Bottom Roughness Research Articles

A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions

Inspired by the lubrication framework, in this paper we consider a micropolar fluid flow through a rough thin domain, whose thickness is considered as the small parameter ε while the roughness at the bottom is defined by a periodical function with period of order εℓ and amplitude εδ, with δ> ℓ >1. Assuming nonzero boundary conditions on the rough bottom and by means of a version of the unfolding method, we identify a critical case δ = 3/2ℓ − 1/2 and obtain three macroscopic models coupling the effects of the rough bottom and the nonzero boundary conditions. In every case we provide the corresponding micropolar Reynolds equation. We apply these results to carry out a numerical study of a model of squeeze-film bearing lubricated with a micropolar fluid. Our simulations reveal the impact of the roughness coupled with the nonzero boundary conditions on the performance of the bearing, and suggest that the introduction of a rough geometry may contribute to enhancing the mechanical properties of the device.

Spin-down of a barotropic vortex by irregular small-scale topography

This study examines the impact of small-scale irregular topographic features on the dynamics and evolution of large-scale barotropic flows in the ocean. A multiscale theory is developed, which makes it possible to represent large-scale effects of the bottom roughness without explicitly resolving small-scale variability. The analytical model reveals that the key mechanism of topographic control involves the generation of a small-scale eddy field associated with considerable Reynolds stresses. These eddy stresses are inversely proportional to the large-scale velocity and adversely affect mean circulation patterns. The multiscale model is applied to the problem of topography-induced spin-down of a large circularly symmetric vortex and is validated by corresponding topography-resolving simulations. The small-scale bathymetry chosen for this configuration conforms to the Goff–Jordan statistical spectrum. While the multiscale model formally assumes a substantial separation between the scales of interacting flow components, it is remarkably accurate even when scale separation is virtually non-existent.

Midfrequency sound transmission from mobile sources in a deep Arctic ocean at short and medium ranges: Time-domain modeling and data analysis

Midfrequency (2300–3000 Hz) LFM sweeps (3 s-long, one per minute) and CW 57 s-long signals at multiple frequencies (950, 1050, 1150, 2800, 2900, and 3000 Hz) were transmitted by two mobile sources EMATTs moving at three knots in circular patterns under ice in the Beaufort Sea on March 12, 2016. Acoustic pressure time series were recorded on five vertically and horizontally separated receivers Acousonde, which provided different combinations of source-receiver ranges (0.3–10 km) and depths (45–183 m). A time-domain model of propagation and reverberation is suggested that accounts for refraction in water column and scattering from ocean boundaries (bottom and ice). Effects of spatial variations of the environment, particularly the two shallow ducts, at 0–75 m and 75–250 m water depths, as well as bottom and ice roughness, are demonstrated. Preliminary results of the model-data comparisons are presented. Possibilities for remote sensing of the arctic environment are discussed. [Work supported by ONR.]

ADCP‐based estimates of lateral turbulent Reynolds stresses in wavy coastal environments

AbstractWe assess the use of a four‐beam, Janus‐type ADCP for the measurement of lateral Reynolds stress () in wavy coastal environments. The calculation of derives either from the fluctuating beam velocity equations or directly from the fluctuating part of the Cartesian velocities (), with each requiring different assumptions. We adapt existing wave‐turbulence decomposition strategies to isolate the lateral turbulent motions at frequencies below those of surface gravity waves. The performance of the proposed method is evaluated via comparisons with independent ADV‐based stress estimates at two sites. Comparisons show good quantitative agreement over the tidal cycle, and indicate that ADCPs can effectively resolve lateral turbulent fluxes via ensemble‐averaging. Assessment of ensemble‐averaged turbulence cospectra indicates that the proposed approach is effective in isolating the low‐frequency (below the waveband) turbulent stresses from wave‐induced errors. Furthermore, the vertical structure of the turbulent Reynolds stresses is examined as a function of tidal phase in an unstratified, tidally‐driven flow over a rough coral reef seabed in weak swell conditions. Observations and analysis indicate that lateral fluxes are tied to the cross‐shore (lateral) gradient of the mean alongshore flow, though vertical and lateral stresses are primarily driven by bottom‐generated turbulence. Scaling considerations indicate that cross‐shore transport by lateral turbulent mixing could be relevant to coral reef shelves with steep cross‐reef slopes and rough bottoms.

