Momentum Mixing Research Articles

Kondo impurity on the honeycomb lattice at half-filling

We consider a Kondo-like impurity interacting with fermions on a honeycomb latticeat half-filling, as in the case of graphene. We derive from the lattice model aneffective one-dimensional continuum theory which has, in general, four flavors withangular momentum mixing in the presence of internode scattering processes andsix couplings in the spin-isotropic case. Under particular conditions, however,it can be reduced to a single-coupling multichannel pseudogap Kondo model.We finally calculate, for the case of the presence of an energy dependent Fermivelocity, induced by Coulomb interaction, the critical coupling in the large-N expansion, the magnetic susceptibility and the specific heat.

Numerical Investigations of Mean Winds Within Canopies of Regularly Arrayed Cubical Buildings Under Neutral Stability Conditions

Recently, several attempts have been made to model the wind velocity in an urban canopy in order to accurately predict the mixing and transport of momentum, heat, and pollutants within and above the canopy on an urban scale. For this purpose, unverified assumptions made by Macdonald (Boundary-Layer Meteorol 97:25–45, 2000) to develop a model for the profile of the mean wind velocity within an urban canopy have been used. In the present study, in order to provide foundations for improving the urban canopy models, the properties of the spatially-averaged mean quantities used to make these assumptions have been investigated by performing large-eddy simulations (LES) of the airflow around square and staggered arrays of cubical blocks with the following plan area densities: λ p = 0.05, 0.11, 0.16, 0.20, 0.25, and 0.33. The LES results confirm that the discrepancy between the spatial average of wind velocity and Macdonald’s five-point average of wind velocity can be large in both types of arrays for large λ p . It is also confirmed that Prandtl’s mixing length varies significantly with height within the canopy, contrary to Macdonald’s assumption for both types of arrays and for both small and large λ p . On the other hand, in accordance with Macdonald’s assumption, the sectional drag coefficient is found to be almost constant with height except in the case of staggered arrays with high λ p .

Axisymmetric Synthetic Jets: An Experimental and Theoretical Examination

The flowfield of a round synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied in this paper. The self-similar behavior exhibited by both synthetic and continuous turbulent jets leads to the hypothesis that synthetic jetsmay bemodeled using similarity analysis, just as continuous turbulent jets aremodeled. Accordingly, synthetic jets are modeled using both the Schlichting solution to boundary-layer equations in cylindrical coordinates and the Landau–Squire solution to the Navier–Stokes equations in spherical coordinates, for which the virtual viscosity coefficient of a continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet for bothmodels is obtained from the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flowfield is observed to consist of two regions, as distinguished by the centerline velocity decay: namely, a developing and adeveloped region. The developing region is characterized by a velocity increase followed by a plateau, for which the axial extent of this region scales with the stroke length L. The developed region is identified by the centerline velocity decaying as x , and it is within this region that the jet models are applicable. The velocity decay rate and spreading rate of synthetic jets are observed to increase with stroke ratio L=d, while being independent of the Reynolds number Re. This dependency on stroke ratio is attributed to the increase in impulse and energy of the emerging vortex rings as the stroke ratio increases and their subsequent enhanced interaction. The geometry of the actuator is additionally seen to impact the spreading and decay rates by means of influencing the initial conditions at the orifice. The experiments verify that byusing the adjusted value of the virtual viscosity, the theoreticalmodels of a continuous turbulent jetmay still be used to model a periodic synthetic jet. The virtual viscosity of the synthetic jets under test proves to be larger than that of equivalent turbulent continuous jet based on the same momentum flux. The enhanced viscosity is attributed to the additional momentum transfer and mixing brought about by the periodic introduction and breakdown of the vortex rings in synthetic jets.

On the Relationship between SST Gradients, Boundary Layer Winds, and Convergence over the Tropical Oceans

Abstract A linear mixed layer model that skillfully reproduces observed surface winds and convergence over the tropical oceans is used to examine the relative influence of boundary layer and free-tropospheric processes on the distribution of climatological surface winds and convergence. The semiempirical model assumes a subcloud-layer momentum force balance between pressure gradients, Coriolis acceleration, linearized friction, and downward momentum mixing, and it utilizes boundary conditions from the 40-yr ECMWF Re-Analysis (ERA-40). Observed pressure gradients are linearly decomposed into boundary layer (defined as the region below 850 hPa) and free-tropospheric components, and the surface winds and convergence associated with these components are computed. Results show that surface zonal winds are predominantly associated with a combination of free-tropospheric pressure gradients and downward momentum mixing, whereas the distribution of convergence is primarily due to boundary layer temperature gradients, which are closely related to SST gradients. The authors conclude that the climatological distribution of boundary layer convergence is primarily a function of the pattern of SST gradients and is better regarded as a cause rather than a consequence of deep convection.

