Journal articles: 'Undular hydraulic jump'

1

Reinauer, Roger, and Willi H. Hager. "Non-breaking undular hydraulic jump." Journal of Hydraulic Research 33, no. 5 (September 1995): 683–98. http://dx.doi.org/10.1080/00221689509498564.

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2

Ohtsu, Iwao, Youichi Yasuda, and Hiroshi Gotoh. "Non-Breaking Undular Hydraulic Jump." Journal of Hydraulic Research 34, no. 4 (July 1996): 567–73. http://dx.doi.org/10.1080/00221689609498479.

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3

THORPE, S. A., and I. KAVCIC. "The circular internal hydraulic jump." Journal of Fluid Mechanics 610 (August 8, 2008): 99–129. http://dx.doi.org/10.1017/s0022112008002553.

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Circular hydraulic jumps are familiar in single layers. Here we report the discovery of similar jumps in two-layer flows. A thin jet of fluid impinging vertically onto a rigid horizontal plane surface submerged in a deep layer of less-dense miscible fluid spreads radially, and a near-circular internal jump forms within a few centimetres from the point of impact with the plane surface. A jump is similarly formed as a jet of relatively less-dense fluid rises to the surface of a deep layer of fluid, but it appears less stable or permanent in form. Several experiments are made to examine the case of a downward jet onto a horizontal plate, the base of a square or circular container. The inlet Reynolds numbers, Re, of the jet range from 112 to 1790. Initially jumps have an undular, laminar form with typically 2–4 stationary waves on the interface between the dense and less-dense layers but, as the depth of the dense layer beyond the jump increases, the transitions become more abrupt and turbulent, resulting in mixing between the two layers. During the transition to a turbulent regime, single and sometimes moving multiple cusps are observed around the periphery of jumps. A semi-empirical model is devised that relates the parameters of the laboratory experiment, i.e. flow rate, inlet nozzle radius, kinematic viscosity and reduced gravity, to the layer depth beyond the jump and the radius at which an undular jump occurs. The experiments imply that surface tension is not an essential ingredient in the formation of circular hydraulic jumps and demonstrate that stationary jumps can exist in stratified shear flows which can be represented as two discrete layers. No stationary circular undular jumps are found, however, in the case of a downward jet of dense fluid when the overlying, less-dense, fluid is stratified, but a stationary turbulent transition is observed. This has implications for the existence of stationary jumps in continuously stratified geophysical flows: results based on two-layer models may be misleading. It is shown that the Froude number at which a transition of finite width occurs in a radially diverging flow may be less than unity.

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4

Ohtsu, Iwao, Youichi Yasuda, and Hiroshi Gotoh. "Hydraulic condition for undular-jump formations." Journal of Hydraulic Research 39, no. 2 (April 2001): 203–9. http://dx.doi.org/10.1080/00221680109499821.

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5

Chanson, H. "Hydraulic condition for undular-jump formations." Journal of Hydraulic Research 40, no. 3 (May 2002): 379–84. http://dx.doi.org/10.1080/00221680209499953.

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6

Rostami, Fatemeh, Saeed Reza Sabbagh Yazdi, Md Azlin Md Said, and Mahdi Shahrokhi. "Numerical simulation of undular jumps on graveled bed using volume of fluid method." Water Science and Technology 66, no. 5 (September 1, 2012): 909–17. http://dx.doi.org/10.2166/wst.2012.213.

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Undular hydraulic jumps are characterized by a smooth rise of the free surface, followed by a train of stationary waves. These jumps sometimes occur in natural waterways and rivers. Numerical difficulties are especially distinct when the flow condition is close to the critical value because of the high sensitivity of the near-critical flow field to flow and channel conditions. Furthermore, the free surface has a wavy shape, which may indicate the occurrence of several transitions from supercritical to subcritical states and vice versa (i.e., undular hydraulic jumps). In this study, a flow model is used to predict an undular hydraulic jump in a rectangular open channel. The model is based on the general two-dimensional, Reynolds-averaged, Navier–Stokes flow equations. The resulting set of partial differential equations is solved using the FLOW-3D solver. The results are compared with the experimental data to validate the model. The comparative analysis shows that the proposed model yields good results. Several types of undular hydraulic jumps occurring in different situations are then simulated to prove the potential application of the model.

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7

RIABENKO, Alexander A., Volodymyr V. CHERNYUK, Oksana A. KLYUHA, Oksana A. HALYCH, and Dmytro M. POPLAVSKIY. "Mathematical and hydraulic modelling of undular jump." Journal of Civil Engineering, Environment and Architecture XXXII, no. 3/II/2015 (December 1, 2015): 379–91. http://dx.doi.org/10.7862/rb.2015.162.

