Vertical Momentum Transfer Research Articles

Field study of atmospheric boundary layer observation in a hilly Gobi Desert region and comparison with the CALMET/CALPUFF model

Abstract A field campaign consisting of atmospheric boundary layer (ABL) observations and tracer experiments was conducted in September 2016 in a hilly region of the Gobi Desert in northwest China. High-frequency wind shears were observed between 70 and 200 m based on both 100-meter tower data and wind profiles. The ABL observations indicated that sub-layers of different atmospheric stability present within the ABL weakened the vertical transfer of momentum and tracer gas, resulting in low wind speed and high surface concentration. The CALMET model showed thermal heterogeneity to some extent in the temperature fields and mixing height distributions, and large deviations in the friction velocity between the model and observations were noted. The comparison of the CALPUFF model with the tracer measurements indicated a general tendency toward under-prediction of the concentration in the far distance because of wind shears and vertical thermal discontinuity. The results of the SCIPUFF model showed the same trend as those of CALPUFF, and comparisons demonstrated a good consistency of the two models.

Effects of wave-induced vertical Reynolds stress on upper-ocean momentum transfer over the Scotian Shelf during extreme weather events

The effects of wave-induced vertical Reynolds stress (WIVRS) on the upper-ocean momentum transfer over the Scotian Shelf (ScS) are examined using a coupled wave-circulation modeling system during two extreme storm events: Hurricane Earl and Winter Storm Echo. The effects of WIVRS are specified in the circulation model using the wave pressure-slope stress ( τP) suggested by Mellor (2013). The inclusion of τP enhances the downward momentum transfer within the surface layer when the storm passes overhead associated with strong vertical gradients of τP, leading to relatively weak vertical shears of horizontal currents and thus weak turbulent Reynolds stress (τT) in the upper-ocean layer. This in turn weakens the vertical momentum transfer to deeper water through τT just after the storm passage. The reduced downward momentum transfer after the storm due to the inclusion of τP is found to be in better agreements with both the ADCP observations and the HF-radar observations. The ADCP observations show a relatively slow decay of upper-ocean currents, and the HF-radar observations show relatively strong clockwise-rotating near-inertial surface currents over the offshore area of the ScS just after the storm passage. The model results also demonstrate that the effects of τP are more pronounced during Hurricane Earl due to deeper penetration depths of τP associated with stronger winds (up to 33 m/s) than those during Winter Storm Echo (wind speeds up to 25 m/s).

Discharge Estimation at the Apex of Compound Meandering Channels

A new method is proposed to calculate flow in a compound meandering channel by considering the momentum transfer between different zones. Vertical momentum transfer, at the horizontal interface of the lower main channel and the meander belt; and the horizontal momentum transfer, at the vertical interfaces between the meander belt and the adjoining outer floodplains. Modelling of this analytical method for the bend apex section is carried out, for a control volume of unit length. Calibration has been carried out for different laboratory channels and a natural river, demonstrating that the present model is capable of providing an adequate prediction of discharge in experimental as well as in field study. A constant value of 0.01 as the momentum transfer coefficient is verified to act at the interacting interfaces for the meandering channels. The zonal velocity for each subsection is determined, which facilitates prediction of discharge distribution.

Upscale Impact of Mesoscale Convective Systems and Its Parameterization in an Idealized GCM for an MJO Analog above the Equator

Abstract The Madden–Julian oscillation (MJO) typically contains several superclusters and numerous embedded mesoscale convective systems (MCSs). It is hypothesized here that the poorly simulated MJOs in current coarse-resolution global climate models (GCMs) is related to the inadequate treatment of unresolved MCSs. So its parameterization should provide the missing collective effects of MCSs. However, a satisfactory understanding of the upscale impact of MCSs on the MJO is still lacking. A simple two-dimensional multicloud model is used as an idealized GCM with clear deficiencies. Eddy transfer of momentum and temperature by the MCSs, predicted by the mesoscale equatorial synoptic dynamics (MESD) model, is added to this idealized GCM. The upscale impact of westward-moving MCSs promotes eastward propagation of the MJO analog, consistent with the theoretical prediction of the MESD model. Furthermore, the upscale impact of upshear-moving MCSs significantly intensifies the westerly wind burst because of two-way feedback between easterly vertical shear and eddy momentum transfer with low-level eastward momentum forcing. Finally, a basic parameterization of the upscale impact of upshear-moving MCSs modulated by deep heating excess and vertical shear strength significantly improves key features of the MJO analog in the idealized GCM with clear deficiencies. A three-way interaction mechanism between the MJO analog, parameterized upscale impact of MCSs, and background vertical shear is identified.

