Lateral Momentum Flux Research Articles

The Role of Bed Morphology and Channel Curvature on the Redistribution of Momentum in a Series of Meander Bends, Pearl River, USA

AbstractThree primary driving factors are responsible for the lateral flux of streamwise momentum within meander bends: topographic steering of the flow related to changes in channel morphology, rapid changes in channel curvature, and curvature‐driven helical motion. While these factors have been studied previously, their relative contributions to the net redistribution of streamwise momentum within a series of consecutive bends have not yet been fully documented. This study explores the relative contributions of these three mechanisms to the redistribution of streamwise momentum using three‐dimensional velocity data obtained along six consecutive meander bends on the Pearl River (Louisiana, USA) for two different discharges. The magnitudes of lateral momentum flux are systematically compared to spatial series of channel width, bed shape, and channel curvature to elucidate the interactions between channel form and flow structure. Results show that the lateral flux of streamwise momentum is primarily driven by topographic steering with values of momentum flux due to curvature‐driven secondary circulation on average an order of magnitude less than values of flux related to topographic steering. The spatial patterns of the lateral flux components show that momentum redistribution due to topographic steering is highest at the entrance to the bend, and momentum redistribution due to secondary circulation is typically highest downstream of the apex. The results of this study emphasize the important role that interaction between process and form plays in dynamics of natural meandering rivers.

Quantifying 3D Gravity Wave Drag in a Library of Tropical Convection‐Permitting Simulations for Data‐Driven Parameterizations

AbstractAtmospheric gravity waves (GWs) span a broad range of length scales. As a result, the un‐resolved and under‐resolved GWs have to be represented using a sub‐grid scale (SGS) parameterization in general circulation models (GCMs). In recent years, machine learning (ML) techniques have emerged as novel methods for SGS modeling of climate processes. In the widely used approach of supervised (offline) learning, the true representation of the SGS terms have to be properly extracted from high‐fidelity data (e.g., GW‐resolving simulations). However, this is a non‐trivial task, and the quality of the ML‐based parameterization significantly hinges on the quality of these SGS terms. Here, we compare three methods to extract 3D GW fluxes and the resulting drag (Gravity Wave Drag [GWD]) from high‐resolution simulations: Helmholtz decomposition, and spatial filtering to compute the Reynolds stress and the full SGS stress. In addition to previous studies that focused only on vertical fluxes by GWs, we also quantify the SGS GWD due to lateral momentum fluxes. We build and utilize a library of tropical high‐resolution (Δx = 3 km) simulations using weather research and forecasting model. Results show that the SGS lateral momentum fluxes could have a significant contribution to the total GWD. Moreover, when estimating GWD due to lateral effects, interactions between the SGS and the resolved large‐scale flow need to be considered. The sensitivity of the results to different filter type and length scale (dependent on GCM resolution) is also explored to inform the scale‐awareness in the development of data‐driven parameterizations.

The quantitative response of pollutant spatial distribution and mixing dynamics to confluent conditions in an asymmetric open-channel confluence

River confluences are key nodes of pollutant transport in fluvial ecosystems and they are accompanied by complex hydrodynamic and mixing processes. The generalization and quantitative response of mixing to highly variable confluent conditions remain unclear. This studyinvestigates the spatial distribution and mixing process of pollutants through a series of meticulous experiments in an asymmetric open-channel confluence. Furthermore, we propose quantitative responses and characterization equations for the mixing rate and mixing metric for various confluent conditions, namely junction angle, momentum flux ratio, and width-depth ratio. The spatial distribution of pollutants have a strong three-dimensional structure, with a narrow-long pollution belt near the tributary and an almost vertical mixing interface adjacent to the downstream junction corner; this interface exhibits a logarithmic growth trend downstream and is affected by shear layer distortion. The standard deviation of the cross-sectional pollutant concentration at the confluence decreases gradually along with the downstream mixing of convergent flows, and the fitting curve slope increases as the junction angle, momentum ratio, and width-depth ratio increase. The mixing rate is promoted by the enhancements of helical motion, lateral advection, and turbulent diffusion caused by the strengthening of mutual deflection and lateral momentum flux under a large junction angle and momentum ratio, as well as the reductions of vertical velocity gradient and cross-sectional area under large width-depth ratio conditions. Sufficient and complete mixing occurs under a larger momentum ratio condition of >1 within a short distance of 4–5 widths of the main channel. In addition, the mixing metric shows a strong linear relationship with each of the three confluent conditions. In summary, the significant (p < 0.001) quantitative responses of the mixing rate and mixing metric can be characterized by a polynomial equation. These results have major implications for the systematic understanding of the three-dimensional distribution characteristics, mixing patterns, and mixing dynamics of pollutants at asymmetric confluences, as well as for the prediction or calculation of the downstream mixing metric.