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8

Castro-Orgaz, Oscar. "Weakly undular hydraulic jump: effects of friction." Journal of Hydraulic Research 48, no. 4 (August 2010): 453–65. http://dx.doi.org/10.1080/00221686.2010.491646.

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9

Di Nucci, Carmine, and Aniello Russo Spena. "Weakly undular hydraulic jump: effects of friction." Journal of Hydraulic Research 49, no. 3 (June 2011): 409–12. http://dx.doi.org/10.1080/00221686.2011.569217.

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10

Castro-Orgaz, Oscar, Willi H. Hager, and Subhasish Dey. "Depth-averaged model for undular hydraulic jump." Journal of Hydraulic Research 53, no. 3 (October 24, 2014): 351–63. http://dx.doi.org/10.1080/00221686.2014.967820.

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11

Castro-Orgaz, Oscar, and Willi H. Hager. "Observations on undular hydraulic jump in movable bed." Journal of Hydraulic Research 49, no. 5 (September 26, 2011): 689–92. http://dx.doi.org/10.1080/00221686.2011.593879.

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12

Cummins, Patrick F., and Laurence Armi. "Upstream Internal Jumps in Stratified Sill Flow: Observations of Formation, Evolution, and Release." Journal of Physical Oceanography 40, no. 6 (June 1, 2010): 1419–26. http://dx.doi.org/10.1175/2010jpo4435.1.

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Abstract The time-dependent response of upstream undular bores and internal hydraulic jumps from initial formation to eventual release is documented. Two events, characterized by qualitatively different responses, are discussed. In the first case, an undular bore develops upstream of the sill crest. This disturbance remains upstream through the ebb tidal flow but is transformed to a hydraulic jump as its amplitude increases. Toward the end of ebb tide, it is released and subsequently disperses into a group of solitary-like waves. During the second event, an upstream jump also develops at an early stage of the tide. However, it is subsequently swept downstream by the tidal flow such that the upstream region then appears featureless. Approaching slack tide, as an exchange flow becomes established, a large bore or gravity current is emitted. The different responses seen in these two events are interpreted in terms of the Froude number associated with the near-surface stratification.

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13

Magdalena, I., F. J. Sutjianto, Andrew, A. Sani, and R. Anastasia. "Dispersive Model for Undular Hydraulic Jump Behind a Weir." Journal of Physics: Conference Series 1751 (January 2021): 012005. http://dx.doi.org/10.1088/1742-6596/1751/1/012005.

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14

MORI, Akio, Tadaoki ITAKURA, Kouji MORIHIRA, and Shuji TAKADA. "Interaction between hydraulic jump and turbulent boundary layer-Three dimensional undular jump." PROCEEDINGS OF HYDRAULIC ENGINEERING 36 (1992): 367–72. http://dx.doi.org/10.2208/prohe.36.367.

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15

Jurisits, Richard, Wilhelm Schneider, and Yee Seok Bae. "A multiple-scales solution of the undular hydraulic jump problem." PAMM 7, no. 1 (December 2007): 4120007–8. http://dx.doi.org/10.1002/pamm.200700755.

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16

Smyth, N. F., and P. E. Holloway. "Hydraulic Jump and Undular Bore Formation on a Shelf Break." Journal of Physical Oceanography 18, no. 7 (July 1988): 947–62. http://dx.doi.org/10.1175/1520-0485(1988)018<0947:hjaubf>2.0.co;2.

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17

Ogden, K. A., and Karl R. Helfrich. "Internal hydraulic jumps in two-layer flows with upstream shear." Journal of Fluid Mechanics 789 (January 15, 2016): 64–92. http://dx.doi.org/10.1017/jfm.2015.727.

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Internal hydraulic jumps in flows with upstream shear are investigated using two-layer shock-joining theories and numerical solutions of the Navier–Stokes equations. The role of upstream shear has not previously been thoroughly investigated, although it is important in many oceanographic situations, including exchange flows. The full solution spaces of several two-layer theories, distinguished by how dissipation is distributed between the layers, with upstream shear are found, and the physically allowable solution space is identified. These two-layer theories are then evaluated using more realistic numerical simulations that have continuous density and velocity profiles and permit turbulence and mixing. Two-dimensional numerical simulations show that none of the two-layer theories reliably predicts the relation between jump height and speed over the full range of allowable solutions. The numerical simulations also show that different qualitative types of jumps can occur, including undular bores, energy-conserving conjugate state transitions, smooth-front jumps with trailing turbulence and overturning turbulent jumps. Simulation results are used to investigate mixing, which increases with jump height and upstream shear. A few three-dimensional simulations results were undertaken and are in quantitative agreement with the two-dimensional simulations.

