Theory of free surface flow over rough seeping beds

A new theory is developed for the steady free surface flow over a horizontal rough bed with uniform upward seepage normal to the bed. The theory is based on the Reynolds averaged Navier-Stokes (RANS) equations applied to the flow domain that is divided into a fully turbulent outer layer and an inner layer (viscous sublayer plus buffer layer), which is a transition zone from viscous to turbulent regime. In the outer layer, the Reynolds stress far exceeds viscous shear stress, varying gradually with vertical distance. Near the free surface, the velocity gradient in vertical direction becomes lesser giving rise to wake flow. On the other hand, in the composite inner layer close to the bed, the viscous shear stress exists together with the turbulent stress. Thus, for the outer layer, a logarithmic law having modified coefficients from the traditional logarithmic law is obtained for the streamwise velocity, whereas for the inner layer, a fifth-degree polynomial including effective height of protrusions holds. The exact velocity expressions for inner and outer layer, which contain principal terms in addition to infinitesimally small terms, are in agreement with the experimental data obtained from laboratory measurements through an acoustic Doppler velocimeter. The experiments were run on two conditions of no seepage and a low upward seepage. Expressions for the Reynolds stress are also derived and computed for validation by the experimental data

A Reynolds Averaged Theory of Turbulent Shear Flows over Stable Sinusoidal Beds and Formation of Sand Waves

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Turbulence in mobile-bed streams

This study is devoted to quantify the near-bed turbulence parameters in mobile-bed flows with bed-load transport. A reduction in near-bed velocity fluctuations due to the decrease of flow velocity relative to particle velocity of the transporting particles results in an excessive near-bed damping in Reynolds shear stress (RSS) distributions. The bed particles are associated with the momentum provided from the flow to maintain their motion overcoming the bed resistance. It leads to a reduction in RSS magnitude over the entire flow depth. In the logarithmic law, the von Kármán coefficient decreases in presence of bed-load transport. The turbulent kinetic energy budget reveals that for the bed-load transport, the pressure energy diffusion rate near the bed changes sharply to a negative magnitude, implying a gain in turbulence production. According to the quadrant analysis, sweep events in mobile-bed flows are the principal mechanism of bed-load transport. The universal probability density functions for turbulence parameters given by Bose and Dey have been successfully applied in mobile-bed flows

Plant-Derived SAC domain of PAR-4 (Prostate Apoptosis Response 4) Exhibits Growth Inhibitory Effects in Prostate Cancer Cells

The gene Par-4 (Prostate Apoptosis Response 4) was originally identified in prostate cancer cells undergoing apoptosis and its product Par-4 showed cancer specific pro-apoptotic activity. Particularly, the SAC domain of Par-4 (SAC-Par-4) selectively kills cancer cells leaving normal cells unaffected. The therapeutic significance of bioactive SAC-Par-4 is enormous in cancer biology; however, its large scale production is still a matter of concern. Here we report the production of SAC-Par-4-GFP fusion protein coupled to translational enhancer sequence (5′ AMV) and apoplast signal peptide (aTP) in transgenic Nicotiana tabacum cv. Samsun NN plants under the control of a unique recombinant promoter M24. Transgene integration was confirmed by genomic DNA PCR, Southern and Northern blotting, Real-time PCR, and Nuclear run-on assays. Results of Western blot analysis and ELISA confirmed expression of recombinant SAC-Par-4-GFP protein and it was as high as 0.15% of total soluble protein. In addition, we found that targeting of plant recombinant SAC-Par-4-GFP to the apoplast and endoplasmic reticulum (ER) was essential for the stability of plant recombinant protein in comparison to the bacterial derived SAC-Par-4. Deglycosylation analysis demonstrated that ER-targeted SAC-Par-4-GFP-SEKDEL undergoes O-linked glycosylation unlike apoplast-targeted SAC-Par-4-GFP. Furthermore, various in vitro studies like mammalian cells proliferation assay (MTT), apoptosis induction assays, and NF-κB suppression suggested the cytotoxic and apoptotic properties of plant-derived SAC-Par-4-GFP against multiple prostate cancer cell lines. Additionally, pre-treatment of MAT-LyLu prostate cancer cells with purified SAC-Par-4-GFP significantly delayed the onset of tumor in a syngeneic rat prostate cancer model. Taken altogether, we proclaim that plant made SAC-Par-4 may become a useful alternate therapy for effectively alleviating cancer in the new era