Turbulence structures and entrainment length scales in large offshore wind farms

Abstract. The flow inside and around large offshore wind farms can range from smaller structures associated with the mechanical turbulence generated by wind turbines to larger structures indicative of the mesoscale flow. In this study, we explore the variation in turbulence structures and dominant scales of vertical entrainment above large offshore wind farms located in the North Sea, using data obtained from a research aircraft. The aircraft was flown upstream, downstream, and above wind farm clusters. Under neutrally stratified conditions, there is high ambient turbulence in the atmosphere and an elevated energy dissipation rate compared to stable conditions. The intensity of small-scale turbulence structures is increased above and downstream of the wind farm, and it prevails over mesoscale fluctuations. But in stable stratification, mesoscale flow structures are not only dominant upstream of the wind farm but also downstream. We observed that the vertical flux of horizontal momentum is the main source of energy recovery in large offshore wind farms, and it strongly depends on the magnitude of the length scales of the vertical wind velocity component. The dominant length scales of entrainment range from 20 to ∼60 m above the wind farm in all stratification strengths, and in the wake flow these scales range from 10 to ∼100 m only under near-neutral stratification. For strongly stable conditions, negligible vertical entrainment of momentum was observed even just 2 km downstream of large wind farms. We also observed that there is a significant lateral momentum flux above the offshore wind farms, especially under strongly stable conditions, which suggests that these wind farms do not satisfy the conditions of an “infinite wind farm”.

Effect of Lateral Outflow on Three‐Dimensional Flow Structure in a River Delta

Spatial and temporal patterns in three-dimensional flow structure are linked to channel processes and morphology in many environments. However, there is not yet an understanding of how the flow structure is influenced by channelized and gradually distributed lateral outflows that are often prevalent in river deltas. This study presents an analysis of three-dimensional flow structure data collected from Wax Lake Delta, a naturally developing river-dominated delta in the northern Gulf of Mexico. Three hydrographic surveys were conducted using a boat-mounted acoustic Doppler current profiler at two sites: a channelized outflow zone and a distributary channel experiencing unchannelized lateral outflow. The flow structure was analyzed to identify secondary circulation cells induced by both types of lateral outflow. For channelized outflow, coherent cells were observed. However, minimal presence of coherent structures was observed for unchannelized lateral outflow. The results suggest that the formation of detectable secondary circulation cells may depend upon a threshold value of the ratio of the lateral momentum flux along the length of the outflow zone and primary flow momentum flux. The threshold lies in between 0.211 and 0.375 km−1 for the conditions tested. This research contributes novel field measurements of flow structure in an actively prograding river delta and offers important implications for coastal restoration by linking three-dimensional flow structure to lateral outflow.

Spatial and temporal variations in near‐surface energy fluxes in an Alpine valley under synoptically undisturbed and clear‐sky conditions