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18

Cummins, Patrick F., Laurence Armi, and Svein Vagle. "Upstream Internal Hydraulic Jumps." Journal of Physical Oceanography 36, no. 5 (May 1, 2006): 753–69. http://dx.doi.org/10.1175/jpo2894.1.

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Abstract In stratified tidal flow over a sill, the character of the upstream response is determined by a Froude number Fs based on the stratification near the surface. This is distinguished from the Froude number governing the response in the neighborhood of the sill crest, which is based on the weak density step associated with a flow bifurcation. For moderate values of Fs, the upstream response consists of nonlinear waves or a weak undular bore. For larger values of Fs, a strong, quasi-stationary, internal hydraulic jump dominates the upstream response. At sufficiently large values of Fs, the upstream bore is swept downstream and lost. Acoustic backscatter and velocity data are presented for the case of a strong internal bore or gravity current in a tidally modulated sill flow. Numerical simulations with varying near-surface stratification are presented to illustrate the upstream responses at different values of Fs. The theory of two-layer hydraulic flows is invoked to account for the development of the upstream jump.

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19

OHMOTO, Terunori, Norimitsu NARIAI, and Kouichi YAKITA. "Three Dimensional Flow Structure of Undular Hydraulic Jump in Stepped Open Channel." Journal of applied mechanics 5 (2002): 673–80. http://dx.doi.org/10.2208/journalam.5.673.

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20

Uchida, Tatsuhiko. "An Enhanced Depth-integrated Model for Flows over a Negative Step with Hydraulic Jump." E3S Web of Conferences 40 (2018): 05017. http://dx.doi.org/10.1051/e3sconf/20184005017.

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Depth-integrated models play an important role of predicting flows for several practical problems. There are many contributions to develop an enhanced depth-integrated model to have the ability of evaluating vertical flow structures. However, it is still challenging for the depth integrated models to calculate flows over a negative step accompanying a hydraulic jump, because the separation zone behind the step and the pattern of the hydraulic jump depend on the several hydraulic conditions such as Froude number, step height and downstream water depth. In this study, assuming gravel bed rivers in which the bed is covered with relatively large roughness, an enhanced depth integrated model is developed to calculate various hydraulic jump patterns generated downstream from the negative step. The present method is based on General Bottom Velocity Computation method employing Dynamic Wall Law with 4th degree polynomial velocity distribution (GBVC4-DWL). The model with the virtual bed slope behind the negative step and the critical slope of wave breaking is validated through the comparisons with the experimental results on flows over a negative step for submerged jet. weak jump and undular jump conditions. Then the essential terms of equations which compose the present method to calculate the flow downstream of the negative step are investigated.

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21

Wang, Chunli, and S. Li. "Hydraulic Jump and Resultant Flow Choking in a Circular Sewer Pipe of Steep Slope." Water 10, no. 11 (November 16, 2018): 1674. http://dx.doi.org/10.3390/w10111674.

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Urban flood caused by storm-water runoff has been problematic for many regions. There is a need to improve the design and hydraulic performance of storm sewer-pipes, which will help reduce the impact of urban flood. Such a need has motivated the current study. This paper investigates the flow behaviour in a circular pipe of steep slope, in which supercritical flow descends the steep terrain and forms a hydraulic jump under control acting downstream. So far, the jump behaviour and resultant flow choking in a circular pipe are poorly understood. This paper formulates the problem of the hydraulic jump in a circular pipe of slope on the basis of the momentum principle and solves it by using iterative methods. The solutions include the filling ratio and flow field downstream of an undular jump and a direct jump. For the first time, the Froude number’s dependence on the pipe slope has been quantified. For a given slope, it is possible to have two different filling ratios (or equivalently discharges) that associate with the same Froude number value. This paper reports detailed results of the initial versus sequent depth of the hydraulic jumps and quantitatively delineates the slope-filling ratio space between flow-choking and choking-free zones. For the design of storm sewers in a hilly area, it is necessary to correct the current design guidelines, which rely mostly on the uniform flow theory and suggest filling ratios as high as 85%. The corrections are either decreasing the filling ratio or increasing the pipe diameter to achieve choking-free flow in a circular pipe.