Hydrodynamic effects of the ratio of rotor diameter to water depth: An experimental study

A series of flume experiments were carried out to investigate the influence of tidal turbine rotor diameter to depth ratio on the hydrodynamic process of wake flow using two different diameter rotor discs of the same porosity. Time-varying velocities were measured by an Acoustic Doppler Velocimeter at 8 cross-sections over the distance of 10 diameters downstream, and the three-dimensional structures of wake flow and turbulence fields were obtained. Immediately downstream, the peak of velocity deficit occurred at the wake core and the value was greater for the large diameter-depth ratio. Strong wake turbulence was mainly located in the shear stress layer around wake core. However, the attenuation processes of wake hydrodynamics were different under two diameter-depth ratios. The momentum transfer was caused by Reynolds shear stress in both transverse and vertical directions. The vertical momentum transfer process was much more significant above the wake core than the lateral transfer process, but it decayed rapidly in near wake as the diameter-depth ratio enlarged. The experimental results provide detailed data to better understand the wake propagation processes behind rotor discs.

The Reynolds wave shear stress in partially reflected waves

Wind–waves play a relevant role in the downward flux of mass, momentum and heat, and in their balances. Thus, they are quite significant in small- and large-scale processes like global warming, especially in continental shelf. There is still no consensus on the effectiveness of different mechanisms in enhancing, e.g., the carbon dioxide (CO2) uptake in the continental shelves with respect to the open ocean. To our best knowledge, the role of partial reflections of short and long waves in the budget has been largely neglected without a specific justification, even though reflection in water waves is a recurring phenomenon. Presumably, this is a consequence of the difficulties in performing experiments with variable reflection coefficient and phase shift of the waves approaching coastal structures. We report experiments on the vertical momentum transfer in partially reflecting waves propagating on a flat horizontal bottom. We measured the free surface level and the fluid velocity, and estimated the Reynolds wave–generated shear stress. A set of experiments using paddle waves or a paddle plus wind waves and a reflection coefficient ranging from 0.10−0.75, with a phase shift of π/4−π rad, confirms the theoretical model. The results indicate that reflection must be carefully considered in the correct interpretation of data, particularly when considering momentum transfer in the vertical. The new contributions in the paper are (i) the adoption of a generation–absorption system that controls the reflection coefficient and phase shift between incident and reflected waves; (ii) the quantification of the phase shift influence on the vertical momentum transfer and its horizontal variability; (iii) the consequences for locally–generated wind–waves and wind generated surface currents. To our knowledge, these are the first experiments where the characteristics of the reflected waves have been imposed, allowing a thoroughly analysis of their effects on the flow field.

Interaction of Waves with Idealized High‐Relief Bottom Roughness

AbstractConsiderable uncertainty exists about how to represent wave bottom friction in coastal systems like reefs where orbital excursions are similar to roughness element size. Here, interactions between waves and large bottom roughness were investigated using Large Eddy Simulations of oscillatory flow over infinite hemisphere arrays. Wave amplitude, period, and hemisphere spacing were varied to investigate the dependence of kinematics and dynamics on dimensionless parameters. The net effect of topography on the oscillatory flow was assessed using a spatially and phase‐averaged Navier‐Stokes framework. Dynamics depended strongly on Keulegan‐Carpenter number (KC), the ratio of wave orbital excursion to roughness element size. For , flow separation was weak, form drag was small, stress gradients were negligible, and the main effect of topography on the flow was the inertial force associated with acceleration around roughness elements. For , strong flow separation occurred, and both drag and inertial forces were important. Phase‐dependent dispersive stresses were the main mechanism for vertical momentum transfer between the canopy layer and the overlying water column. Friction factors based on the drag force increased with KC for , different from previously proposed empirical curves, but approached these curves for high KC. Friction factors based on the total force decreased with increasing KC and were consistent with previously proposed curves. These results highlight the importance of distinguishing the total force on the bottom, the drag force that removes energy from the flow, and the shear stress above the canopy layer, which were very different for the parameter range in this study.

