Vertical Velocity Profiles Research Articles

Methods to Evaluate Subcolumn Profiles Based on Two‐Point Diagnostics

AbstractIn atmospheric models, stochastic generation of subgrid‐scale profiles or “subcolumns” has been used for a variety of purposes. Such subcolumns can be generated from subgrid probability density functions (PDFs) at different vertical levels, when such PDFs are available. To do so, the generator needs to decide how strongly points should be correlated in the vertical, that is, how much the values should be overlapped. This is sometimes called “PDF overlap.” To assess vertical correlation in a simplified, observable setting, here the vertical correlation of vertical velocity in subcloud layers is examined. Doppler lidar is used to evaluate the vertical profiles of vertical velocity produced by a large‐eddy simulation (LES) model and the Subgrid Importance Latin Hypercube Sampler (SILHS) subcolumn generator. In order to diagnose unrealistic features in subcolumn profiles, various statistical diagnostics are examined here, including the bivariate PDF of vertical velocity at two separated points (i.e., altitudes), the two‐point velocity correlation, the integral correlation length, the PDF of two‐point velocity differences, and the skewness and kurtosis of two‐point velocity differences. The profiles produced by LES match lidar well, except that they are too smooth at small scales. The profiles produced by SILHS exhibit sharp jumps from updraft to downdraft that are not observed in the lidar data. To reduce the generation of these unrealistically sharp jumps, the SILHS sampling method is revised. The diagnostics confirm that the revised sampling method reduces the overprediction of sharp jumps.

The Paris low-level jet during PANAME 2022 and its impact on the summertime urban heat island

Abstract. The low-level jet (LLJ) and the urban heat island (UHI) are common nocturnal phenomena. While the UHI has been studied extensively, interactions of the LLJ and the urban atmosphere in general (and the UHI in particular) have received less attention. In the framework of the PANAME (PAris region urbaN Atmospheric observations and models for Multidisciplinary rEsearch) initiative in the Paris region, continuous profiles of horizontal wind speed and vertical velocity were recorded with two Doppler wind lidars (DWLs) – for the first time allowing for a detailed investigation of the summertime LLJ characteristics in the region. Jets are detected for 70 % of the examined nights, often simultaneously at an urban and a suburban site, highlighting the LLJ regional spatial extent. Emerging at around sunset, the mean LLJ duration is ∼ 10 h, the mean wind speed is 9 m s−1, and the average core height is 400 m above the city. The temporal evolution of many events shows signatures that indicate that the inertial oscillation mechanism plays a role in the jet development: a clockwise veering of the wind direction and a rapid acceleration followed by a slower deceleration. The horizontal wind shear below the LLJ core induces variance in the vertical velocity (σw2) above the urban canopy layer. It is shown that σw2 is a powerful predictor for regional contrast in air temperature, as the UHI intensity decreases exponentially with increasing σw2 and strong UHI values only occur when σw2 is very weak. This study demonstrates how DWL observations in cities provide valuable insights into near-surface processes relevant to human and environmental health.

Assessing Turbulence Model Performance in OpenFOAM for Natural Convection Simulations

Abstract Natural convection processes are pivotal in various engineering applications, necessitating accurate and reliable computational fluid dynamics (CFD) models for their simulation. This study evaluates the efficacy of different turbulence models implemented in OpenFOAM for a natural convection scenario, aiming to identify the most suitable model for capturing complex thermal and fluid dynamic behaviors. We compared several turbulence models, including the k − ε, k − ω, and k − ω SST, using a benchmark thermal convection case. Our methodology involved setting up the simulations to reflect realistic thermal gradients and boundary conditions, followed by a rigorous analysis of temperature distribution, vertical velocity profiles, and computational efficiency. The results indicate that the k − ω SST achieved the lowest averaged root mean square error (RMSE) values for temperature (0.076) and vertical velocity (0.03) while also requiring the fewest convergence iterations (314) compared to k − ε (411) and k − ω (1474). These findings demonstrate that the k − ω SST model is a suitable compromise between accuracy and computational cost for engineering applications. This study underscores the importance of selecting an appropriate turbulence model in OpenFOAM to enhance the accuracy of natural convection simulations, which can significantly influence design and safety considerations in engineering systems.