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22

Grillhofer, Wolfgang, and Wilhelm Schneider. "The undular hydraulic jump in turbulent open channel flow at large Reynolds numbers." Physics of Fluids 15, no. 3 (March 2003): 730–35. http://dx.doi.org/10.1063/1.1538249.

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23

Steinrück, H., W. Schneider, and W. Grillhofer. "A multiple scales analysis of the undular hydraulic jump in turbulent open channel flow." Fluid Dynamics Research 33, no. 1-2 (July 2003): 41–55. http://dx.doi.org/10.1016/s0169-5983(03)00041-8.

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24

Rostami, Fatemeh, Mahdi Shahrokhi, Md Azlin Md Saod, and Saeed Reza Sabbagh Yazdi. "RETRACTED: Numerical simulation of undular hydraulic jump on smooth bed using volume of fluid method." Applied Mathematical Modelling 37, no. 3 (February 2013): 1514–22. http://dx.doi.org/10.1016/j.apm.2012.03.048.

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25

CONNELL, R. J., D. KULASIRI, J. LENNON, and D. F. HILL. "COMPUTATIONAL MODELING OF TURBULENT VELOCITY STRUCTURES FOR AN OPEN CHANNEL FLOW USING KARHUNEN–LOÉVE EXPANSION." International Journal of Computational Methods 04, no. 03 (September 2007): 493–519. http://dx.doi.org/10.1142/s0219876207001242.

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This paper develops an analytical two-part covariance kernel from velocity correlations across a two-dimensional (vertical and flow directions) Particle Image Velocimetry (PIV) flow field. This will form the basis of a model of wave action in flood water that includes the underlying turbulence velocity field using Karhunen–Loéve (KL) expansion. The PIV data was from the supercritical flow area immediately upstream of an undular hydraulic jump. This paper derives a one-dimensional solution for the associated integral equations. It also discusses a relationship between the two parts of the kernel and the turbulent production and turbulent dissipation.

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Pasha, Ghufran Ahmed, and Norio Tanaka. "Undular hydraulic jump formation and energy loss in a flow through emergent vegetation of varying thickness and density." Ocean Engineering 141 (September 2017): 308–25. http://dx.doi.org/10.1016/j.oceaneng.2017.06.049.

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27

Zerihun, Yebegaeshet T. "Non-Hydrostatic Transitional Open-Channel Flows from a Supercritical to a Subcritical State." Slovak Journal of Civil Engineering 29, no. 2 (June 1, 2021): 39–48. http://dx.doi.org/10.2478/sjce-2021-0012.

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Abstract In this study, a depth-averaged numerical model was employed to investigate the two-dimensional flow features of transitional open-channel flows from a supercritical to a subcritical state. Compared to a shallow-water model, the proposed model incorporates supplementary terms to account for the effects of non-uniform velocity and non-hydrostatic pressure distributions. The model equation was solved numerically by means of the Adams–Bashforth–Moulton scheme. A wide variety of transitional open-channel flow problems such as hydraulic jumps was considered for assessing the suitability of the numerical model. The results of the model for the free-surface profile, pressure distribution, and characteristics of the first wave of an undular jump were compared with the experimental data, and the agreement was found to be satisfactory. Despite the effects of the three-dimensional characteristics of the flow and the bulking of the flow caused by air entrainment, the model performed reasonably well with respect to the simulations of the mean flow characteristics of the curvilinear turbulent flow problems. Furthermore, the results of this investigation confirmed that the model is more suitable for analyzing near-critical turbulent flow problems without cross-channel shock waves.

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28

Grubišić, Vanda, Stefano Serafin, Lukas Strauss, Samuel J. Haimov, Jeffrey R. French, and Larry D. Oolman. "Wave-Induced Boundary Layer Separation in the Lee of the Medicine Bow Mountains. Part II: Numerical Modeling." Journal of the Atmospheric Sciences 72, no. 12 (November 30, 2015): 4865–84. http://dx.doi.org/10.1175/jas-d-14-0381.1.