Eddy dynamics over continental slopes under retrograde winds: Insights from a model inter-comparison

Mesoscale eddies are ubiquitous in the ocean and play a key role in exchanges across continental slopes. In this study the properties of wind-driven baroclinic turbulence are investigated using eddy-resolving process simulations, focusing on the case of retrograde winds that arises around the margins of the subtropical gyres. In contrast to a flat-bottomed ocean, over steep slopes eddies develop from baroclinic instabilities are confined to the top few hundred meters. Deeper in the water column baroclinic instability and vertical momentum transfer are suppressed, so wind-input momentum is exported toward the open ocean by eddies before traversing down to the ocean bed. Close to the sloping topography, eddy energy sourced from the upper ocean is converted to potential energy, steepening isopycnals and driving bottom-trapped prograde flows. This process is associated with upgradient lateral buoyancy fluxes and downgradient isopycnal potential vorticity fluxes, and cannot be reproduced via linear stability calculations.These properties of wind-driven shelf/slope turbulence are contrasted against simulations with flat bathymetry. The key differences described above hinge on the flow close to the steep topographic slope, which may be sensitive to the model’s vertical coordinate system. The simulations are therefore replicated using models that employ geopotential coordinates, terrain-following coordinates, and isopycnal coordinates. Quantitative inter-model discrepancies in the momentum and energy budgets are much more pronounced in the presence of a steep bottom slope. However, the key findings of this study are consistent across the models, suggesting that they are robust and warrant incorporation into parameterizations of eddy transfer across continental slopes.

Effects of thinning a forest stand on sub-canopy turbulence

The density of a forest canopy affects the degree of influence of vegetation on the mean and turbulence flow fields. Thinning a forest in situ is difficult and expensive therefore many studies investigating the effects of changing canopy density have been done in wind tunnels or with modeling. Here, we analyze data collected at 0.13h, 0.83h, and 1.13h (canopy height; h=21m) as the surrounding loblolly pine stand was progressively thinned three times. The first thinning removed the understory and the two subsequent thinnings removed whole trees leading to a 60% reduction in the overall stand density. As the forest was thinned, turbulence and wind speed near the surface (0.13h) increased and became more connected with above the canopy (1.13h). The variation of the three-dimensional wind components increased for 0.13h when the understory was thinned. Turbulence at 0.83h and 1.13h increased when whole trees were removed (2nd and 3rd thinning). An increase in the peak spectral power of the 0.13h vertical velocity indicated an increase in the influence of larger eddies surviving through the canopy, but these did not affect the vertical turbulence or momentum transfer.

Dam Discharge Events Alter Water Flow in an Estuary in Spain

Three-year observations suggest that increased sediment concentrations inhibit vertical transfer of momentum between water layers for more than 2 months after a high-discharge event.

Parameterization of gaseous dry deposition in atmospheric chemistry models: Sensitivity to aerodynamic resistance formulations under statically stable conditions

Turbulence controls the vertical transfer of momentum, heat and trace constituents in the atmospheric boundary layer. In the lowest 10% of this layer lies the surface boundary layer (SBL) where the vertical fluxes of transferred quantities have been successfully parameterized using the Monin-Obukhov similarity theory in weather forecast, climate and atmospheric chemistry models. However, there is a large degree of empiricism in the stability-correction parameterizations used to formulate eddy diffusivity and aerodynamic resistance particularly under strongly stable ambient conditions. Although the influence of uncertainties in stability-correction parameterizations on eddy diffusivity is actively studied in boundary-layer meteorological modeling, its impact on dry deposition in atmospheric chemistry modeling is not well characterized. In this study, we address this gap by providing the mathematical basis for the relationship between the formulations of vertical surface flux used in meteorological and atmospheric chemistry modeling communities, and by examining the sensitivity of the modeled dry deposition velocities in statically stable SBL to the choice of stability-correction parameterizations used in three operational and/or research environmental models (GEM/GEM-MACH, ECMWF IFS and CMAQ-MM5). Aerodynamic resistances (ra) calculated by the three sets of parameterizations are notably different from each other and are also different from those calculated by a “z-less” scaling formulation under strongly stable conditions (the bulk Richardson number > 0.2). Furthermore, we show that many atmospheric chemistry models calculate ra using formulations which are inconsistent with the derivation of micro-meteorological parameters. Finally, practical implications of the differences in stability-correction algorithms are discussed for the computations of dry deposition velocities of SO2, O3 and reactive bromine compounds for specific cases of stable SBL.