Turbulent unsteady flow profiles over an adverse slope

When an unsteady free surface flow encounters an adverse slope, it results in a decelerating flow up the adverse slope. The time dependent turbulent flow is treated here by appropriately reducing the two-dimensional Reynolds averaged Navier-Stokes equation along with the equation of continuity considering turbulence closure. With suitable choice of parameters, the resulting differential equations are numerically solved to compute free surface and streamwise velocity profiles with time. It is found that initially the advancing free surface is convex upwards for a short time, followed by a jump of the free surface with a negative streamwise velocity that is a backwater rolling breaker due to deceleration of flow. At later time, however, the velocity becomes positive, that is, the breakers roll forward. This dual feature of motion, that is a surge followed by rolling breakers, is repeated for sometime before the jumps stop. The theoretical analysis presented here is motivated by tidal bores propagating upstream in an estuarine river

Universal probability distributions of turbulence in open channel flows

Universal probability density functions (PDFs) of two-dimensional turbulent velocity fluctuations, Reynolds shear stress and conditional Reynolds shear stresses in flows over smooth and rough beds are obtained using a Gram-Charlier series expansion based on the exponential distribution. To include skewness and kurtosis, the series is truncated up to moments of Order 4. The distributions of PDFs obtained theoretically and from the experimental data are in agreement. The conditional Reynolds shear stresses related to the ejections and sweeps are well represented by the exponential distribution, but those related to the outward and inward interactions depart from the theoretical distributions

Gravity waves on turbulent shear flow: Reynolds averaged approach

Gravity waves propagating over free-surface flows with shallow depth are well-known phenomena. The small-amplitude sinusoidal wave and Korteweg-de Vries (KdV) equations are based on potential-flow theory being widely used to describe water-wave propagation. The KdV equation leads to two basic flow patterns, as follows: (1) cnoidal waves, and (2) solitary waves. However, in case of a real Newtonian fluid, the bed resistance and the rapid motion of fluid generate turbulence (eddies) in the medium. The effects of turbulence are taken into account in this paper by using the equations for the surface elevation η and depth-averaged flow velocity U developed previously. These equations are based on the Reynolds-averaged Navier-Stokes (RANS) equations for turbulent flow in open channels. The wave profile can be approximated by a form a coskξ^/(1−b coskξ^), where a and b are constant amplitudes; k = wave number; ξ^ = dimensionless horizontal distance given by (x−ct)/h; x = horizontal distance; c = wave velocity; t = time; and h = undisturbed flow depth. Such a profile has the characteristic that the peaks are narrower but higher compared to wider but shallower troughs. The effects of streamflow on wave propagations are also considered. If the waves travel in the direction of the streamflow, there is a lengthening effect on the peaks and troughs, whereas if the waves travel against the direction of streamflow, they become shorter

Reynolds averaged theory of turbulent shear flows over undulating beds and formation of sand waves

Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation, a theory of turbulent shear flow over an undulating sand bed is developed addressing the instability criterion of plane sand beds in free-surface flows leading to the formation of sand waves. In the analysis, the integration of RANS equations leads to generalized Saint Venant equations, in which the time-averaged streamwise velocity is characterized by a power law obtained from turbulence closure, treating the curvilinear streamlines by the Boussinesq approximation. As a consequence, the modified pressure distribution has a departure from the traditionally linear hydrostatic pressure distribution. The instability analysis of a plane sand bed yields the curves of the Froude number versus nondimensional wave number, determining an instability zone for which at lower Froude numbers (less than 0.8), the plane bed becomes unstable with the formation of dunes; whereas at higher Froude numbers, the plane bed becomes unstable with the formation of standing waves and antidunes. For higher Froude numbers, the experimental data for antidunes lie within the unstable zone; while for lower Froude numbers, the same is found for dunes with some experimental scatter

Circular far-wake flow behind a sphere: solutions to the second-order

The theory of hydrodynamic phenomenon of the axisymmetric circular far-wake flow behind a sphere is revisited here by the generalized similarity solution of the governing momentum equations to obtain the solutions to the second - order in respect of the inverse distance from the sphere center. In case of a laminar wake, the nonlinear equation is derived from the Navier – Stokes equations; while in case of a turbulent wake, it is obtained from the Reynolds averaged Navier – Stokes equations and the eddy viscosity concept. The first - order Oseen - type linearization yields solutions well - known in the literature, but the second - order solutions obtained here are novel