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Abstract Mountain waves and rotors in the lee of the Medicine Bow Mountains in southeastern Wyoming are investigated in a two-part paper. Part I by French et al. delivers a detailed observational account of two rotor events: one displays characteristics of a hydraulic jump and the other displays characteristics of a classic lee-wave rotor. In Part II, presented here, results of high-resolution numerical simulations are conveyed and physical processes involved in the formation and dynamical evolution of these two rotor events are examined. The simulation results reveal that the origin of the observed rotors lies in boundary layer separation, induced by wave perturbations whose amplitudes reach maxima at or near the mountain top. An undular hydraulic jump that gave rise to a rotor in one of these events was found to be triggered by midtropospheric wave breaking and an ensuing strong downslope windstorm. Lee waves spawning rotors developed under conditions favoring wave energy trapping at low levels in different phases of these two events. The upstream shift of the boundary layer separation zone, documented to occur over a relatively short period of time in both events, is shown to be the manifestation of a transition in flow regimes, from downslope windstorms to trapped lee waves, in response to a rapid change in the upstream environment, related to the passage of a short-wave synoptic disturbance aloft. The model results also suggest that the secondary obstacles surrounding the Medicine Bow Mountains play a role in the dynamics of wave and rotor events by promoting lee-wave resonance in the complex terrain of southeastern Wyoming.

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Pasha, Ghufran Ahmed, and Norio Tanaka. "Critical Resistance Affecting Sub- to Super-Critical Transition Flow by Vegetation." Journal of Earthquake and Tsunami 13, no. 01 (February 2019): 1950004. http://dx.doi.org/10.1142/s1793431119500040.

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In order to design a vegetation structure to mitigate floods resulting from extreme events like tsunamis, vegetation density and thickness (width) are important parameters. Flow passing through vegetation faces great resistance, which results in a backwater rise on upstream (U/S) vegetation, increases the water slope inside the vegetation, and for some cases, forms a hydraulic jump downstream (D/S) of the vegetation, thus transforming a subcritical flow to supercritical [Pasha, G. A. and Tanaka, N. [2017] “Undular hydraulic jump formation and energy loss in a flow through emergent vegetation of varying thickness and density,” Ocean Eng. 141, 308–325.]. Like the concepts of critical velocity and critical slope, this paper introduces the concept of “critical resistance of vegetation,” which is defined as “resistance offered by vegetation that transforms a subcritical flow to supercritical.” An analytical approach to find the water depths U/S, inside, and D/S of vegetation is introduced and validated well by laboratory experiments. Critical resistance was determined against vegetation of variable densities ([Formula: see text], where [Formula: see text] of each cylinder in the cross-stream direction, [Formula: see text] of the cylinder), thicknesses (dn, where [Formula: see text] of a cylinder and [Formula: see text] of cylinders in a stream-wise direction per unit of cross-stream width), and the initial Froude number (Fro). A subcritical flow ([Formula: see text], without vegetation) was transformed to a supercritical flow (D/S vegetation) with a range of Froude numbers of 1.6–1.9, 1.1–1.2, and 0.85–0.98 against [Formula: see text] ratios of 0.25, 1.09, and 2.13, respectively, thus defining [Formula: see text] as the critical resistance. However, altering vegetation thickness did not change the results.

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30

White, Brian L., and Karl R. Helfrich. "A model for internal bores in continuous stratification." Journal of Fluid Mechanics 761 (November 21, 2014): 282–304. http://dx.doi.org/10.1017/jfm.2014.599.

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AbstractWe describe a model for the speed of an internal bore as a function of amplitude in continuous stratification of arbitrary form. The model is developed from the Dubreil-Jacotin–Long theory for nonlinear solitary waves in the conjugate flow limit, which represents an internal hydraulic jump, by allowing dissipation across the jump. The bore speeds predicted by the model are consistent in both the small- and large-amplitude limits with the waveguide intrinsic to the ambient stratification. The model therefore represents a significant advancement over previous theories limited to sharp two-layer stratification. The model shows good agreement with Navier–Stokes simulations of both undular and turbulent internal bores generated by dam break into a continuously stratified ambient with a finite pycnocline, predicting both the front speed as well as the velocity and density structure through the bore. A model is required for the structure of the energy dissipation, and we introduce a one-parameter closure that produces excellent agreement with numerical results, particularly in the parameter limit that maximizes the overall dissipation. By varying the dissipation parameter, the model reproduces previous two-layer theories in the thin-pycnocline limit, and suggests an improved two-layer front speed relationship. It is demonstrated that, even for the sharp two-layer limit, continuous stratification, and particularly the nonlinear waveguide, must be accounted for in order to accurately predict the bore speed and structure.

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31

TAKEMURA, Yoshiharu, and Shoji FUKUOKA. "ANALYSIS OF THE FLOW IN UNDULAR AND HYDRAULIC JUMP STILLING BASINS USING NON-HYDROSTATIC QUASI-THREE DIMENSIONAL MODEL CONSIDERING FLOW EQUATIONS ON BOUNDARY SURFACES." Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering) 75, no. 1 (2019): 61–80. http://dx.doi.org/10.2208/jscejhe.75.61.