Higher angular momentum mixing in a non-spherical color superconductor with violating time reversal invariance

The angular momentum mixing in a non-spherical color superconductor (CSC) with a nonzero azimuthal quantum number and therefore violating time reversal invariance has been examined. The mixing is bound to occur because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading-order QCD running coupling constant and the nonlinearity of the gap equation. The free energy with mixing is lower than that with p-wave pairing only, but still higher than that of the spherical color-spin-locked (CSL) state.

Angular momentum mixing dynamics of attractive Bose–Einstein condensates on a deformed ring

The Hamiltonian of an attractive N-boson system confined on a ring is diagonalized. The particles have strong correlation as a result of a quantum phase transition in the strong-interaction phase, where the yrast states are quasi-degenerate. It is found that a small deformation of the ring will mix the quasi-degenerate yrast states to form cluster states which break the spatial symmetry explicitly. The time evolution of the average angular momentum in an elliptic ring exhibits strong oscillation.

Angular momentum mixing in single flavor color superconductivity with transverse pairing

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity (CSC) cannot be restricted in a single non- s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC of massless quarks with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only, though the amount of the free energy drop is numerically small. Consequently the most stable pairing state in the ultra-relativistic limit remains the spherical color-spin-locked state (CSL).

MECHANISMS OF CONTAMINANT TRANSPORT IN A MULTI‐BASIN LAKE

Tracer studies are combined with a three-dimensional (3-D) numerical modeling study to provide a robust description of hydrodynamic and particle transport in Clear Lake, a multi-basin, polymictic lake in northern California, USA. The focus is on the mechanisms of transport of contaminants away from the vicinity of the Sulphur Bank Mercury Mine and out of the Oaks Arm to the rest of the lake and the hydraulic connection existing among the sub-basins of the lake. Under stratified conditions, the rate of spreading of the tracer was found to be large. In less than a week the tracer spread from the eastern end of the Oaks Arm to the other basins. Under non-stratified conditions, the tracer spread more slowly and had a concentration that gradually diminished with distance from the injection location. The numerical results showed that the mechanisms accounting for these observed patterns occur in pulses, with maximum rates coinciding with the stratified periods. Stratification acts first to enhance the currents by inhibiting vertical momentum mixing and decoupling the surface currents from bottom friction. The diversity of the flow structures that results from the interaction of the wind and the density fields in the lake is responsible for the high dispersion rates. Contaminants originating in the Oaks Arm are shown to be transported into the Lower Arm following the surface currents and into the Upper Arm mainly through the bottom currents. It was also shown that, under stratified conditions, both the baroclinic (density driven) gradients and the wind forcing act jointly to exacerbate the interbasin exchange.

Dust emissions in the West African heat trough the role of the diurnal cycle and of extratropical disturbances

The summertime West African heat trough (HT) is one of the most active dust sources in the world. A detailed case study during May/June 2006 based upon analyses from the European Centre for Medium-Range Weather Forecasts and a new Meteosat dust product illustrates two important mechanisms of dust emissions in this region: (1) The dry continental-scale HT circulation exhibits a strong diurnal cycle characterized by nocturnal low-level jets and downward mixing of momentum to the surface during the build-up of the planetary boundary layer in the morning. This leads to strong gusty surface winds and dust emission, mostly along the northern side of the HT, but also within the southerly monsoon flow. Transports lead to an accumulation of dust near the axis of the HT. (2) Triggered by a lee cyclogenesis south of the Atlas Mountains, the Intertropical Discontinuity that separates dry Saharan and moist monsoonal air shifts northward and allows deep moist convection to penetrate into the Sahara. The evaporation of precipitation in the dry desert air also generates strong gusty winds and dust emissions. This study helps to clarify the physical mechanisms for a previously discovered relation between the annual cycles of dustiness on one hand and near-surface convergence and gustiness on the other hand.