Контроль течений на поверхности прибрежных морских акваторий дистанционными методами

Object and purpose of research. The compare analysis carried out on the vorticies structure optical satellite pictures observation of the sea surface and the velocities field obtained by the ground HF Doppler radar. The purpose of this research is estimation of the possibility on fast monitoring feasibility assessment for the changes in littoral waters dynamics through joint application of satellite surveillance, radar probing of sea currents, wind data and numerical simulation of water circulation in the area under investigation. Materials and methods. The Sea surface observation data obtained by the satellites Sentinel 1 and 2 and by the coastal Doppler HF radar Sea Sonde in the South-east Black Sea area are analyzing. The additional data on the satellite observation of this area and on the wind condition is used from LANCE processing system [9, 10] and reanalysis NCEP/NCAR [11, 12]. The comparative analysis is carried out on the large vertical structures (LVS) establishing in the research coastal area. The numerical modeling of the water mass circulation in this area is carried out by the software package COHERENS (Belgian Institute of Natural Science) to investigate the role of the wind conditions at LVS appearance in the research area. Main results. The LVS in the vicinity of Sea coast line could be generated, as satellites observations demonstrated, by the vortices arrived along the coast line from the east-south direction in accordance with the Black Sea general circulation flow. Such vortices could be induced by the bottom roughness, rivers discharges and another local sources. Another LVS source could be connected with the wind impact in some affordable direction as demonstrated by the numerical modeling of the coastal water circulation. The continuous currents measurements at the Sea surface by Doppler HF coastal Radar supply the valuable data for further details on the space –time variation of LVS parameters and operational forecast of the hydrology regime in the aquatic areas. The operative numerical modelling of the wind impact to the surface currents structures formation provides the efficient estimation of the local large vorticity structure appearance in the research area. Conclusion. Satellite radar and optical observation provide the large scale control on the Sea surface dynamics conditions, but that is limited by relatively long interval between satellite tracks over the region of interest and do not acquire optical data at the cloud cover. The additional data could be operative obtain from the open internet resource in satellite optical, radar and meteorological data (LANCE, NCEP/NCAR), to get the more details development of the Sea surface dynamics. Sub-satellite Sea currents measurements by HF Doppler radar are useful for the reliable interpretation of satellite pictures and for the proper forecast of the aquatic area dynamics. Operative numerical modelling of the Sea coastal water circulation in accordance with variable meteo data combining with dynamic processes remote measurements could be efficient for the forecast of the environment parameters variation due the water mass transfer. In general the presented results demonstrates the combined application possibilities of the satellite observations, coastal Doppler radar measurements, internet data and operative numerical modelling for operational oceanographic and ecological monitoring of Sea coastal areas with heavy pollution load.

Topographic Stabilization of Ocean Rings

AbstractCoherent large‐scale vortices in the open ocean can retain their structure and properties for periods as long as several years. However, the patterns of potential vorticity in such vortices suggest that they are baroclinically unstable and therefore should rapidly disintegrate. This study proposes a plausible explanation of the longevity of large‐scale ocean rings based on bottom roughness, which restricts flow in the lower layer and thereby stabilizes the eddy. We perform a series of simulations in which topography is represented by the observationally derived Goff‐Jordan spectrum. We demonstrate that topography stabilizes coherent vortices and dramatically prolongs their lifespan. In contrast, the same vortices in the flat‐bottom model exhibit strong instability and fragmentation on the timescale of weeks. A critical depth variance exists that allows vortices to remain stable and circularly symmetric indefinitely. Our investigation underscores the essential role played by topography in the dynamics of large‐ and meso‐scale flows.