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32

Rostami, Fatemeh, Mahdi Shahrokhi, Md Azlin Md Saod, and Saeed Reza Sabbagh Yazdi. "Retraction notice to ‘Numerical simulation of undular hydraulic jump on smooth bed using volume of fluid method’ [Appl. Math. Model. 37 (3) (2013) 1514–1522]." Applied Mathematical Modelling 38, no. 7-8 (April 2014): 2302. http://dx.doi.org/10.1016/j.apm.2014.01.010.

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33

Knupp, Kevin. "Observational Analysis of a Gust Front to Bore to Solitary Wave Transition within an Evolving Nocturnal Boundary Layer." Journal of the Atmospheric Sciences 63, no. 8 (August 1, 2006): 2016–35. http://dx.doi.org/10.1175/jas3731.1.

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Abstract The evolution of a gust front to bore to solitary wave transition, and comprehensive information on the evolving nocturnal boundary layer (NBL) associated with this change, are described with analysis of radar and profiler measurements. The observations were obtained on 21 June 2002 in the Oklahoma panhandle during the International H2O Project. The evolution of this system, from a strong bore (initiated by a vigorous gust front) to a solitary wave, was observed over a 4-h period with Doppler radar and surface measurements. Detailed information on the mature bore structure was obtained by a cluster of profiling instruments including two boundary layer wind profilers, a lidar ceilometer, and a microwave profiling radiometer. A strong bore was initiated by an extensive gust front that perturbed an incipient NBL whose development (prior to sunset) was enhanced by shading from the parent mesoscale convective system. At the time of bore formation, the NBL was about 300 m deep and exhibited a surface temperature about 4 K less than the afternoon maximum. Initially, the bore assumed kinematic properties similar to those of a gust front. As the NBL stabilized, the bore matured and exhibited undular formations over 30–60-km segments along the bore axis. A 30-km-wide cloud field accompanied the mature bore system within three hours of its formation. System-relative airflow within the cloud field was front-to-rear and exhibited a primary hydraulic jump updraft (4–5 m s−1 magnitude) within the bore core. The bore core exhibited a low, smooth cloud base, a cloud depth of 2.5 km, nearly adiabatic liquid water content, and pronounced turbulence. The maximum parcel displacements within the bore were about 2 km (sufficient for marginal convective initiation), and the net parcel displacement from before to after bore passage was 0.6–0.9 km.

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34

WELLS, M. G., and J. S. WETTLAUFER. "The long-term circulation driven by density currents in a two-layer stratified basin." Journal of Fluid Mechanics 572 (January 23, 2007): 37–58. http://dx.doi.org/10.1017/s0022112006003478.

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Experimentation and theory are used to study the long-term dynamics of a two-dimensional density current flowing into a two-layer stratified basin. When the initial Richardson number, $\hbox{\it Ri}_{\rho}^{\hbox{\scriptsize\it in}}$, characterizing the ratio of the background stratification to the buoyancy flux of the density current, is less than the critical value of $\hbox{\it Ri}_{\rho}^{*} \,{=}\, 21-27$, it is found that the density current penetrates the stratified interface. This result is ostensibly independent of slope for angles between 30° and 90°. If the current does not initially penetrate the interface, then it slowly increases the density of the top layer until the interfacial density difference is reduced sufficiently to drive penetration. The time scale for this to occur, $t_{p} \,{=}\, (\hbox{\it Ri}^{\hbox{\scriptsize\it in}}_{\rho} - \hbox{\it Ri}_{\rho}^{*}) L/B^{1/3}$, is explicitly a function of the buoyancy flux B and the length of the basin L. The initial Richardson number, $\hbox{\it Ri}^{\hbox{\scriptsize\it in}}_{\rho}$, is a function of depth, the initial reduced gravity of the interface and a weak function of slope angle. In the absence of initial penetration for very steep slopes of 75° and 90°, we observe that penetrative convection at the interface leads to significant local entrainment. In consequence, the top layer thickens and the interfacial entrainment rate increases as the fifth power of the interfacial Froude number. In contrast, such a process is not observed at comparable interfacial Froude numbers on lower slopes of 30°, 45° and 60°, thereby demonstrating the important role of impact angle on penetrative convection. We attribute the increased interfacial entrainment by the steep density currents as the result of the transition from an undular bore to a turbulent hydraulic jump at the point where the density current intrudes. We discuss the applicability of the observed circulation to the stability of the Arctic halocline where we find $0.56\,{\lesssim}\, t_{p} \,{\lesssim}\,1.2$ years for a range of contemporary oceanographic conditions.