Characteristics of gusts with different velocity profiles and control parameters

The characteristics of gust flow are essential for gust response and alleviation. To investigate the influence of control parameters on gusts with different velocity profiles, four vertical gust profiles were designed. Methods were proposed to generate them with two pitching airfoils in a low-speed water tunnel. The velocity field was measured via phase-locked particle image velocimetry. The coefficient of determination R2 was proposed to evaluate the generated gust profile quality, which referred to the quality of the vertical velocity profile. The influence of control parameters on different gust profiles was investigated, and the cause of the profile distortion was explored. For continuous sine gusts, the gust ratio GR increased approximately linearly with the pitching amplitude, while the gust ratio initially increased and then decreased with increasing frequency. As the two control parameters increased, the flow uniformity decreased because the airfoil wakes disturbed the measured flow field. In terms of continuous 1-cosine gusts, the gust ratio increased nonlinearly with pitching amplitude. Compared with those of the sine gusts, the GR values of the 1-cosine gusts were higher, whereas the R2 values were lower. In addition, the discrete and continuous gust profiles had similar distortion near the peaks. However, discrete gusts had lower R2 values than continuous gusts because the starting and stopping vortices of the pitching airfoils disturbed the gust flow. Based on these findings, a method to improve the profile quality and field uniformity by increasing the spacing of the pitching airfoils was proposed. This work can support further studies of gust response and alleviation during complex gust encounters.

Features of Earth’s lower ionosphere during solar eclipse and sunset and sunrise hours according to measurements by the API method near Nizhny Novgorod

We present the results of experimental studies into the response of Earth’s lower ionosphere to a partial solar eclipse. The studies have been carried out using the method of resonant scattering of radio waves by artificial periodic irregularities (APIs) in ionospheric plasma. The irregularities were created in the field of a standing wave when a powerful radio wave, generated by radiation to the zenith by transmitters of the mid-latitude heating facility SURA, was reflected from the ionosphere. During location of a periodic structure by probe radio waves when the Wolf—Bragg backscattering condition was met, a scattered signal was received and its amplitude and phase were measured. After the end of the impact on the ionosphere, the irregularities gradually disappeared (relaxed). We have examined variations in characteristics of scattered signals. During the eclipse, the scattered signal amplitude increased by 30–40 dB, and the relaxation time increased 1.5–2.0 times. In some cases, stratification of the signal amplitude in the D-region was observed due to stratification of the electron density profile. By analyzing altitude profiles of relaxation time, we obtained neutral component temperature and density, height of the turbopause, and turbulent velocity. The velocity of vertical regular motion of plasma at each height was measured from the time variation in the scattered signal phase. From the results of measurements of scattered signal characteristics during four partial eclipses, we have obtained that the neutral component temperature decreases, on average, 50–70 K. Variations in the temperature, vertical plasma velocity, and turbopause level exhibited deep quasi-periodic variations with periods from 15 min to several hours, typical of internal gravity wave propagation. The vertical temperature and velocity profiles showed changes with altitude on scales ranging from 5 to 30 km. Comparison between the results of studies of the lower ionosphere during sunrise-sunset hours has revealed that its response during a partial eclipse and the transition to the night regime is identical. According to the measurements by the partial reflection method, during the August 01, 2008 eclipse there was a decrease in the electron density in the D-region 3–5 times. We have concluded that during an eclipse there was a significant change in both the ionized and neutral components of the atmosphere in the lower ionosphere.

Особенности нижней ионосферы Земли во время затмений Солнца и в заходно-восходные часы по измерениям методом ИПН вблизи Нижнего Новгорода

We present the results of experimental studies into the response of Earth’s lower ionosphere to a partial solar eclipse. The studies have been carried out using the method of resonant scattering of radio waves by artificial periodic irregularities (APIs) in ionospheric plasma. The irregularities were created in the field of a standing wave when a powerful radio wave, generated by radiation to the zenith by transmitters of the mid-latitude SURA heating facility, was reflected from the ionosphere. During the eclipse, the scattered signal amplitude increased by 30–40 dB, and the relaxation time increased 1.5–2.0 times. In some cases, stratification of the signal amplitude in the D-region was observed due to stratification of the electron density profile. By analyzing altitude profiles of relaxation time, we obtained neutral component temperature and density, height of the turbopause, and turbulent velocity. The velocity of vertical regular motion of plasma at each height was measured from the time variation in the scattered signal phase. From the results of measurements of scattered signal characteristics during four partial eclipses, we have obtained that the neutral component temperature decreases, on average, 50–70 K. Variations in the temperature, vertical plasma velocity, and turbopause level exhibited deep quasi-periodic variations with periods from 15 min to several hours, typical of internal gravity wave propagation. The vertical temperature and velocity profiles showed changes with altitude on scales ranging from 5 to 30 km. Comparison between the results of studies of the lower ionosphere during sunrise-sunset hours has revealed that its response during a partial eclipse and the transition to the night regime is identical. According to the measurements by the partial reflection method, during the August 01, 2008 eclipse there was a decrease in the electron density in the D-region 3–5 times. We have concluded that during an eclipse there was a significant change in both the ionized and neutral components of the atmosphere in the lower ionosphere.