Lock-release gravity currents propagating over roughness elements

The influence of bottom roughness on the development of lock-release gravity currents is investigated through laboratory experiments using Particle Image Velocimetry. The bottom roughness is represented by arrays of vertical LEGO bricks with a constant spacing while varying lambda , the relative height of the roughness elements to the gravity current depth. Depending on lambda , the roughness elements may affect the gravity current propagation: for small lambda the current behaves like moving over a smooth bottom, while for larger lambda the propagation speed is reduced and the internal structure of the current, including both the head and the tail, is significantly modified. As lambda increases, stronger recirculation areas between the roughness elements develop interacting with the overlying layer and giving rise to small-scale vortical structures of opposite sign within the whole depth of the current. The additional drag force induced by the bottom roughness adds significant complexity to the flow dynamics and modifies the characteristics of the current.

Uncertainties Associated With Simulating Regional Sea Surface Height and Tides: A Case Study of the East China Seas

Modeling sea surface height (SSH) and tides is important but challenging in shelf seas. The Eastern China Seas (ECSs) is such a shelf sea with large inter-model deviations in prior studies. In order to assess and compare the possible uncertainty sources, numerical scenarios of varying the open boundary forcing, bottom roughness length scale, atmospheric forcing, grid resolution, and regional bathymetry were conducted in a hydrodynamic model of the ECSs. Results indicate that bathymetry data and open boundary forcing with inadequate accuracy generate uncertainties in SSH and tides locally and throughout the basin. An increase in bottom roughness enhances tidal dissipation and shifts amphidromes to the left relative to the incoming Kelvin waves, causing SSH variations in the ECSs. Refining the model resolution from 4 to 2 km mainly affects nearshore SSH and tides due to minor changes in depicted coastlines. Using different reanalysis meteorological data appears more important on the episodic than annual scale. It is highlighted that some uncertainty sources have opposing effects on SSH or tides and counteract their individual biases, making it difficult to achieve a realistic simulation. For example, increasing bottom roughness can not only compensate effects of overestimated tidal amplitude at open boundaries, but also balance out the overestimated M2 phase along the West Coast of Korea in a coarser-resolution model. Based on findings in this study, suggestions are provided for further reducing uncertainties in SSH and tide modeling in the ECSs and other shelf seas.

A new discrete element modelling approach to simulate the behaviour of dense assemblies of true polyhedra

A new molecular dynamics-like modelling approach aimed at simulating the mechanical behaviour of true polyhedra dense assemblies is presented. Thanks to an improved version of the Gilbert-Johnson-Keerthi contact detection algorithm called GJK − TD, this approach involves no edge or corner rounding and accounts for multipoint face − face or edge − face contacts between any set of two particles. Furthermore, torques equations are simply and efficiently solved using an improved leap-frog Verlet non-iterative method suggested by Omelyan [I.P. Omelyan, Molecular Simulation, 22 : 3, 213–236 (1999)], in which no periodic renormalization of the quaternions is necessary. The potential of this new discrete element approach is then highlighted by simulating the gravity packing of frictionless polyhedra and the gavity flow of frictional polyhedra down an incline, and comparing the results with those reported in the literature. Of particular interest in the stationary flow regime, a linear decrease of the bulk solid fraction and a power law decrease of the bulk coordination number with increasing inertial number are observed, thus generalizing to polyhedra these observations initially made with disks in plane shear flow by da Cruz and co-workers [F.da Cruz, S. Emam, M. Prochnow, J.N. Roux and F. Chevoir, Phys. Rev. E 72, 021309, (2005)]. Beyond this regime, in the collisional regime, the granular temperature was found to achieve its maximum a few particle diameter above the rough bottom, suggesting the localization of significant particle agitation close to the flowing bed.

