The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Part I presents the statistical theory of turbulence, and Part 2 the coherent structures in open-channel flows and boundary layers. The book is intended for advanced students and researchers in hydraulic research, fluid mechanics, environmental sciences and related disciplines. References Index.

Turbulence in open-channel flows

Localized fluid flow measurements with an He-Ne laser spectrometer

Scale effects arise due to force ratios which are not identical between a model and its real-world prototype and result in deviations between the up-scaled model and prototype observations. This review article considers mechanical, Froude and Reynolds model–prototype similarities, describes scale effects for typical hydraulic flow phenomena and discusses how scale effects are avoided, compensated or corrected. Four approaches are addressed to obtain model–prototype similarity, to quantify scale effects and to define limiting criteria under which they can be neglected. These are inspectional analysis, dimensional analysis, calibration and scale series, which are applied to landslide generated impulse waves. Tables include both limiting criteria to avoid significant scale effects and typical scales of physical hydraulic engineering models for a wide variety of hydraulic flow phenomena. The article further shows why it is challenging to model sediment transport and distensible structures in a physical hydrau...

Scale effects in physical hydraulic engineering models

[1] Dunes are present in nearly all fluvial channels and are vital in predicting flow resistance, sediment transport, and deposition within many rivers. Progress in understanding the fluid dynamics associated with alluvial dunes has been significant in the last 15 years and has witnessed huge advances in field, laboratory, and numerical investigations. Progress has been made in detailing the principal features of mean and turbulent flow over asymmetric dunes that possess flow separation in their leesides and how these forms affect both downstream boundary layer structure and stress partitioning over the dune. Additionally, the links between sediment transport over dunes and instantaneous coherent flow structures are being increasingly understood, with the feedback of dune three-dimensionality upon flow and sediment dynamics over these bed forms beginning to be recognized as vital. Such research now provides an outstanding background for beginning to address areas of greater complexity that will enable a fuller understanding of these important natural features. This review paper summarizes the principal features of mean and turbulent flow over alluvial sand dunes. Five areas are then highlighted and discussed as a possible focus for future research: (1) the influence of dune leeside angle upon flow processes in the dune wake and downstream flow field, (2) the influence of three-dimensionality in dune shape upon the generation of turbulence and distribution of bed shear stress, (3) flow field modification resulting from bed form superimposition and amalgamation, (4) the scale and topology of dune-related turbulence and its interactions with sediment transport and the flow surface, and (5) the influence of suspended sediment on the dune flow field and dune morphology.

/pdf/the-fluid-dynamics-of-river-dunes-a-review-and-some-future-2nrjtixo1r.pdf

The fluid dynamics of river dunes: A review and some future research directions

Optical fibre probe measurements of bubbly flow in hydraulic jumps

http://staff.civil.uq.edu.au/h.chanson/reprints/Wang_et_al_etfs_2015.pdf

Interaction between free-surface, two-phase flow and total pressure in hydraulic jump

A hydraulic jump is a turbulent shear flow with a free-surface roller. The turbulent flow pattern is characterised by the development of instantaneous three-dimensional turbulent structures throughout the air–water column up to the free surface. The length and time scales of the turbulent structures are key information to describe the turbulent processes, which is of significant importance for the improvement of numerical models and physical measurement techniques. However, few physical data are available so far due to the complexity of the measurement. This paper presents an investigation of a series of characteristic turbulent scales for hydraulic jumps, covering the length and time scales of turbulent flow structures in bubbly flow, on free surface and at the impingement point. The bubbly-flow turbulent scales are obtained for Fr = 7.5 with 3.4 × 104 < Re < 1.4 × 105 in both longitudinal and transverse directions, and are compared with the free-surface scales. The results highlight three-dimensional flow patterns with anisotropic turbulence field. The turbulent structures are observed with different length and time scales respectively in the shear flow region and free-surface recirculation region. The bubbly structures next to the roller surface and the free-surface fluctuation structures show comparable length and time scales, both larger than the scales of vortical structures in the shear flow and smaller than the scales of impingement perimeter at the jump toe. A decomposition of physical signals indicates that the large turbulent scales are related to the unsteady motion of the flow in the upper part of the roller, while the high-frequency velocity turbulence dominates in the lower part of the roller. Scale effects cannot be ignored for Reynolds number smaller than 4 × 104, mainly linked to the formation of large eddies in the shear layer. The present study provides a comprehensive assessment of turbulent scales in hydraulic jump, including the analyses of first data set of longitudinal bubbly-flow integral scales and transverse jump toe perimeter integral scales.

Experimental assessment of characteristic turbulent scales in two-phase flow of hydraulic jump: from bottom to free surface

Effect of air velocity on nanoparticles dispersion in the wake of a vehicle model: Wind tunnel experiments

Experimental investigation of the grid-generated turbulence features in a free surface flow

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