AbstractDiurnal cycles of turbulent sensible and latent heat fluxes are typically closely related to the diurnal cycles of solar irradiation under synoptically undisturbed and clear‐sky conditions. In mountainous terrain, large variations can occur in the topographic and surface properties, which modify the local radiation budget and thus turbulent energy fluxes and the surface energy balance. Another characteristic of mountainous terrain is local, thermally driven circulation systems, such as the slope‐ and valley‐wind system, which can equally affect turbulent exchange. Observations of near‐surface radiative and turbulent fluxes are presented from six eddy‐covariance stations in an approximately east–west‐oriented major Alpine valley for undisturbed and clear‐sky conditions. Median diurnal cycles over the whole year are compared at the six sites and related to local terrain characteristics and the thermally driven wind systems. At a scale that is smaller than grid cells in current operational global forecast models, heat, moisture, and momentum fluxes show a large spatial variability in the magnitudes and their diurnal cycles. Lowest heat fluxes are observed on the north‐facing sidewall, where solar irradiation and thus available energy are reduced compared with the valley floor and south‐facing sidewall. Differences in the land surface characteristics further affect the partitioning of the available energy into sensible and latent heat fluxes. The median sensible heat flux reaches its daily peak already before solar noon at several sites, which appears to be related to the transition from down‐valley to up‐valley winds. In contrast to flat and homogeneous terrain, horizontal heat fluxes and lateral momentum fluxes can reach magnitudes that are similar to the magnitudes of vertical heat fluxes and longitudinal momentum fluxes, respectively.

Near- and far-field structure of shallow mixing layers between parallel streams

Abstract

Lateral Momentum Fluxes at the Confluence of the Negro and Solimões Rivers

Hydrodynamic zones of river confluences are remarkable not only for the turbulent mixing induced by the shear layer at the center of the mixing interface but also for the lateral momentum fluxes associated with channel topography. Detailed characterizations of lateral momentum transfers in river confluences, however, are few. In this study, contributions to the lateral momentum fluxes in the confluence of the Negro and Solimões rivers in Brazil were calculated based on a comprehensive set of field data. Results show that the lateral fluxes by the mean flow exceed the turbulent fluxes by two orders of magnitude. Furthermore, the Reynolds stress along the far field of the Solimões side of the Amazon channel scales with or surpasses the Reynolds stress at the interface with the Negro side. The importance of the shear layer in the lateral mixing is thus overshadowed by the competing hydrodynamic processes. This configuration partially explains the long distance required to complete the mixing of the waters of the two tributary rivers.

경사가 있는 지형의 거칠기 아층에서 풍향시어와 운동량 플럭스의 특성

We have analyzed wind and eddy covariance data collected within roughness sub- layer over sloping terrain. The study site is located on non-flat terrain with slopes in both south-north and east-west directions. The surface elevation change is smaller than the height of roughness element such as building and tree. This study examines the directional wind shear for data collected at three levels in the lowest 10 m in the roughness sublayer. The wind direc- tion shear is caused by drag of roughness element and terrain-induced motions at this site. Small directional shear occurs when wind speed at 10 m is strong and wind direction at 10 m is southerly which is the same direction as upslope flow near surface at this site during daytime. Correlation between vertical shear of lateral momentum and lateral momentum flux is smaller over steeply sloped surface compared to mildly sloped surface and lateral momentum flux is not down-gradient over steeply sloped surface. Quadrant analysis shows that the relative contri- bution of four quadrants to momentum flux depends on both surface slope and wind direction