Wave Dissipation and Mean Circulation on a Shore Platform Under Storm Wave Conditions

AbstractWhile wave processes on shore platforms have been recently advanced by a number of field‐based studies, few attention has been paid to the role of bed roughness on wave dissipation and wave setup dynamics in these environments. This study reports on a new field experiment conducted under storm wave conditions on a gently sloping shore platform which was instrumented from 10 m water depth up to the shoreline. Data analyses are complemented with numerical simulations performed with a 3D fully coupled modeling system using a vortex force formalism to represent the effects of short waves on the mean circulation. An accurate representation of wave dissipation by both depth‐induced breaking and bottom friction is found essential to reproduce the transformation of short waves across the platform and the resulting wave setup. Wave energy dissipation by bottom friction is dominant in the subtidal part of the platform and contributes to about 40% of the total wave energy dissipation. The enhanced wave bottom friction on the platform decreases the wave height before breaking, which reduces the contribution of wave forces to the wave setup compared to a smooth bottom (mechanism 1). Conversely, an idealized analysis of the cross‐shore momentum balance reveals that the wave‐induced circulation increases the wave setup, this process being enhanced on a rough bottom (mechanism 2). The contribution of mechanism 2 increases with the bottom slope, accounting for up to 26% of the wave setup for a 1:20 sloping shore platform, and overcoming mechanism 1.

Modeling of Barrier Breaching During Hurricanes Sandy and Matthew

AbstractPhysical processes driving barrier island change during storms are important to understand to mitigate coastal hazards and to evaluate conceptual models for barrier evolution. Spatial variations in barrier island topography, landcover characteristics, and nearshore and back‐barrier hydrodynamics can yield complex morphological change that requires models of increasing resolution and physical complexity to predict. Using the Coupled Ocean‐Atmosphere‐Wave‐Sediment Transport (COAWST) modeling system, we investigated two barrier island breaches that occurred on Fire Island, NY during Hurricane Sandy (2012) and at Matanzas, FL during Hurricane Matthew (2016). The model employed a recently implemented infragravity (IG) wave driver to represent the important effects of IG waves on nearshore water levels and sediment transport. The model simulated breaching and other changes with good skill at both locations, resolving differences in the processes and evolution. The breach simulated at Fire Island was 250 m west of the observed breach, whereas the breach simulated at Matanzas was within 100 m of the observed breach. Implementation of the vegetation module of COAWST to allow three‐dimensional drag over dune vegetation at Fire Island improved model skill by decreasing flows across the back‐barrier, as opposed to varying bottom roughness that did not positively alter model response. Analysis of breach processes at Matanzas indicated that both far‐field and local hydrodynamics influenced breach creation and evolution, including remotely generated waves and surge, but also surge propagation through back‐barrier waterways. This work underscores the importance of resolving the complexity of nearshore and back‐barrier systems when predicting barrier island change during extreme events.

Devising a procedure to calculate and analyze parameters for passing the flood and breakthrough wave taking into consideration the topographical and hydraulic riverbed irregularities

It has been established that the most likely period of breakthrough wave occurrence is the time of spring flooding or heavy rain when water-head facilities are subjected to significant loads that lead to the collapse of their individual elements or the entire structure. In addition, the possibility of man-made accidents that can occur at any time cannot be ruled out. It has been proven that breakthrough wave formation depends on the nature of the destruction or the overflow through a water-head facility. For the study reported in this paper, a model of the kinematics of riverbed and breakthrough flows was used, which is based on the equations of flow, washout, and transport of sediments that are averaged for the depths of the stream. The differential equations describing the nonstationary flow averaged for depth are solved using the numerical grid system FST2DH (2D Depth-averaged Flow and Sediment Transport Model), which implements a finite-element method on the plan of a riverbed's topographic region. These tools are publicly available, which allows their wide application to specific loads and boundary conditions of mathematical models. The construction of an estimation grid involving the setting of boundary conditions and the use of geoinformation system tools makes it possible to simulate the destruction of a culvert of the pressure circuit and obtain results for a specific case of an actual riverbed and a water-head facility. It has been established that there is a decrease in the speed of wave propagation along the profile, from 3 m/s to 1 m/s. The impact of bottom irregularities, the effect of floodplains, and the variety of bottom roughness have also been assessed, compared to the results of their calculation based on one-dimensional models given in the regulatory documents. Hydraulic calculations were carried out taking into consideration the related properties of the main layer of the floodplain, which consists of peat accumulations, and the heterogeneity of the depths and roughness of floodplain surfaces of soils. It has been established that there is almost no erosion of supports in the floodplain zone in this case. It was found that as the distance between the flow and breakthrough intersection increases, there is a decrease in the height of the head from 2.1 m to 1.25 m.