Evolution of Turbulent Boundary Conditions on the Surface of Large Barchan Dunes: Anomalies in Aerodynamic Roughness and Shear Velocity, Aeolian Threshold, and the Role of Dune Skewness

AbstractWe recorded aerodynamic roughness and shear velocity along transects on and around mature crescent‐shaped barchan dunes of and height above the horizontal rock‐covered Qatar desert by fitting to the log‐law time‐averaged vertical velocity profiles acquired from triads of ultrasonic anemometers penetrating the inner turbulent boundary layer. Shear velocity first decreased, then recovered as air climbed on the dune, with a local maximum ahead of the crest as predicted by the Jackson and Hunt (1975, https://doi.org/10.1002/qj.49710143015) theory. Unlike flows over gentler bedforms without a slope discontinuity, an anomalous peak of shear velocity also arose on the dune centerline at the brink, which the theory attributed to skewness in the dune transect profile. The onset of aeolian transport produced a log‐law passing through the Bagnold (1941, https://doi.org/10.1007/978‐94‐009‐5682‐7) focal point. It was bracketed by noticeable hysteretic peaks in the correlation between wind speed and entrained sand flux. The dunes' rocky surroundings and topography produced an aerodynamic roughness at odds with the Nikuradse (1933, https://ntrs.nasa.gov/citations/19930093938) data for fully developed turbulent boundary layers. Large‐eddy numerical simulations illustrated the sensitivity of shear velocity to wide changes in aerodynamic roughness from desert floor to dune surface.

Turbulence and sediment deposition in a channel with floating vegetation

Floating canopies of vegetation alter the vertical profile of flow velocity within and below canopies, which in turn impacts sediment deposition below canopies. This study explored the impacts of channel-average velocity (U0), vegetation density (a), and relative flow depth (hg/H, where hg is the height of the free flow region below the floating canopy and H is the entire flow depth) on the longitudinal distributions of near-bed turbulent kinetic energy (TKE) and sediment deposition in a channel with a floating vegetation canopy. Below a floating canopy, sediment deposition was correlated with the near-bed TKE. For the low-density and low-velocity cases, sediment deposition was spatially uniform across the entire channel because the near-bed TKE was lower than the critical value for sediment resuspension. As the vegetation density and channel-average velocity increased, the near-bed TKE increased and surpassed the critical TKE, which caused resuspension and reduced deposition below the canopy relative to the upstream reference. For the same vegetation density and channel-average velocity, a lower relative flow depth (hg/H) produced a higher below-canopy depth-averaged velocity and near-bed TKE, resulting in less deposition below the canopy. A model was proposed for predicting the longitudinal evolution of near-bed TKE based on the predicted flow velocity below the canopy throughout the channel. The longitudinal evolution of deposition below a floating canopy was predicted by combining the predicted near-bed TKE with the deposition probability. The predicted near-bed TKE and deposition matched laboratory measurements. Finally, the proposed model can be used to predict the longitudinal profile of deposition below a real Eichhornia crassipes canopy.

Quantification of Mixing Depth Using the Gradient Richardson Number in Submerged Aquatic Vegetation Meadows

AbstractUpper layer thickness (mixing depth) is an essential parameter for estimating the dissolved inorganic carbon and carbon flux at the water surface based on their association with the vertical flux of dissolved inorganic carbon. Previous studies quantified the mixing depth without SAV meadow or penetration depth in the SAV meadow without stratification and wind stress. However, mixing depth related to interaction with submerged aquatic vegetations (SAVs), stratification, and wind stress has yet to be quantified in the previous studies. Our study is the first to quantify the theoretical mixing depth with SAVs according to wind stress, SAV height, and drag coefficient. Theoretical mixing depth was quantified from modeled vertical temperature profile, vertical profile of horizontal velocity, and gradient Richardson number (Rig,veg). We found that mixing depth at a Rig,veg of 100 demonstrated good agreement with numerical results on average, with the mixing depth estimated in this study (hU,this study) showing high applicability to observations at Komuke Lagoon. Moreover, hU,this study increased with the increasing wind stress and decreasing drag coefficient and SAV height. Further, we found that SAV meadows with stratification and wind stress could be divided into four hydrodynamic regimes: non‐vegetated layers, upper vegetated layers, thermoclines, and benthic boundary layers. Our findings help us estimate mixing depth or vertical flux without complicated numerical simulation and understand flow interaction with SAV, wind stress, and stratification.