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35

Gargano, Rudy, and Willi H. Hager. "Undular Hydraulic Jumps in Circular Conduits." Journal of Hydraulic Engineering 128, no. 11 (November 2002): 1008–13. http://dx.doi.org/10.1061/(asce)0733-9429(2002)128:11(1008).

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36

GOTOH, Hiroshi, Youichi YASUDA, and Iwao OHTSU. "FLOW CHARACTERISTICS OF UNDULAR HYDRAULIC JUMPS." PROCEEDINGS OF HYDRAULIC ENGINEERING 45 (2001): 439–44. http://dx.doi.org/10.2208/prohe.45.439.

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37

Bose, Sujit K., Oscar Castro-Orgaz, and Subhasish Dey. "Free Surface Profiles of Undular Hydraulic Jumps." Journal of Hydraulic Engineering 138, no. 4 (April 2012): 362–66. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0000510.

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38

OHTSU, Iwao, Youichi YASUDA, and Hiroshi GOTOH. "HYDRAULIC CONDITION FOR FORMATION OF UNDULAR JUMPS." PROCEEDINGS OF HYDRAULIC ENGINEERING 42 (1998): 673–78. http://dx.doi.org/10.2208/prohe.42.673.

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39

Montes, J. S., and H. Chanson. "Characteristics of Undular Hydraulic Jumps: Experiments and Analysis." Journal of Hydraulic Engineering 124, no. 2 (February 1998): 192–205. http://dx.doi.org/10.1061/(asce)0733-9429(1998)124:2(192).

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Ali, Amina, Ghufran Ahmad Pasha, Usman Ghani, Afzal Ahmed, and Fakhar Muhammad Abbas. "Investigating Role of Vegetation in Protection of Houses during Floods." Civil Engineering Journal 5, no. 12 (December 3, 2019): 2598–613. http://dx.doi.org/10.28991/cej-2019-03091436.

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Flood flows have the potential to cause substantial damage to infrastructure, mankind, livestock and agricultural land which all stacks up to greatly affect the financial condition of the region. During 2010 Pakistan floods, more than two million houses were damaged partly or totally [1]. To minimize these types of destructions, inland vegetation can be considered a natural barrier to dissipate the energy of flood flow and limits widespread inundation. This study involves volume of fluid (VOF) modelling approach to figure out the role of vegetation of finite width in energy reduction of flood flow, in front of houses, against: vegetation of varying Aspect Ratio (A/R width-length ratio) and distance between vegetation & houses (Lr). Channel domain was built in ANSYS workbench toolkit and meshing was done in meshing building toolkit. For the postprocessing and simulation, FLUENT was used. Various contour plots & profiles of cross stream-wise velocities and water level measurements are presented in this paper. The simulation results of cross stream-wise velocities and water level measurements were identical with experimental data. At vegetation upstream and downstream, velocity reduction observed in higher A/R (2.40) compared to vegetation of A/R-1. Whereas, outside the vegetation and near the walls of channel domain flow velocities were high. The water level was raised on the upstream side of the vegetation due to resistance offered by vegetation. On the upstream side of vegetation, the rise in backwater depth increased by increasing A/R. Contrarily, on the downstream side of vegetation, an undular hydraulic jump was observed in between vegetation and a house. By increasing A/R, the energy loss increases under constant vegetation conditions (G/d = 0.24, Fro = 0.70; G = spacing of each cylinder in cross-stream direction and d= diameter of cylinder and Fro = initial Froude number) and increase in house distance from 1W to 2W, the energy reduction increased from 2.40% to 3.15% which was further increased to 5.04% for another 5W increase in house distance, where W is the vegetation width. Simulation results also shown that with increasing Froude no from 0.60 to 0.70 water level depth has also an incremental pattern which ultimately results in increase in energy dissipation along the varying building distance (1W, 2W & 5W). Thus, to minimize the structural damage, a structure must be located at a safe distance away from the vegetation where flow becomes sub-critical.

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Dasgupta, Ratul, and Gaurav Tomar. "Viscous Undular Hydraulic Jumps of Moderate Reynolds Number Flows." Procedia IUTAM 15 (2015): 300–304. http://dx.doi.org/10.1016/j.piutam.2015.04.042.

