Non-hydrostatic Pressure Distribution Research Articles

Experimental study of flash flood surges down a rough sloping channel

Flood waves resulting from flash floods and natural dam overtopping have been responsible for numerous losses. In the present study, surging waters down a flat stepped waterway (θ = 3.4°) were investigated in a 24 m long chute. Wave front propagation data were successfully compared with Hunt's [1982, 1984] theory. Visual observations highlighted strong aeration of the leading edge. Instantaneous distributions of void fractions showed a marked change in shape for (t − ts)* ∼ 1.3, which may be caused by some major differences between the wave leading edge and the flow behind, including nonhydrostatic pressure distributions, plug‐slug flow regime, and different boundary friction regime. Practically, the results quantified the large amount of entrained air (i.e., “white waters”) at the wave front, which in turn, reduces buoyancy and could affect sediment motion at the leading edge because the sediment relative density is inversely proportional to the entrained air content.

Numerical Solution of Boussinesq Equations to Simulate Dam-Break Flows

To investigate the effect of nonhydrostatic pressure distribution, dam-break flows are simulated by numerically solving the one-dimensional Boussinesq equations by using a fourth-order explicit finite-difference scheme. The computed water surface profiles for different depth ratios have undulations near the bore front for depth ratios greater than 0.4. The results obtained by using the Saint Venant equations and the Boussinesq equations are compared to determine the contribution of individual Boussinesq terms in the simulation of dam-break flow. It is found that, for typical engineering applications, the Saint Venant equations give sufficiently accurate results for the maximum flow depth and the time to reach this value at a location downstream of the dam.

Numerical study of flows with multiple free surfaces

AbstractThis paper demonstrates that a numerical method based on the generalized simplified marker and cell (GENSMAC) flow solver and Youngs' volume of fluid (Y‐VOF) surface‐tracking technique is an effective tool for studying the basic mechanics of hydraulic engineering problems with multiple free surfaces and non‐hydrostatic pressure distributions. Two‐dimensional flow equations in a vertical plane are solved numerically for this purpose. The numerical results are compared with experimental data and earlier numerical results based on a higher‐order depth‐averaged flow model available in the literature. Two classical problems, (i) flow in a free overfall and (ii) flow past a floor slot, are considered. The numerical results correspond very well with the experimental data for both sub‐critical and supercritical flows. Copyright © 2001 John Wiley & Sons, Ltd.

An implicit numerical algorithm for solving non-hydrostatic free-surface flow problems

Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady free-surface flows, using a non-hydrostatic pressure distribution. In this model, the Reynolds equations and the kinematic free-surface boundary condition are solved simultaneously, so that the water surface elevation can be integrated into the solution and solved for, together with the velocity and pressure fields. An efficient numerical algorithm has been developed, deploying implicit parameters similar to those used in the Crank–Nicholson method, and generating a block tri-diagonal algebraic system of equations. The model has been applied to simulate a range of unsteady flow problems involving relatively strong vertical accelerations. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply. Copyright © 2001 John Wiley & Sons, Ltd.

Magnetic Shear and Cross‐Field Currents: Roles in the Evolution of the Pre–Coronal Mass Ejection Corona

A widely used approximation in modeling the solar corona is to assume that the magnetic field is force free, in which case all electric currents flow parallel to the magnetic field. However, observations of the large-scale corona show clearly the presence of nonradial density variations and thus, presumably, nonradial pressure gradients. In equilibrium, such pressure gradients must be balanced by magnetic forces arising from cross-field currents. It is possible that these deviations from force-free conditions play a significant role in the evolution of the corona, particularly in the evolution leading to the large-scale eruptions known as coronal mass ejections (CMEs). In this work we explore the role of cross-field currents in the evolution of a model corona involving a simple magnetic arcade in magnetostatic equilibrium, neglecting the solar wind flow. Our formalism builds on the generating-function approach used in some force-free modeling but transcends the limitation to force-free conditions by introducing a second generating function representing a nonhydrostatic pressure distribution and associated cross-field electric currents. The results show that the presence of cross-field currents makes our model corona more prone to eruptive behavior than a strictly force-free corona. This effect may be relevant to the onset of CMEs, suggesting that the coronal conditions most likely to result in mass ejections are those in which both field-aligned and cross-field currents are present.