Note on the Bulk Estimate of the Energy Dissipation Rate in the Oceanic Bottom Boundary Layer

The dissipation of the kinetic energy (KE) associated with oceanic flows is believed to occur primarily in the oceanic bottom boundary layer (BBL), where bottom drag converts the KE from mean flows to heat loss through irreversible mixing at molecular scales. Due to the practical difficulties associated with direct observations on small-scale turbulence close to the seafloor, most up-to-date estimates on bottom drag rely on a simple bulk formula (CdU3) proposed by G.I. Taylor that relates the integrated BBL dissipation rate to a drag coefficient (Cd) as well as a flow magnitude outside of the BBL (U). Using output from several turbulence-resolving direct numerical simulations, it is shown that the true BBL-integrated dissipation rate is approximately 90% of that estimated using the classic bulk formula, applied here to the simplest scenario where a mean flow is present over a flat and hydrodynamically smooth bottom. It is further argued that Taylor’s formula only provides an upper bound estimate and should be applied with caution in the future quantification of BBL dissipation; the performance of the bulk formula depends on the distribution of velocity and shear stress near the bottom, which, in the real ocean, could be disrupted by bottom roughness.

Seagrass Meadows Reduce Wind-Wave Driven Sediment Resuspension in a Sheltered Environment

Seagrass meadows are prominent in many coastal zones worldwide and significant contributors to global primary production. The large bottom roughness (or canopy) created by seagrass meadows substantially alters near-bed hydrodynamics and sediment transport. In this study, we investigate how a seagrass meadow in a low-energy environment (forced by local winds) modifies near-bed mean and wave-driven flows and assess how this relates to suspended sediment concentration (SSC). A two-week field study was conducted at Garden Island in southwestern Australia, a shallow and sheltered coastal region subjected to large diurnal sea-breeze cycles, typical of many low-energy environments where seagrasses are found. The mean and turbulent flow structure, along with optical estimates of SSC, were measured within both a seagrass canopy and over an adjacent bare bed. Near-bed mean current velocities within the seagrass canopy were on average 35% of the velocity above the canopy. Oscillatory wave velocities were less attenuated than mean current velocities, with near-bed values on average being 83% of those above the canopy. Mean and maximum shear velocities inferred from currents and waves above the canopy frequently exceeded the threshold for sediment resuspension, but no significant variation was observed in the SSC. However, a significant correlation was observed between SSC and bed shear stress estimated using near-bed velocities inside the canopy. When sediment was resuspended, there were substantial differences between the SSCs within and above the canopy layer, with higher levels confined within the canopy. This study demonstrates the importance of measuring near-bed hydrodynamic processes directly within seagrass canopies for predicting the role seagrass meadows play in regulating local rates of sediment resuspension.

Characteristics of cryogenic abrasive air-jet direct-write machining: A comparison with abrasive air-jet direct-write machining at oblique angles