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Lennon, J. M., and D. F. Hill. "Particle Image Velocity Measurements of Undular and Hydraulic Jumps." Journal of Hydraulic Engineering 132, no. 12 (December 2006): 1283–94. http://dx.doi.org/10.1061/(asce)0733-9429(2006)132:12(1283).

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Jurisits, Richard, and Wilhelm Schneider. "Undular hydraulic jumps arising in non-developed turbulent flows." Acta Mechanica 223, no. 8 (April 28, 2012): 1723–38. http://dx.doi.org/10.1007/s00707-012-0666-4.

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EL, G. A., R. H. J. GRIMSHAW, and N. F. SMYTH. "Transcritical shallow-water flow past topography: finite-amplitude theory." Journal of Fluid Mechanics 640 (November 4, 2009): 187–214. http://dx.doi.org/10.1017/s0022112009991315.

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We consider shallow-water flow past a broad bottom ridge, localized in the flow direction, using the framework of the forced Su–Gardner (SG) system of equations, with a primary focus on the transcritical regime when the Froude number of the oncoming flow is close to unity. These equations are an asymptotic long-wave approximation of the full Euler system, obtained without a simultaneous expansion in the wave amplitude, and hence are expected to be superior to the usual weakly nonlinear Boussinesq-type models in reproducing the quantitative features of fully nonlinear shallow-water flows. A combination of the local transcritical hydraulic solution over the localized topography, which produces upstream and downstream hydraulic jumps, and unsteady undular bore solutions describing the resolution of these hydraulic jumps, is used to describe various flow regimes depending on the combination of the topography height and the Froude number. We take advantage of the recently developed modulation theory of SG undular bores to derive the main parameters of transcritical fully nonlinear shallow-water flow, such as the leading solitary wave amplitudes for the upstream and downstream undular bores, the speeds of the undular bores edges and the drag force. Our results confirm that most of the features of the previously developed description in the framework of the unidirectional forced Korteweg–de Vries (KdV) model hold up qualitatively for finite amplitude waves, while the quantitative description can be obtained in the framework of the bidirectional forced SG system. Our analytic solutions agree with numerical simulations of the forced SG equations within the range of applicability of these equations.

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Chanson, H., and J. S. Montes. "Characteristics of Undular Hydraulic Jumps: Experimental Apparatus and Flow Patterns." Journal of Hydraulic Engineering 121, no. 2 (February 1995): 129–44. http://dx.doi.org/10.1061/(asce)0733-9429(1995)121:2(129).

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Ohtsu, Iwao, Youichi Yasuda, and Hiroshi Gotoh. "Flow Conditions of Undular Hydraulic Jumps in Horizontal Rectangular Channels." Journal of Hydraulic Engineering 129, no. 12 (December 2003): 948–55. http://dx.doi.org/10.1061/(asce)0733-9429(2003)129:12(948).

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Roy Biswas, Tirtha, Subhasish Dey, and Dhrubajyoti Sen. "Undular Hydraulic Jumps: Critical Analysis of 2D RANS-VOF Simulations." Journal of Hydraulic Engineering 147, no. 11 (November 2021): 06021017. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0001939.

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Berman, A. S., T. S. Lundgren, and A. Cheng. "Asynchronous whirl in a rotating cylinder partially filled with liquid." Journal of Fluid Mechanics 150 (January 1985): 311–27. http://dx.doi.org/10.1017/s0022112085000143.

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Experimental and analytical results are presented for the self-excited oscillations that occur in a partially filled centrifuge when centrifugal forces interact with shallow-water waves. Periodic and aperiodic modulations of the basic whirl phenomena are both observed and calculated. The surface waves are found to be hydraulic jumps, undular bores or solitary waves.

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GOTOH, Hiroshi, Youichi YASUDA, and Iwao OHTSU. "Effect of channel slope on flow characteristics of undular hydraulic jumps." Journal of applied mechanics 7 (2004): 953–60. http://dx.doi.org/10.2208/journalam.7.953.

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Ohtsu, Iwao, Youichi Yasuda, Hiroshi Gotoh, Willi H. Hager, Roger Reinauer, H. Chanson, and J. S. Montes. "Discussions and Closure: Characteristics of Undular Hydraulic Jumps: Experimental Apparatus and Flow Patterns." Journal of Hydraulic Engineering 123, no. 2 (February 1997): 161–64. http://dx.doi.org/10.1061/(asce)0733-9429(1997)123:2(161).

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Journal articles on the topic 'Undular hydraulic jump'

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