Influence of Time-Varying Freestream Conditions on the Dynamics of Unsteady Boundary-Layer Separation

Unsteady flow separation of a turbulent boundary layer under dynamic pressure gradients is investigated using the Large-Eddy Simulation technique. The unsteadiness is introduced by prescribing an oscillating freestream vertical-velocity profile at the top boundary of the domain. Although previous studies, including Ambrogi et al. (Journal of Fluid Mechanics, Vol. 945, Aug. 2022, p. A10) and Ambrogi et al. (Journal of Fluid Mechanics, Vol. 972, Oct. 2023, p. A36), focused on the kinematics of the flow and the effects of the oscillation frequency on flow separation, the goal of this paper is to analyze the effects of three time-varying freestream-forcing profiles while the oscillation frequency is kept the same for all Cases. Whereas in Case A the freestream-velocity profile changes from suction–blowing to blowing–suction in a complete cycle, Cases B and C are both suction–blowing only and the strength of the adverse pressure gradient is modulated in time. Moreover, the boundary layer in Case B never approaches a zero-pressure gradient condition. A closed separation bubble is formed for all Cases; however, its dimensions change depending on the far-field forcing. The time evolution of turbulent kinetic energy (TKE) reveals an advection mechanism of turbulent structures out of the domain for all Cases. Whereas in Case A and C the high-TKE region, generated in the separated shear layer, is washed out of the domain as a rigid body, in Case B the separation bubble remains present and the advection mechanism of TKE is characterized by a breathing pattern.

Hydraulic conditions created by a ‘large’ diameter Cylindrical Bristle Cluster fish pass

Cylindrical Bristle Clusters (CBCs) provide a multi-species fish passage solution at sloped weirs. Configurations trialled to date (min. diagonal spacing between CBCs up to 0.17 m) were designed to facilitate passage of relatively small (e.g. < 30 cm) potamodromous species and may hamper the movements of larger bodied (e.g. > 40 cm) fishes, such as adult anadromous salmonids. Therefore, in this study, the hydraulic conditions created by an array of large diameter (0.13 m) CBCs positioned farther apart than in previous studies (min. diagonal spacing 0.29 m) was assessed to determine whether conditions would be suitable for facilitating the passage of small-bodied fish while also providing sufficient space for larger individuals to manoeuvre. Two experiments were conducted in an open channel flume. Experiment 1 quantified the hydraulic conditions created by a model Crump weir when unmodified and with CBCs installed in supercritical flow (Fr 1.23–3.01) on the 1:5 downstream sloping face under a low (0.08 m3 s−1) and high (0.23 m3 s−1) discharge. Patches of low water velocity were created in the wake of the CBCs, and the median (time and space averaged) velocity was reduced under both low (30.1%) and high (22.3%) discharge. Based on estimated burst swimming speeds of two common European species, the roach (Rutilus rutilus) and brown trout (Salmo trutta) (0.16 m long, swimming at 15.1 °C), this reduction in velocity would facilitate upstream passage. Experiment 2 documented the vertical velocity profile and shear stress characteristics (a measure of turbulence) within the CBC array. Unlike in Experiment 1, the CBCs were installed on the flat base of the flume and under subcritical flow (Fr = 0.31) to generate sufficient water depth. The velocity was reduced (up to 22.5%) at depths that did not exceed (> 2 cm above) the height of the bristles. Above these depths, velocity was (up to 14.6%) higher compared to open channel conditions upstream of the CBC array and a vertical shear layer was evident. As the main hydraulic benefits of CBCs occur at depths that do not exceed the bristles, their height should be tailored to site specific conditions (e.g. size of target fish species and/or depth of water at infrastructure). Field-based research is needed to determine velocity reduction at longer weirs and under a wider range of flows than can be tested under flume conditions. How the hydraulic characteristics of submerged CBCs differ from those described here with those that occur in the field when installed on a steep sloping weir under supercritical flow should be further investigated.

