compared with those of previous researchers. The present model also agrees satisfactorily with the experimental data of nonuniform sediments.

Origin of the scaling laws of sediment transport

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 + σ)/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 + σ)/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 + σ)/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘−Z’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 − σ)’, ‘−4/(3 − σ)’ and ‘−(1 + σ)/(3 − σ)’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

Mechanics of advection of suspended particles in turbulent flow

In this paper, we explore the mechanics and the turbulent structure of two-phase (fluid–solid particle) flow system, for the first time, by considering the dynamic equilibrium coupled with suspended solid particle concentration, fluid flow and energetics of the two-phase flow system. The continuity, momentum and turbulent kinetic energy (TKE) equations of the fluid and the solid phases are treated separately to derive a generalized relationship of the two-phase flow system aided by suitable closure relationships. The results obtained from the numerical solution of resulting equations show that the particle concentration and the TKE diminish with an increase in the Rouse number, while the horizontal velocity component increases. On the other hand, the TKE flux, diffusion and production rates increase with an increase in the Rouse number, while the TKE dissipation rate decreases. In the vicinity of the reference level (that is, the hypothetical level from which the particles come in suspension), the Kolmogorov number increases with an increase in the Rouse number. However, as the vertical distance increases, this behaviour becomes reverse. A close observation of the turbulent length scales reveals that the Prandtls mixing length decreases with an increase in the Rouse number, but the Taylor microscale and the Kolmogorov length scale increase.

Stochastic mechanics of loose boundary particle transport in turbulent flow

In a turbulent wall shear flow, we explore, for the first time, the stochastic mechanics of loose boundary particle transport, having variable particle protrusions due to various cohesionless particle packing densities. The mean transport probabilities in contact and detachment modes are obtained. The mean transport probabilities in these modes as a function of Shields number (nondimensional fluid induced shear stress at the boundary) for different relative particle sizes (ratio of boundary roughness height to target particle diameter) and shear Reynolds numbers (ratio of fluid inertia to viscous damping) are presented. The transport probability in contact mode increases with an increase in Shields number attaining a peak and then decreases, while that in detachment mode increases monotonically. For the hydraulically transitional and rough flow regimes, the transport probability curves in contact mode for a given relative particle size of greater than or equal to unity attain their peaks corresponding to ...

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.

Hydrodynamics of submerged turbulent plane offset jets

The results of an experimental study on the turbulent flow characteristics in submerged plane offset jets are presented. The vertical profiles of time-averaged velocity components and Reynolds stresses at different horizontal locations are depicted to illustrate their variations across the pre-attachment, impingement, and wall jet regions. The characteristic lengths and the jet profile of submerged offset jets in the pre-attachment region are determined from the velocity profiles. The regional profiles of velocity and Reynolds stresses are analyzed in the context of the self-similarity, the decay of their representative scales, and the development of the length scales. The self-similarity characteristics in the pre-attachment and wall jet regions are preserved better than those in the impingement region. The turbulent kinetic energy (TKE) fluxes suggest that within the jet layer in the pre-attachment region, an upward advection of low-speed fluid streaks induces a strong retardation to the jet; while in t...

Theory of Turbulent Flow over a Wavy Boundary

AbstractA new mathematical framework of the steady unseparated turbulent flow over a wavy (sinusoidal) boundary is derived by treating the Reynolds averaged Navier-Stokes (RANS) equations. Theoretical formulations for the flow profile, boundary shear stress and Reynolds shear stress distributions are obtained assuming a power law of streamwise velocity and accounting for the effects of curvilinear streamlines induced by the wavy boundary. The flow profiles, and distributions of boundary shear stress and Reynolds shear stress are computed for different flow parameters and presented in graphical forms. In subcritical flow, the flow profile is out of phase with the wavy boundary; while the boundary shear stress distribution is almost in phase with the wavy boundary. Instead, the flow profile and the boundary shear stress distribution in supercritical flow are opposite to those in subcritical flow. Upstream of the crest of wavy boundary the vertical distribution of the Reynolds shear stress is characterized b...

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...

Mechanics of Sediment Transport: Particle Scale of Entrainment to Continuum Scale of Bedload Flux

AbstractA mechanistic-cum-stochastic theory describing the sediment transport phenomenon from the particle scale of entrainment to the continuum scale of bedload flux under a steady unidirectional ...