• The velocity model of abrasive particles in the radial direction is modified. • Abrasive air-jet (AAJ) direct-writing of PDMS at 15° is presented. • Cryogenic abrasive air-jet (CAAJ) direct-writing of PDMS is presented. • CFD models of AAJ and CAAJ direct-writing are established. • "U"-shaped micro-channels are obtained by CAAJ and compared against AAJ at 15°. Cryogenic abrasive air-jet (CAAJ) machining technology is performed simultaneously with the occurrence of the glass transition for PDMS material. However, the mask material is also cooled with cryogenic PDMS cooling. Then, they both show significant brittle characteristics. Therefore, this leads to very poor selectivity between the mask and the PDMS. To solve this problem, CAAJ direct-write machining under unmasking conditions are proposed based on the modified velocity model of abrasive particles in the radial direction. This technique was used to direct-write machined the PDMS materials under small SOD. Then, the effect of cryogenic conditions on machining characteristics of PDMS micro-channels was studied by comparing the abrasive air-jet direct-write machining at oblique angles and CAAJ direct-write machining technologies through a series of experimental studies and CFD simulations. The results show that the material removal mode is transformed to a semi-brittle one, which greatly improves erosion removal efficiency, aspect ratio and bottom surface roughness of the micro-channel. On the other hand, the change in the viscosity of the jet medium has a crucial influence on the geometry of the micro-channel. The rebound direction of abrasive particles changes, and the sidewall of micro-channels is secondarily eroded due to an increase in jet medium viscosity in CAAJ. This, in turn, leads to a micro-channel with "U"-shaped profile. In addition, during CAAJ direct-write machining, sliding, scratching, and rolling of abrasive particles caused by bubble bursting can effectively reduce the bottom surface roughness of the micro-channel.

Формула расхода воды через плоский щитовой затвор в открытом русле

The purpose of the research is to analyze the influence of the flow kinematic structure on the measuring accuracy of the water flow through the flat sluice gate in the open channel. For the simulation and analysis of the flow through the sluice gate, the DisCo4 software-computer complex developed by the author was used based on the numerical solution of the system of equations (RANS) and continuity by the finite volume method in the three-dimensional formulation. It was found that installation of the sluice gate on the thin transverse wall can signifi cantly reduce the effect of the channel bottom roughness on the water flow through the gate. The analytical formula for discharge through the flat sluice gate of the considered structure is proposed. Regardless of the channel roughness, the scatter of calculated discharges in the range of ratios of the height of the hole to the depth relative to the lower edge of the hole Hg /H < 0.3 is no more than 3%.

Calibration of a 3D hydrodynamic model for a hypertidal estuary with complex irregular bathymetry using adaptive parametrization of bottom roughness and eddy viscosity

This study introduces a new scheme to make both turbulence and flow resistance modeling a dynamic function of tidal water depths and flow direction. The k−ε turbulence model is continuously adapted to local depth conditions and the Manning n bed roughness values are continuously made locally dependent on the direction of flow. Turbulence structure, production, and attenuation in estuaries are highly influenced by the fact that the flow occurs in ‘shallow water’. In hypertidal estuaries with complex bathymetries, the depths are highly variable in both time and space. In this paper, an adaptive correction scheme is introduced to dynamically adjust (in time and space) the k−ε turbulence model as a function of local flow depth. Furthermore, in the flow reversal portions of tidal rivers, flow direction changes cyclically during flood tides and ebb tides. This causes a direction-based pattern of bedforms that significantly affects the directional values of hydrodynamic bed resistance (Manning n). In this paper, an adaptive scheme accounts for flow directionality. The modifications are incorporated into a three-dimensional numerical hydrodynamic model (Delft3D). The resulting simulated water levels of the Koksoak hypertidal estuary are presented and are demonstratively in better agreement with observations than water levels simulated when not using the corrections. The results suggest that the proposed schemes can improve the accuracy of the turbulence and bed roughness models for simulations of shallow hypertidal estuarine flows with complex river bathymetries.

Fabrication of Microgrooves by Synchronous Hybrid Laser and Shaped Tube Electrochemical Milling.