Toward on-demand measurements of greenhouse gas emissions using an uncrewed aircraft AirCore system

Abstract. This paper evaluates the performance of a multirotor uncrewed aircraft and AirCore system (UAAS) for measuring vertical profiles of wind velocity (speed and direction) and the mole fractions of methane (CH4) and carbon dioxide (CO2), and it presents a use case that combines UAAS measurements and dispersion modeling to quantify CH4 emissions from a dairy farm. To evaluate the atmospheric sensing performance of the UAAS, four field deployments were performed at three locations in the San Joaquin Valley of California where CH4 hotspots were observed downwind of dairy farms. A comparison of the observations collected on board the UAAS and an 11 m meteorological tower show that the UAAS can measure wind velocity trends with a root mean squared error varying between 0.4 and 1.1 m s−1 when the wind magnitude is less than 3.5 m s−1. Findings from UAAS flight deployments and a calibration experiment also show that the UAAS can reliably resolve temporal variations in the mole fractions of CH4 and CO2 occurring over periods of 10 s or longer. Results from the UAAS and dispersion modeling use case further demonstrate that UAASs have great potential as low-cost tools for detecting and quantifying CH4 emissions in near real time.

Spatially distributed atmospheric boundary layer properties in Houston – A value-added observational dataset

In 2022, Houston, TX became a nexus for field campaigns aiming to further our understanding of the feedbacks between convective clouds, aerosols and atmospheric boundary layer (ABL) properties. Houston’s proximity to the Gulf of Mexico and Galveston Bay motivated the collection of spatially distributed observations to disentangle coastal and urban processes. This paper presents a value-added ABL dataset derived from observations collected by eight research teams over 46 days between 2 June - 18 September 2022. The dataset spans 14 sites distributed within a ~80-km radius around Houston. Measurements from three types of instruments are analyzed to objectively provide estimates of nine ABL parameters, both thermodynamic (potential temperature, and relative humidity profiles and thermodynamic ABL depth) and dynamic (horizontal wind speed and direction, mean vertical velocity, updraft and downdraft speed profiles, and dynamical ABL depth). Contextual information about cloud occurrence is also provided. The dataset is prepared on a uniform time-height grid of 1 h and 30 m resolution to facilitate its use as a benchmark for forthcoming numerical simulations and the fundamental study of atmospheric processes.

Experiments on flow velocity profiles in mountain river channels

ABSTRACT Research on the vertical profiles of flow velocity in mountainous river channels is limited, particularly in scenarios where complex bed geometries are absent. Due to the coarse roughness and seepage flow on streambeds composed of gravel, the conventional formulae for flow velocity profiles derived from fluvial river channels do not apply to mountainous river channels. Based on flume experiments with a bed packed with natural gravel and a slope ranging from 0.006 to 0.16, we derived a theoretical formula for flow velocity profiles. This new formula integrates the influence of the subsurface flow and velocity reduction near the water surface, demonstrating a strong alignment with measurements. Our findings indicate that for shallow water flow over rough bed surfaces, the turbulence intensity diminishes along the vertical direction in the near-bed region while remaining relatively constant in the upper water body. Contrary to conventional theories which attribute the increase in flow resistance and the decrease in sediment transport rates in mountainous river channels to form drag, our study emphasizes that the subsurface flow plays a significant role in the overall flow resistance of mountainous river channels and should not be overlooked.

Wind farm power curve characterization under different atmospheric stability regimes

Wind farm power curves are particularly relevant in different applications. A better understanding of wind farm power curves under different atmospheric regimes is sought. In the present work, the atmospheric stability regime was identified by the vertical gradient of the potential temperature. Vertical profile of the wind velocity presented a clearly different pattern during the stable and unstable regimes. Analysis was performed considering 5 years of data from three wind farms, each corresponding to different mesoscale wind. Power curves are presented as a function of atmospheric stability. For each wind farm, we utilized wind velocity and temperature data measurements of a correspondent near the tower location. Clearly different patterns of wind farm power curves were observed as a function of the stability regime, with clear differences in the dependence of mesoscale wind regimes. For the same mean velocity, wind power production is greater for higher values of turbulence intensity TI.