Investigation of shallow mixing layers by BGK finite volume model

Turbulent shallow mixing layers and their associated vortical structures are ubiquitous in rivers, estuaries and coasts. Examples of these flows can be found in compound/composite channels, at the confluence of two rivers, at harbour entrances and at groyne fields. A finite volume 2D model, based on the averaging of the 3D shallow water equations with respect to depth and in which the numerical fluxes are obtained from the Bhatnagar–Gross–Krook (BGK) Boltzmann equation, is applied to shallow mixing layers for which experimental results are available. This model is hereafter referred to as the BGK model or BGK scheme. The BGK scheme is explicit, second order in time and space and conserves both mass and momentum. The BGK relaxation time is locally evaluated from the classical turbulence model of Smagorinsky. The BGK model accurately represents the mean flow field such as mean velocity profile, mean spread of the mixing layer, mean position of the mixing layer centreline and mean surface water profile. In addition, the Kelvin–Helmholtz (KH) instability including inception, vortex roll up, vortex growth by pairing and the eventual decay of the vortices by bed shear is well represented by the model. On the other hand, the magnitude of the turbulence intensity is over-predicted by the shallow water model. This discrepancy is partly due to the fact that the turbulence forcing assumed may not represent the actual random perturbations that may exist in the laboratory experiments and partly due to the inability of the depth-averaged shallow water equations to allow for the redistribution of turbulent energy along the vertical direction, since these governing equations do not model the 3D turbulence. Thus, the depth-averaged shallow water equations are well suited for investigating the KH stability and for predicting mean flow field including velocity profiles and transversal mixing of mass momentum in shallow environments. Accurate prediction of turbulence statistics would require resolving the small 3D scales with respect to water depth.

Three-body correlation in nLi studied via low-lying E1 excitation

We have studied the structure of the Borromean nucleus 11Li via the Coulomb breakup with a Pb target at 70 MeV/nucleon. Momentum vectors of the breakup particles, Li and two neutrons, were measured in coincidence to reconstruct the B(E1) energy spectrum. The strong E1 transitions were observed at Erel ∼ 0.3 MeV with the B(E1) = 1.42(18)e2 fm2 ( = 4.5(6)W.u.), which is the largest E1 strength ever observed in such low excitation energies. This result gives an evidence that the two valence neutrons have spatial dineutron-like correlation. The correlation of the two neutrons is supported by the non-energy weighted E1 cluster sum rule which provides the mean opening angle of (θ12) = 48-18+14 degrees for the two valence neutrons relative to the center of the core. It is suggested that this narrow angle can be related to the angular momentum mixing in the halo neutrons of 11Li.

Upgrades to the Boundary-Layer Scheme in the Met Office Numerical Weather Prediction Model

Recent upgrades to the boundary-layer scheme in the UK Met Office operational global Numerical Weather Prediction model are documented. These comprise a reduction in turbulent mixing in stable conditions over the sea, and the inclusion of non-local momentum mixing in convective conditions. The dependence of low-level winds on changing stability is shown to have been significantly improved. Crucially, it is also found that these improvements in local performance have been achieved without degrading the model skill in terms of synoptic evolution—something that has proved difficult to achieve in the past in many operational models. In fact some aspects of the large-scale flow (e.g. zonal mean winds) have been slightly improved.

Effects of canopy morphology and thermal stability on mean flow and turbulence statistics observed inside a mixed hardwood forest

The influences of thermal stability and seasonal changes in canopy morphology on mean flow and turbulence statistics in a mixed hardwood forest are presented from a year long field experiment at the University of Michigan Biological Station AmeriFlux site. A secondary wind speed maximum at z/ h = 0.07 ( z is height above ground and h is mean canopy height) below the level of peak vegetation area density (VAD) in the understory (young white pines) is observed more frequently and is more pronounced in fully leafed (closed) canopy than defoliated (open) canopy, and in stable than near-neutral and unstable conditions. A secondary wind speed maximum at z/ h = 0.58 is observed only in the closed canopy below the level of peak VAD in the upper canopy (crowns of mature aspen trees), which occurs less frequently and is less pronounced than that at z/ h = 0.07. Horizontal mean winds in the forest are observed to flow to the left (counter-clockwise) of that at the canopy top. The degrees of turning of the mean winds increase with increasing depth into the forest except a reversal (clockwise) near the forest floor in the closed canopy. The degrees of turning are greater in the closed canopy than the open canopy but smaller in near-neutral than unstable and stable conditions. The attenuations of Reynolds stress, correlation coefficient and velocity variances with increasing depth into the forest are more rapid in the closed canopy and in stable conditions. But the relative turbulence intensities are greater in the closed canopy than in the open canopy and decrease with increasing stability. In near-neutral stability, the zero-plane displacement height ( d) for the closed canopy decreases with increasing wind speed (∼0.81 h on average), while d for the open canopy does not show a clear dependence on wind speed (∼0.65 h on average). The bulk drag coefficient ( C D h ) measured at the canopy top is much greater over the closed canopy than the open canopy, contrary to earlier observations over a deciduous forest. But C D h * = C D h / VAI (VAI is vegetation area index) is about the same over the closed and open canopies (∼0.03 in near-neutral stability). The drag coefficient ( C d) for the parameterization of drag force in mean momentum budget equations in closure models increases with decreasing wind speed and varies with height. The drag coefficient ( C d LES ) for the parameterization of drag force in prognostic momentum equations in large-eddy simulations of airflow in plant canopies is smaller than C d, and the ratio C d LES / C d is greater in the open canopy than closed canopy and in stable than near-neutral and unstable conditions due to smaller relative turbulence intensities. All drag coefficients decrease and the displacement height increases with increasing stability, which indicates that these estimated aerodynamic parameters are not entirely the properties of vegetation elements, but are influenced by vertical turbulent mixing of momentum. Both eddy-diffusivity and mixing-lengths for momentum transfer decrease with increasing stability. An evidence of non-local transport is shown by peak values in estimated eddy-diffusivity and mixing-lengths below the crowns of mature aspen trees in the closed canopy. Otherwise, the eddy-diffusivity decreases with increasing depth into the forest, while the mixing-lengths above the level of the peaks are greater in the open canopy and the opposite is true below the level of the peaks.