Structure of a turbulent bore in a homogeneous liquid

A mathematical model for the propagation of nonlinear long waves is constructed with allowance for nonhydrostatic pressure distribution and the development of a surface boundary layer due to wave breaking. The problem of the structure of a bore in a homogeneous liquid is solved. In particular, the transition of a wave bore to a turbulent bore as its amplitude increases is described within a single model.

Free-surface flow over curved surfaces: Part II: Computational model

SUMMARY In Part I a detailed derivation of a more general shallow water equation set was developed via a perturbation analysis. A finite element computational model of these more general equations is now constructed and the model behavior is compared with conventional shallow water formulations applied to an outletworks flume. © 1998 John Wiley & Sons, Ltd. The momentum equations derived in Part I are in non-conservative form and are written for a specific distance above the bed to include effects due to curvature. The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is indeed affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. In Part II these equations are depth-integrated and incorporated in a computational model. This form of the equations may be useful in handling non-smooth conditions. The weak form solution for the no-curvature condition that would be encountered downstream of the spillway can be made to properly conserve momentum and mass through a hydraulic jump, whereas other forms of the equations may not. In the case in which there is bed curvature, these equations will contain additional terms due to the bed curvature which, while finite through the jump, will make an additional contribution that can cause an error in the jump location. Therefore, in the vicinity of the jump these equations, which properly conserve mass and momentum for the no-curvature case, will conserve mass precisely in the curved bed state only. Generally, in practical cases the strong jump is restricted to the region downstream of the spillway face where the bed contains no curvature. Several recent finite element schemes for the shallow water equations utilize the Petrov‐ Galerkin approach [1,2] and are considered in Reference [3]. Such a scheme is constructed here for the system developed in Part I to handle bed curvature effects. The treatment proceeds as follows: first the model equations are summarized and an appropriate test function is devised. Next, the finite element Petrov‐Galerkin system is presented and the treatment of boundary * Correspondence to: USAE Waterways Exp. Station, Vicksburg, MS, USA.

Free-surface flow over curved surfaces: Part I: Perturbation analysis

The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed-fitted co-ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II. © 1998 John Wiley & Sons, Ltd.

The use of a one-dimensional depth-averaged moment of momentum equation for the nonhydrostatic pressure condition

A depth-averaged model formulated in the Cartesian coordinate system for curved open-channel flows is extended to solve problems where the effects of nonhydrostatic pressure distribution and nonuniform velocity distribution are significant. The nonhydrostatic pressure condition is added to the z-direction momentum equation assuming that the pressure deviation from the hydrostatic condition at the channel bed decreases linearly to the water surface. The pressure-effect terms are modified in both the moment of momentum and momentum equations. The resulting system of nonlinear equations is solved by a finite-element method. The derived model is then applied to four sophisticated nonuniform flow experiments from the literature. A comparison of the actual experimental results with their numerical prediction results, as calculated with the model, is presented. Generally speaking, a fairly good agreement for the depth-averaged velocities as well as reasonable perturbation profiles were obtained from this comparison. Therefore, it can be said that the depth-averaged model for open-channel flow is reasonably accurate under the given conditions. Key words: open-channel flow, depth-averaged method, finite-element method, nonhydrostatic pressure, nonuniform flow.

Conjugate depths of hydraulic jump in free torrent overflow

1. The existing methods of determining the downstream limit depth for which the conjugate depth form with previous overflow is still possible yield large differences with respect to each other. 2. The proposed method is intended for N>1 and takes into account the nonhydrostatic pressure distribution and the actual potential energy depending on H and N. 3. Experimental verification of the proposed method showed satisfactory agreement with the analyses for the entire investigation range.

Free Flow Discharge Characteristics of Throatless Flumes

A theoretical analysis of the free flow discharge characteristics of the throatless flume is presented. A pressure correction factor which accounts for the nonhydrostatic pressure distribution at t...