The fabrication of deep microgrooves has become an issue that needs to be addressed with the introduction of difficult-to-cut materials and ever-increasing stringent quality requirements. However, both laser machining and electrochemical machining could not fulfill the requirements of high machining efficiency and precision with good surface quality. In this paper, laser and shaped tube electrochemical milling (Laser-STEM) were initially employed to fabricate microgrooves. The mechanisms of the Laser-STEM process were studied theoretically and experimentally. With the developed experimental setup, the influences of laser power and voltage on the width, depth and bottom surface roughness of the fabricated microgrooves were studied. Results have shown a laser power of less than 6 W could enhance the electrochemical machining rate without forming a deep kerf at the bottom during Laser-STEM. The machining accuracy or localization of electrochemicals could be improved with laser assistance, whilst the laser with a high-power density would deteriorate the surface roughness of the bottom machining area. Experimental results have proved that both the machining efficiency and the machining precision can be enhanced by synchronous laser-assisted STEM, compared with that of pure electrochemical milling. The machining side gap was decreased by 62.5% while using a laser power of 6 W in Laser-STEM. The laser-assistance effects were beneficial to reduce the surface roughness of the microgrooves machined by Laser-STEM, with the proper voltage. A laser power of 3 W was preferred to obtain the smallest surface roughness value. Additionally, the machining efficiency of layer-by-layer Laser-STEM can be improved utilizing a constant layer thickness (CLT) mode, while fabricating microgrooves with a high aspect ratio. Finally, microgrooves with a width of 1.79 mm, a depth of 6.49 mm and a surface roughness of 2.5 μm were successfully fabricated.

Numerical investigation of the effects of distributary bathymetry and roughness on tidal hydrodynamics of Wax Lake region under calm conditions

In this paper, we investigate the effects of the bathymetry of the floodplain distributaries using a 2-dimensional hydrodynamic model of the Wax Lake Outlet (WLO), delta and floodplain (Louisiana, USA), using Delft3D. Modelling the tidal-fluvial interaction of this region is challenging because of its complex network of low-lying floodplain distributaries and vegetation coverage. This investigation addresses this interaction by generating the evolution of the flood-map that is used in the calibration and validation phase of the Surface Water and Ocean Topography (SWOT) mission. Accordingly, the model is set up for one week of calm conditions from October 14th to 20th in 2016. Boundary conditions applied at the edges of the 36 × 23 km2 domain include the offshore water level with tidal oscillations, the upstream volumetric river discharge rate and wind time-series (applied spatially uniformly). The topo-bathymetry of the domain is a product of the Pre-Delta-X mission; however, it has considerable uncertainties to represent the small distributaries, especially in the forested section of the region. This paper tackles this uncertainty by parametrically enhancing and calibrating the primary Digital Terrain Model (DTM). The performance of the model is assessed using the water-level time series measured by the stations spread throughout the floodplain, delta and main river. The results show that the morphology of the distributaries play a major role in the hydrodynamic of Wax Lake region under calm conditions. The hydrodynamic of the WLO and floodplain is considerably affected by the discharge capacity of the distributaries (changed by editing their width and depth) due to change of the balance between roughness and topographic convergence. In WLO, higher discharge capacity leads to higher overall roughness friction force, thereby dampening the amplitude of the water-level signal and vice versa. On the other hand, increasing the bottom roughness of the WLO increases the water level in the floodplain, with more considerable effect in the low tides. The calibrated model well matches the measurements along the Wax Lake Outlet. However, the main discrepancies are in the stations further away from the WLO. The tests conducted in this research suggest that the excessive roughness due to uneven bed along the distributaries and vegetation are, respectively, the potentially-responsible parameters for the remaining discrepancies in low- and high-tide periods.

Oblique undular hydraulic jumps in turbulent free‐surface flows

AbstractSteady turbulent near‐critical free‐surface flow over a slightly inclined bottom with an oblique roughness discontinuity is considered. An asymptotic analysis for Froude numbers close to the critical value 1 and large Reynolds numbers results in an extended Korteweg–de Vries (KdV) equation describing the free‐surface elevation without the need of turbulence modeling. Two new integral relations can be derived from the extended KdV equation. For enlarged downstream bottom roughness, a new type of undular jump solutions with fully developed flow both upstream and downstream exists. Numerical solutions of the extended KdV equation show that an increasing downstream bottom roughness enhances the development of undulations.