The Influence of Transient Flow Distortion on Turbulence in Stable Weak-Wind Conditions

Transport by very weak turbulence near the surface, particularly with strong stratification, often violates existing similarity theory due partly to transient distortion of the wind profile by nonstationary mesoscale motions. This problem is examined with 4 months of flux data at seven levels on a 30-m tower. Difficulties with calculation of fluxes and shear with weak winds and weak turbulence are examined. The distortion of the wind profile assumes a wide variety of forms, but sometimes occurs with a transient wind maximum in the lowest 10 m. Though the vertical mixing of momentum is weak for weak-wind nonstationary conditions, it is often more efficient than predicted by existing similarity theory. In fact for weak-wind stable conditions, the flux-gradient relationship depends more on the curvature of the wind profile than the value of the stability parameter. This statistical study suggests a new direction for future work, but does not unravel the physics of the complex and varied structure for stratified weak-wind conditions.

Angular momentum mixing in a non-spherical color superconductor

We study the angular momentum mixing effects in the color superconductor with non-spherical pairing. We first clarify the concept of the angular momentum mixing with a toy model for non-relativistic and spinless fermions. Then we derive the gap equation for the polar phase of dense QCD by minimizing the CJT free energy. The solution of the gap equation consists of all angular momentum partial waves of odd parity. The corresponding free energy is found to be lower than that reported in the literature with p-wave only.

A Comparison of Two Coastal Barrier Jet Events along the Southeast Alaskan Coast during the SARJET Field Experiment*

Abstract The Southeastern Alaskan Regional Jets experiment investigated the structures and physical processes of barrier jets along the coastal Fairweather Mountains near Juneau, Alaska, from 24 September to 21 October 2004. This paper compares in situ aircraft data and high-resolution simulations from the first intensive observation period (IOP1), which featured a nearly terrain-parallel barrier jet (classical jet) with another coastal jet event (IOP7) that was influenced by offshore-directed gap flows at the coast (hybrid jet). IOP1 featured southerly onshore flow preceding a landfalling trough, which was blocked by the coastal terrain and accelerated down the pressure gradient to produce a 5–10 m s−1 wind enhancement in the alongshore direction in the lowest 1 km MSL. In contrast, IOP7 featured higher surface pressure and colder low-level temperatures to the east (inland) of the study area than did IOP1, which resulted in offshore-directed coastal gap flow exiting Cross Sound below ∼500 m that turned anticyclonically and merged with the ambient flow. Unlike the classical jet (IOP1), IOP7 had a surface warm anomaly adjacent to the steep coastal terrain, while a cold anomaly existed farther offshore within the gap outflow. Above the shallow gap flow (>500 m MSL), there were more classical barrier jet characteristics. High-resolution fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) simulations were performed to compare the structures and underlying dynamics between the two cases. Model trajectories show that coastal winds for IOP1 originated offshore, while much of the coastal flow in IOP7 had gap flow origins near the surface and offshore origins above the gap outflow. A model momentum budget suggests that the vertical mixing of southerly momentum from aloft forced the gap outflow in IOP7 to turn anticyclonically more rapidly than an inertial circle. A simulation of IOP7 with the Cross Sound gap removed (filled in) produced a coastal jet with similar maximum wind speeds to the control but resulted in a reduction in the width of the coastal jet by about 40%.