An automated geometry generation procedure for CWE applications in OpenFOAM: the case study of a thunderstorm downburst moving over Genoa city

AbstractSince a decade, Computational Fluid Dynamics (CFD) simulations for Wind Engineering (WE) on large-scale environments became a norm. Meso-$$\gamma$$ γ scales and microscale can be characterized by a large number of structures as well as complex terrain topographies. CFD simulations over such an area would commonly imply the involvement of a time-consuming geometry preparation in the pre-processing stage. This is also the innovative goal of the present paper for which an automated geometry generation procedure for Computational Wind Engineering (CWE) applications is developed in open-source environments. This paper further expands on the unsteady Reynolds-averaged Navier–Stokes (URANS) simulation of a thunderstorm downburst immersed in a background Atmospheric Boundary Layer (ABL) wind moving over Genoa city, Italy. Recommendations for geometry and grid generation of the present case study are also proposed. The study considers two simultaneous approaching wind conditions, a background ABL wind and a moving downburst (DB), the latter modeled as an impinging jet. The simulated results are compared with available full-scale LiDAR profiler data in terms of the vertical profiles of outflow velocity, showing relatively good agreement in terms of magnitude and profile shape.

Aerodynamic properties of boundary layers along the roof of a large banana screenhouse under near-neutral atmospheric stability

Cultivation under screens and in screenhouses protects the crops from insects and extreme climate conditions and allows water saving. Previous studies considered the aerodynamic properties of boundary layers along two types of screens: a small shading thermal screen covering a hedgerow citrus orchard and a large 50-mesh, insect-proof screen covering a pepper plantation. To extend the previous results, a third type of screen was analysed in this study, a large flat-roof 17-mesh white woven shading screen covering a banana plantation. Vertical profiles of wind speed, air temperature, relative humidity, and friction velocity were measured by a lifting tower, and wind profiles were analysed under near-neutral atmospheric stability. Results show that normalised friction velocity, normalised roughness length, normalised zero plane displacement height and aerodynamic resistance are closer to the previous results of the large insect-proof screenhouse than those of the small shade net.

Impact of boundary conditions on the modeled thermal regime of the Antarctic ice sheet

Abstract. A realistic initialization of ice flow models is critical for predicting future changes in ice sheet mass balance and their associated contribution to sea level rise. The initial thermal state of an ice sheet is particularly important, as it controls ice viscosity and basal conditions, thereby influencing the overall ice velocity. Englacial and subglacial conditions, however, remain poorly understood due to insufficient direct measurements, which complicate the initialization and validation of thermal models. Here, we investigate the impact of using different geothermal heat flux (GHF) datasets and vertical velocity profiles on the thermal state of the Antarctic ice sheet and compare our modeled temperatures to in situ measurements from 15 boreholes. We find that the temperature profile is more sensitive to vertical velocity than to GHF. The basal temperature of grounded ice and the amount of basal melting are influenced by both selection of GHF and vertical velocity. More importantly, we find that the standard approach, which consists of combining basal sliding speed and incompressibility to derive vertical velocities, provides reasonably good results in fast-flow regions (ice velocity &gt;50 m yr−1) but performs poorly in slow-flow regions (ice velocity &lt;50 m yr−1). Furthermore, the modeled temperature profiles in ice streams, where bed geometry is generated using a mass conservation approach, show better agreement with observed borehole temperatures compared to kriging-based bed geometry.

Numerical Calculations for Curved Open Channel Flows with Advanced Depth-Integrated Models

This paper examines the effect of coupling several equations for vertical velocity profiles in a depth-integrated model to clarify the roles of three-dimensional flow structures minimizing the errors from the two-dimensional calculation model. In addition, this paper develops a numerical discretization method for the dispersion terms in the horizontal momentum equations. It is revealed that the use of the 2DC model underestimates the water surface elevation through the comparisons with the experimental datasets, advanced 2DC and 3DC results. The prediction of water surface elevation is considerably improved by taking into account of secondary flow effect with vorticity equations. It is clarified that the accuracy in predicting the water surface elevation is increased with increasing the degree of the function for vertical velocity profiles in advanced 2DC models or the number of vertical grids in 3DC model, while non-hydrostatic pressure and variation in vertical velocity have a second importance.

Dispersion in Shallow Moment Equations

Shallow moment models are extensions of the hyperbolic shallow water equations. They admit variations in the vertical profile of the horizontal velocity. This paper introduces a non-hydrostatic pressure to this framework and shows the systematic derivation of dimensionally reduced dispersive equation systems which still hold information on the vertical profiles of the flow variables. The derivation from a set of balance laws is based on a splitting of the pressure followed by a same-degree polynomial expansion of the velocity and pressure fields in a vertical direction. Dimensional reduction is done via Galerkin projections with weak enforcement of the boundary conditions at the bottom and at the free surface. The resulting equation systems of order zero and one are presented in linear and nonlinear forms for Legendre basis functions and an analysis of dispersive properties is given. A numerical experiment shows convergence towards the resolved reference model in the linear stationary case and demonstrates the reconstruction of vertical profiles.