Vertical momentum transfer by weakly nonlinear inertia-gravity internalwaves

Free inertia-gravity internal waves in a plane-parallel flow are considered in the Boussinesq approximation with account of the horizontal turbulent viscosity and diffusion. The dispersion relation and the wave decay rate are derived in the linear approximation. The effect of critical layers, in which the wave frequency with the Doppler shift is equal to the inertial frequency, on the dispersion curves is considered. It is shown that the dispersion curves are cut off in the low-frequency domain due to the critical layers mentioned above. The verticalwave momentum fluxes are nonzero and can be greater than the corresponding turbulent fluxes. It is shown that the Stokes drift velocity component transverse to the direction of propagation of the wave is nonzero with account of the turbulent viscosity and diffusion.

Vertical momentum transfer by internal waves when eddy viscosity and diffusion are taken into account

Free internal waves are considered in a Boussinesq approximation in the situation when horizontal eddy viscosity and diffusion in a vertically inhomogeneous flow are taken into account. The dispersion relation and wave damping factor are found in a linear approximation. The Stokes drift velocity is determined in the second order of smallness based on the wave amplitude. It has been indicated that the Stokes drift velocity, transverse with respect to the wave propagation direction, differs from zero if the flow-rate transverse component depends on the vertical coordinate. Vertical momentum fluxes differ from zero and can be comparable with or exceed the corresponding turbulent fluxes if eddy viscosity and diffusion are taken into account.

Induced chemistry by scattering of electrons from magnesium oxide

A detailed theoretical study is carried out for electron interactions with magnesium oxide (MgO) with incident energies ranging from 0.01 to 5000 eV. This wide range of energy has allowed us to investigate a variety of processes and report data on resonances through eigenphase study, vertical electronic excitation energies, differential, momentum transfer, and total cross sections (TCS), as well as scattering rate coefficients. MgO has a large number of low-lying π excited states and the present study finds overall a good agreement with earlier reported data. In order to compute total cross sections, we have employed the ab initio R-matrix method (0.01 to ∼20 eV) and the spherical complex optical potential method (∼20 to 5000 eV). The R-matrix calculations are performed using a close-coupling method with the aid of 34 target states, 1436 configuration state functions, and 213 channels employing a static exchange plus polarization model. The present study reports evidence for electron scattering resonances through analysis of eigenphase diagrams at low energies below the ionization threshold. In the absence of any theoretical or experimental data for resonances, we have done double differentiation of TCS to confirm the resonances reported here. The present study is a maiden effort to report excitation cross sections, differential cross sections, momentum transfer cross sections, and scattering rate coefficients at low energies below the ionization threshold of the target. Additionally, in the absence of any experimental data and sparse theoretical data for a total elastic cross section, the present comprehensive study will provide a reference data set over such an extensive impact energy range.

Direct Measurements of Turbulence and Flow Characteristics of a Vertical Axis Wind Turbine Using the Eddy Covariance Method

Turbulence intensity measurements of vertical axis wind turbine (VAWT) are essential to detemineitsefficiency and performance. In this study, the eddy covariance (EC) method was used to characterise the flow and directly measure turbulence of a VAWT in a controlled indoor laboratory using an ultrasonic anemometer (at 10 Hz) at specific grid positions of upwind and downwind (in the wake) of the VAWT. In constrast to numerical simulations, this method has the potential to accurately quantify turbulence of wind turbines and thus able to describe the flow patterns around a VAWTexperimentally. Results show that at the upwind position, some of the swept area of the VAWT obstructed the flow due to the counter current flow generated by the VAWT rotors’ rotation while causing some flows to be diverted and concentrated to the concurrent flow area of the VAWT. In the wake of the VAWT, flow velocities and turbulence decreased and dispersed while at the centre line, vertical turbulence decreased towards the bottom (ground) swept area.This downward transfer of turbulence caused generally negative vertical momentum transfer. However, a slight increase of turbulence was observed at the ground surface due to flow deflection.

