Near-critical free-surface flows: real fluid flow analysis

An open channel flow with a flow depth close to the critical depth is characterised by a curvilinear streamline flow field that results in steady free surface undulations. Near critical flows of practical relevance encompass the undular hydraulic jump when the flow changes from supercritical (F > 1) to subcritical (F < 1), and the undular weir flow over broad-crested weirs where the flow changes from subcritical (F < 1) to supercritical (F > 1). So far these flows were mainly studied based on ideal fluid flow computations, for which the flow is assumed irrotational and, thus, shear forces are absent. While the approach is accurate for critical flow conditions (F = 1) in weir and flumes, near-critical flows involve long distances reaches, and the effect of friction on the flow properties cannot be neglected. In the present study the characteristics of near-critical free-surface flows are reanalysed based on a model accounting for both the streamline curvature and friction effects. Based on the improved model, some better agreement with experimental results is found, thereby highlighting the main frictional features of the flow profiles.     

Ritter’s dry-bed dam-break flows: positive and negative wave dynamics

Dam-break flood waves are associated with major environmental disasters provoked by the sudden release of water stored in reservoirs. Ritter found in 1892 an analytical solution to the wave structure of an ideal fluid released during an instantaneous dam failure, propagating over initially dry horizontal terrain. This solution, though ideal, hence frictionless, is widely used to test numerical solutions of the Shallow Water Equations (SWE), and as educational tool in courses of fluid mechanics, given that it is a peculiar case of the Riemann problem. However, the real wave structure observed experimentally differs in a major portion of the wave profile, including the positive and negative fronts. Given the importance of an accurate prediction of the dam break wave, the positive and negative wave portions originating from the breaking of a dam with initially dry land on the tailwater reach are revisited in this work. First, the propagation features of the dry-front are investigated using an analytical boundary-layer type model (Whitham/Dressler/Chanson model) constructed matching an (outer) inviscid dynamic wave to an (inner) viscous diffusive wave. The analytical solution is evaluated using an accurate numerical solution of the SWE produced using the MUSCL-Hancock finite-volume method, which is tested independently obtaining the solution based on the discontinuous Galerkin finite-element method. The propagation features of the negative wave are poorly reproduced by the SWE during the initial stages of dam break flows, and, thus, are then investigated using the Serre–Green–Naghdi equations for weakly-dispersive fully non-linear water waves, which are solved using a finite volume-finite difference scheme.     

Shallow fluid flow over an obstacle: higher-order non-hydrostatic modeling and breaking waves

Environmental Fluid Mechanics - The simulation of shallow flows over obstacles is an important problem in environmental fluid dynamics, including exchange flows over seabed sills, atmospheric flows...     

Steady open channel flows with curved streamlines: the Fawer approach revised

Rapidly varied open channel flows are characterized by curvilinear streamlines, thereby resulting in a pressure field different from the hydrostatic approach proposed in the standard gradually varied flow theory. This problem is related to environmental hydraulic problems such as the undular hydraulic jump and flow over round-crested weirs, for which streamline curvature effects are significant. The inclusion of the curvilinear streamline effect in an extended energy equation was firstly by Fawer. Most of the extended energy equations currently employed are therefore modified forms of the original Fawer approach. The aim of the present study is to highlight and remind engineers of the outstanding theory presented by Fawer. Herein, his approach for steady open channel flow with curved streamlines is revised and compared with experimental observations. Computational methods are presented in detail and based on present results, it can be observed that more recent and complex models for these problems are similar to the original proposal of Fawer, and hardly more accurate in some instances. Based on the proposed study an useful framework for theoretical models for steady open channel flows with curved streamlines is proposed.     

Undular and broken surges in dam-break flows: a review of wave breaking strategies in a Boussinesq-type framework

Environmental Fluid Mechanics - The water waves resulting from the collapse of a dam are important unsteady free surface flows in civil and environmental engineering. Considering the basic case of...     

A new model for soil–water drainage problems

Seepage flow is an agent related to the transport and dispersion of contamination in groundwater. Steady two-dimensional seepage flow is governed by Laplace’s equation, for which several solution techniques are available. Because computations are complex from a practical point of view, simplified models encompass the Dupuit-Forchheimer approach assuming a horizontal flow. However this approach is inaccurate in seepage problems involving steep drawdowns. In this research, a new theoretical model for 2D seepage flow is proposed based on Fawer’s theory for curved flows Castro-Orgaz (Environ Fluid Mech 10(3):2971–2310, 2010), from which a second-order equation results describing the seepage surface. From this development, a numerical solution for the rectangular dam problem based on the second-order model is presented, whereas a simple first-order equation is found to describe flow to drains under a uniform rainfall. The results of this new model are compared with the full 2D solution of Laplace’s equation for typical test cases, resulting in an excellent agreement.     

Reply to comment on “steady open channel flows with curved streamlines: the Fawer approach revised”

In this reply to a comment to (Environ Fluid Mech 10(3):297–310 [1]), the comparison between the Dressler curved streamline equations and Fawer’s theory is further expanded by momentum considerations. The importance of Fawer’s theory for steady curved open channel flow is thereby highlighted, both from energy and momentum considerations.     

Free surface profiles of near-critical instabilities in open channel flows: undular hydraulic jumps

Environmental Fluid Mechanics - When the Froude number F of a free-surface flow ranges between 0.3 and 3, the flow is unstable and frequently characterised by free surface undulations, with the...