Eddy Transport and Mixing in a Wind- and Buoyancy-Driven Jet on the Sphere

Abstract The baroclinically unstable wind- and buoyancy-driven flow in a zonally reentrant pie-shaped sector on a sphere is numerically modeled and then analyzed using the transformed Eulerian-mean (TEM) formalism. Mean fields are obtained by zonal and time averaging performed at fixed height. The very large latitudinal extent of the basin (50.7°S latitude to the equator) allows the latitude variation of the Coriolis parameter to strongly influence the flow. Persistent zonal jets are observed in the statistically steady state. Reynolds stress terms play an important role in redistributing zonal angular momentum: convergence of the lateral momentum flux gives rise to a strong eastward jet, with an adjacent westward jet equatorward and weaker multiple jets poleward. An equally prominent feature of the flow is a strong and persistent eddy that has the structure of a Kelvin cat’s eye and generally occupies the zonal width of the basin at latitudes 15°–10°S. A strongly mixed surface diabatic zone overlies the near-adiabatic interior, within which Ertel potential vorticity (but not thickness) is homogenized along the mean isopycnals everywhere in the basin where eddies have developed (and thus is not homogenized equatorward of the most energetic eastward jet). A region of low potential vorticity (PV) is formed adjacent to the strong baroclinic front associated with that jet and subsequently maintained by strong convective events. The eddy buoyancy flux is dominated by its skew component over large parts of the near-adiabatic interior, with cross-isopycnal components present only in the vicinity of the main jet and in the surface diabatic layer. Close to the main jet, the cross-isopycnal components are dominantly balanced by the triple correlation terms in the buoyancy variance budget, while the advection of buoyancy variance by the mean flow is not a dominant term in the eddy buoyancy variance budget. Along-isopycnal mixing in the near-adiabatic interior is estimated by applying the effective diffusivity diagnostic of Nakamura. The effective diffusivity is large at the flanks of the mean jet and beneath it and small in the jet core. The apparent horizontal diffusivity for buoyancy obtained from the flux–gradient relationship is the same magnitude as the effective diffusivity, but the structures are rather different. The diapycnal diffusivity is strongest in the surface layer and also in a convectively unstable region that extends to depths of hundreds of meters beneath the equatorward flank of the main jet.

Lateral momentum flux and the spatial evolution of flow within a confluence mixing interface

Mixing interfaces at confluences have been viewed as analogous to shallow mixing layers in which lateral fluxes of momentum generally are viewed as unimportant. This investigation examines the spatial evolution of flow along a confluence mixing interface, focusing on lateral fluxes of momentum. Cross‐stream profiles of depth‐averaged mean velocities indicate that flow within the mixing interface has wake characteristics near the upstream junction corner, mixing‐layer properties within the confluence, and attributes of a weak jet within the downstream channel. Convective acceleration of downstream velocity along the path of the mixing interface is influenced by lateral fluxes of momentum from the converging mean flow. These fluxes exceed turbulence lateral momentum fluxes by one to two orders of magnitude. Flow in the mixing interface is unstable, but lateral expansion of coherent turbulent vortices over distance is limited, possibly due to the inhibiting effects of the converging flow. Similar low‐frequency oscillations in near‐surface velocity fluctuations occur within the stagnation zone and along the mixing interface, suggesting that the dynamics of the stagnation‐zone wake may influence low‐frequency characteristics of flow in the downstream portion of the mixing interface. Patterns of turbulence kinetic energy (k) are influenced by lateral momentum fluxes, which progressively shift the zone of maximum k toward the outer bank. Overall the study shows that lateral momentum fluxes are important in the spatial evolution of flow within confluence mixing interfaces and need to be accounted for in theoretical treatments of these interfaces.

A vortex‐based model of velocity and shear stress in a partially vegetated shallow channel

This paper presents a method for predicting the distributions of velocity and shear stress in shallow channels with a boundary of emergent vegetation. Experiments in a laboratory channel with model vegetation show that the velocity profile exhibits a distinct two‐layer structure, consisting of a rapidly varying shear layer across the vegetation interface and a more gradual boundary layer in the main channel. In addition, coherent vortices are observed which span both layers, and are the dominant contributors to lateral momentum fluxes. From these observations, we propose a model for the vortex‐induced exchange and find expressions for the width of momentum penetration into the vegetation, the velocity and shear stress at the vegetation edge, and the width of the boundary layer in the main channel. These variables, along with a momentum balance in the main channel, comprise a modeling framework which accurately reproduces the observed velocity and shear stress distributions. The predictions for the velocity and shear stress can provide a basis for modeling flood conveyance, overbank sediment transport, and scalar residence time in the vegetated layer.