Mixing properties of a stably stratified parallel shear layer

The results of a laboratory investigation on turbulent mixing of mass and momentum associated with the collapse of Kelvin-Helmholtz waves which develop in a stably stratified parallel shear layer with O(103) Schmidt number are presented. The waves were generated in a stratified, tilting tank using a denser fluid underlying a lighter fluid with a velocity shear between the layers. Detailed velocity and density measurements were conducted simultaneously using particle tracking velocimetry and laser-induced fluorescence techniques. Estimation of the efficiency of mixing, the ratio between the diffusive flux of density responsible for mixing, to the turbulent kinetic energy dissipation rate, suggest it is independent of the initial values of the Reynolds and the bulk Richardson numbers. The measurements of the eddy diffusivities of mass and momentum showed a reasonable agreement with other laboratory-based predictions of turbulent mixing and observational data in atmospheric stably stratified flows.

A Comparison of Two Coastal Barrier Jet Events along the Southeast Alaskan Coast during the SARJET Field Experiment

Abstract The Southeastern Alaskan Regional Jets experiment investigated the structures and physical processes of barrier jets along the coastal Fairweather Mountains near Juneau, Alaska, from 24 September to 21 October 2004. This paper compares in situ aircraft data and high-resolution simulations from the first intensive observation period (IOP1), which featured a nearly terrain-parallel barrier jet (classical jet) with another coastal jet event (IOP7) that was influenced by offshore-directed gap flows at the coast (hybrid jet). IOP1 featured southerly onshore flow preceding a landfalling trough, which was blocked by the coastal terrain and accelerated down the pressure gradient to produce a 5–10 m s−1 wind enhancement in the alongshore direction in the lowest 1 km MSL. In contrast, IOP7 featured higher surface pressure and colder low-level temperatures to the east (inland) of the study area than did IOP1, which resulted in offshore-directed coastal gap flow exiting Cross Sound below ∼500 m that turned anticyclonically and merged with the ambient flow. Unlike the classical jet (IOP1), IOP7 had a surface warm anomaly adjacent to the steep coastal terrain, while a cold anomaly existed farther offshore within the gap outflow. Above the shallow gap flow (>500 m MSL), there were more classical barrier jet characteristics. High-resolution fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) simulations were performed to compare the structures and underlying dynamics between the two cases. Model trajectories show that coastal winds for IOP1 originated offshore, while much of the coastal flow in IOP7 had gap flow origins near the surface and offshore origins above the gap outflow. A model momentum budget suggests that the vertical mixing of southerly momentum from aloft forced the gap outflow in IOP7 to turn anticyclonically more rapidly than an inertial circle. A simulation of IOP7 with the Cross Sound gap removed (filled in) produced a coastal jet with similar maximum wind speeds to the control but resulted in a reduction in the width of the coastal jet by about 40%.

The Tropical Atmospheric El Niño Signal in Satellite Precipitation Data and a Global Climate Model

AbstractAspects of the tropical atmospheric response to El Niño related to the global energy and water cycle are examined using satellite retrievals from the Tropical Rainfall Measuring Mission and the Advanced Microwave Scanning Radiometer-E and simulations from the Goddard Institute for Space Studies (GISS) general circulation model (GCM). The El Niño signal is extracted from climate fields using a linear cross-correlation technique that captures local and remote in-phase and lagged responses. Passive microwave and radar precipitation anomalies for the 1997/98 and 2002/03 El Niños and the intervening La Niña are highly correlated, but anomalies in stratiform–convective rainfall partitioning in the two datasets are not. The GISS GCM produces too much rainfall in general over ocean and too little over land. Its atmospheric response to El Niño is weaker and decays a season too early. Underestimated stratiform rainfall fraction (SRF) and convective downdraft mass flux in the GISS GCM and excessive shallow convective and low stratiform cloud result in latent heating that peaks at lower altitudes than inferred from the data. The GISS GCM also underestimates the column water vapor content throughout the Tropics, which causes it to overestimate outgoing longwave radiation. The response of both quantities to interannual Hadley circulation anomalies is too weak. The GISS GCM’s Walker circulation also exhibits a weak remote response to El Niño, especially over the Maritime Continent and western Indian Ocean. This appears to be a consequence of weak static stability due to the model’s lack of upper-level stratiform anvil heating, excessive low-level heating, and excessive dissipation due to cumulus momentum mixing. Our results suggest that parameterizations of mesoscale updrafts, convective downdrafts, and cumulus-scale pressure gradient effects on momentum transport are keys to a reasonable GISS GCM simulation of tropical interannual variability.

Inertial instability in rotating and stratified fluids: barotropic vortices

The unfolding of inertial instability in intially barotropic vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated barotropic vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability drives an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process. It also shows that the equilibration process can result in anticyclones that are more susceptible to horizontal shear instabilities than they were initially, a phenomenon previously observed in laboratory and numerical studies.