Impact of a binary size distribution on particle erosion due to an impinging gas plume

Solid particles of nonuniform sizes exhibit behaviors not seen in monodisperse distributions. Following a previous study of monodisperse particles, the goal of this study is to investigate effects of a binary‐size distribution on erosion of lunar soil from a rocket landing. The discrete element method is used to examine near‐field (near impingement) and far‐field behavior. For near‐field simulations, small particles preferentially collide with large particles from below, due to a difference in velocity caused by gas forces, which is analogous to behavior for entrainment in gas‐solid fluidized beds. These collisions cause vertical momentum transfer from small to large particles that affects species and total erosion flux. For far‐field simulations, collisions result in an increase in vertical dispersion (binary) and a reduction in maximum horizontal velocity (binary and monodisperse). These results have implications on the most appropriate modeling framework to use for predictions over large distances utilizing wide size distributions. © 2015 American Institute of Chemical Engineers AIChE J, 62: 984–995, 2016

Prognostic Residual Mean Flow in an Ocean General Circulation Model and its Relation to Prognostic Eulerian Mean Flow

AbstractRecent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWA framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, the analysis is verified by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.

Nocturnal intermittency in surface CO2 concentrations in sub-Saharan Africa

An exploratory study of CO2 concentrations and fluxes was conducted during 2013, at a site 12km North of Harare, Zimbabwe. CO2 measurements were made over four adjacent fields of differing surface vegetation. The data illustrate the role of atmospheric intermittency as a mechanism for transferring CO2 between the surface and the atmosphere. At night, limited atmospheric mixing permits CO2 concentrations to increase to levels well above those conventionally reported (exceeding a spatial average of 450ppm on some nights), but these high levels are moderated by a periodic intermittency that appears similar to that observed elsewhere and often associated with the presence of strong, synoptic-scale winds aloft (especially low-level jets). The availability of CO2 data with adequate time resolution facilitates investigation of the general behavior, which is suspected to be a common although rarely observed feature of the lower terrestrial atmosphere. If true, this means that the nocturnal vertical transfer of momentum, heat and mass is not solely through a constrained spectral continuum of turbulence as much as by intermittent bursts, propagating from above and penetrating the surface boundary layer.

Pressure–Slope Momentum Transfer in Ocean Surface Boundary Layers Coupled with Gravity Waves

AbstractThe paper focuses on the consequences of including surface and subsurface, wind-forced pressure–slope momentum transfer into the oceanic water column, a transfer process that competes with now-conventional turbulence transfer based on mixing coefficients. Horizontal homogeneity is stipulated as is customary when introducing a new surface boundary layer model or significantly new vertical momentum transfer physics to an existing model. An introduction to pressure–slope momentum transfer is first provided by a phase-resolved, vertically dependent analytical model that excludes turbulence transfer. There follows a discussion of phase averaging; an appendix is an important adjunct to the discussion. Finally, a coupled wave–circulation model, which includes pressure–slope and turbulence momentum transfer, is presented and numerically executed. The calculated temperatures compare well with measurements from ocean weather station Papa.

Spatial variability of the wave bottom boundary layer over movable rippled beds

[1] Observations of the spatially dependent velocity field over movable bed forms subjected to slightly skewed and asymmetric regular wave forcing were collected. The dynamics between the ripple elements is dominated by coherent vortices, characterized by the swirling strength, and evidenced in the temporal and spectral characterization. Within the boundary layer, spectral energy in the second harmonic (3f0) is amplified at the ripple slopes and is consistent with the location of the expected strongest pressure gradients. First-moment and second-moment velocity statistics were used to address the spatial variability of the intra-ripple hydrodynamics. Estimates of displacement and momentum thicknesses (δ* and δmom) are smaller than suggested by the higher harmonics, but consistently highlight areas of adverse and favorable pressure gradients. Shear stress and roughness estimates were inferred by fitting a logarithmic model to first-moment and second-moment statistics of the velocity field. The maximum Shields parameter was observed to peak at the stoss slope of asymmetric ripples during the strongest and shorter half-wave period (onshore). First-moment roughness estimates are similar in magnitude to bed load parameterizations provided by Li et al. (1997), and about a factor of 3 larger than second-moment estimates. Assessment of the vertical transfer of horizontal momentum derived using a Reynolds decomposition suggests that stresses inferred from the logarithmic law using first-moment velocity statistics appropriately reproduce the mean momentum transfer for the longer and weaker offshore half-wave period.