Gap Flows through Idealized Topography. Part II: Effects of Rotation and Surface Friction

Abstract Numerical simulations are conducted of geostrophically balanced flow over an isolated mountain cut by a horizontal gap. The relative importance of the along-gap synoptic-scale pressure gradient and terrain-induced mesoscale circulations for the generation of gap winds was examined by changing the direction of the synoptic-scale wind relative to the topography. In all cases, the forcing associated with mesoscale circulations generated by the mountain was at least as significant as the synoptic-scale pressure gradient. In the cases where a component of the large-scale flow was directed perpendicular to the ridge, the dynamics were dominated by either the vertical momentum fluxes due to mountain lee waves or by mesoscale pressure gradients associated with upstream blocking or lee troughing. Mesoscale circulations were also important when the large-scale flow was parallel to the ridge because surface friction turned the low-level winds toward the high pressure side of the ridge, partially blocking the flow and enhancing the along-gap pressure gradient. The flow in the interior of a very long uniform gap was also simulated for a case with the synoptic-scale winds parallel to the ridge so that the synoptic-scale pressure gradient was down the gap. The flow in the interior of the long gap was not horizontal and not in a simple dynamical balance between acceleration, the pressure gradient force, and surface friction. Even the flow in the lowest 150 m was gradually subsiding. Subsidence and lateral momentum flux convergence at low levels near the center of the gap were important contributors to the mass and along-gap momentum budgets.

Particle cross‐flow, lateral momentum flux and lateral velocity in a circulating fluidized bed

AbstractLateral and axial profiles of solids cross‐flow flux were measured in a circulating fluidized bed riser of square cross‐section with a sampling probe. The solids cross‐flow flux was found to be higher near the wall, especially near the corners, and lower in the core of the riser. The net solids horizontal flux was outwards in the lower part of the riser and inwards near the top.The lateral solids momentum flux, measured by means of a piezoelectric probe, increased with height and then decreased near the top of the riser. The lateral solids momentum flux first increased with distance from the axis and then decreased towards the wall. It was especially low near the corners.

ピレネー山脈における風下波の数値シミュレーション

A two-dimensional, non hydrostatic, compressible model is used to simulate the airflow over the Pyrenees in two lee wave events (IOP-3 and IOP-9) during the PYREX program. For each case, the mean flow is initialized by a single upstream sounding. The bottom topography used in the model is taken from the real mountain profile after smoothing out the wavelength shorter than 10km.In all cases, the model simulates well several characteristics of the lee waves: the wavelength, amplitude, and position. This is a strong indication that the lee waves observed in these events were excited by non linear wave-wave interactions of long mountain waves, because the topographic forcing in the model has negligible spectral amplitude at the wavelength of the lee waves (∼10km). Sensitivity experiments show that the phases of the lee waves are very sensitive to a small change of the mean wind and that their amplitudes are increased by the addition of smaller-scale topography.In both cases, the simulated downward momentum fluxes agree well with the observed fluxes around 4km height: -15×104N/m in IOP-3 and +10×104N/m in the third day of IOP-9. The simulated fluxes are, however, almost constant through the troposphere, while the observations show rapid decrease of absolute values above 4km height. This overestimation of the simulated momentum fluxes in the upper half of the troposphere is caused by the overestimation of the amplitude of long mountain waves at these heights; these long mountain waves control the vertical profile of the momentum flux there. It is suggested that the time evolution of the mean wind and the lateral momentum flux divergence found in the real atmosphere give rise to this overestimation.

Formulation of Mathematical Watershed-Flow Model

In a macroscopic hydrodynamic approach, a set of one-dimensional spatially varied unsteady flow equations, that include terms for lateral mass flux, lateral momentum flux, overpressure head due to raindrop impact, and boundary shear, are derived from the equation of continuity and the Navier-Stokes equations for the three-dimensional flow of viscous incompressible fluid in cooperation with the kinematic and dynamic boundary conditions on the water and ground surfaces of a watershed. The Darcy-Weisbach equation is employed to evaluate the friction slope, and the laminar uniform flow equation for the Darcy-Weisbach friction coefficient coupled with the Karman-Prandtl logarithmic resistance equation for turbulent flow is used to simulate, as a first approximation, the unknown function of the Darcy-Weisbach friction coefficient for watershed surface flow. The proposed mathematical model for watershed surface flow consists of a set of quasilinear partial differential flow equations of hyperbolic type with the appropriately prescribed initial and boundary conditions.