This work constitutes the second part of an investigation into the mechanical mechanism of laminar-turbulent transition in pipe Poiseuille flow, a canonical wall-bounded-flow problem in turbulence-research. Conventional hydrodynamic-stability studies mainly focus on disturbance effects while paying relatively little attention to the intrinsic mechanical properties of flow structures. In the present study, the tensile-energy-flux vector (renamed from the viscous-energy-flux vector in earlier work) and its divergence are theoretically derived and analyzed for pipe Poiseuille flow. The tensile-energy-flux vector vanishes both at the pipe wall and at the centerline of the pipe. Its divergence equals zero at the radial position 0.707R. Once the tensile force flow reaches its critical threshold value, this base-flow feature identifies 0.707R as a candidate radial location with enhanced susceptibility to localized laminar-turbulent transition. The combination of the critical-tensile-force-flow criterion and the critical-tensile-energy-flux criterion introduces a new critical-tensile-flux criterion. This predicted position lies within the radial oscillation range reported in published transition experiments. When the membrane theory for spherical shells is applied to the virtual fluid-shell element, this critical candidate position corresponds to a zenith angle of 45°. This angle bears a heuristic geometric analogy to the crack orientation observed in uniaxial-compression tests on rock specimens; nevertheless, the physical mechanisms governing solid fracture and hydrodynamic transition are fundamentally different. This paper further demonstrates that the critical-Reynolds-number criterion for pipe-flow laminar-turbulent transition is not an absolute universal constant. Under the working hypothesis that the critical-tensile-flux criterion behaves like a fluid-related property parameter, the ratio between critical tensile energy flux and cross-section-averaged kinetic energy flux exhibits an inverse-Reynolds-number scaling, reminiscent of the well-known inverse relationship between the laminar pipe-friction coefficient and Reynolds number.
Early turbulence in dilute polymer-solution pipe flows and full-chord laminar flow on suction-controlled wings at Reynolds numbers (Re) up to 2,000,000 evidently markedly deviate from the conventional pipe-flow transition criterion with a critical Re of 2000–2300. Inspired by the spherical-shell membrane-force theory from structural mechanics, this work develops a force-balance model employing a virtual constant-thickness spherical fluid shell to interpret these anomalous laminar-turbulent transition behaviors. For low-Reynolds-number laminar pipe flow, the curvature radius of the virtual fluid layer varies inversely with the pressure gradient. Laminar-to-turbulent transition is hypothesized to take place when the shell curvature radius becomes smaller than the physical pipe radius. This condition defines a candidate critical tensile-force-flow threshold, expressed as twice the product of the fluid viscosity and the maximum pipe velocity, divided by the pipe radius. In general, in laminar pipe flow, the wall shear stress represents the flow-direction component of the tensile force flow. At this hypothesized transition threshold, wall shear stress numerically equals the critical-tensile-force-flow value, which yields qualitative consistency with documented early-turbulence observations. Furthermore, the proposed critical-tensile-force-flow concept offers a physical interpretation for high-Reynolds-number laminar pipe flow stabilized by wall suction. For suction-stabilized laminar pipes, the actual physical pipe may be conceptualized as a subsection of a larger hypothetical, virtual pipe that reaches the critical-tensile-force-flow condition. The real-wall shear stress is attenuated by a factor related to the ratio between the average velocity in the actual physical pipe and its center-line maximum velocity. We emphasize that this threshold is treated as a Newtonian hydrodynamic baseline rather than a universal intrinsic fluid-material property; further well-controlled experimental validation is required to test its general applicability.
The Kayanga-Anambé watershed, located in Haute-Casamance (Senegal), is a strategic area for national food security, yet remains exposed to recurrent flooding that threatens hydro-agricultural developments. This study aims to map flood-susceptibility zones using an integrated approach combining Geographic Information Systems (GIS) with a multi-criteria model built on seven (7) parameters: Flow Accumulation, Rainfall Intensity, Land Use, Geology, Slope, Terrain Elevation, and Distance to drainage (FIGUSED). The methodology relies essentially on cross-referencing morphometric factors (slope, drainage density), climatic factors (rainfall intensity), and anthropogenic factors (land use, infrastructure). Data derived from digital elevation models and Sentinel-2 imagery were processed through an Analytic Hierarchy Process (AHP) to weight the influence of each parameter. The results highlight a strong susceptibility of the Anambé basin, exacerbated by gentle slopes and the rapid saturation of hydromorphic soils during monsoon peaks. The high-susceptibility zone (high and very high classes) totals 40.64% of the watershed area, that is 1257.46 km2, corresponding geographically to the Anambé basin and the floodplain of the Kayanga and its tributaries. The most represented class is high susceptibility, at nearly 28%, closely followed by moderate susceptibility at 25.52% of the total area, indicating an overall heightened susceptibility of the watershed to inundation. The resulting susceptibility map thus constitutes an essential decision-support tool for planning agricultural campaigns through SODAGRI and for protecting human settlements in tropical rural areas.
