Vertical Mixing Of Momentum Research Articles

Filament Frontogenesis by Boundary Layer Turbulence

AbstractA submesoscale filament of dense water in the oceanic surface layer can undergo frontogenesis with a secondary circulation that has a surface horizontal convergence and downwelling in its center. This occurs either because of the mesoscale straining deformation or because of the surface boundary layer turbulence that causes vertical eddy momentum flux divergence or, more briefly, vertical momentum mixing. In the latter case the circulation approximately has a linear horizontal momentum balance among the baroclinic pressure gradient, Coriolis force, and vertical momentum mixing, that is, a turbulent thermal wind. The frontogenetic evolution induced by the turbulent mixing sharpens the transverse gradient of the longitudinal velocity (i.e., it increases the vertical vorticity) through convergent advection by the secondary circulation. In an approximate model based on the turbulent thermal wind, the central vorticity approaches a finite-time singularity, and in a more general hydrostatic model, the central vorticity and horizontal convergence are amplified by shrinking the transverse scale to near the model’s resolution limit within a short advective period on the order of a day.

Atmospheric responses to oceanic eddies in the Kuroshio Extension region

AbstractWe examined atmospheric responses to 35,000+ oceanic eddies in the Kuroshio Extension region during the period of 2006–2009. Using satellite data, we showed that cold (warm) eddies cause surface winds to decelerate (accelerate) and reduce (increase) latent and sensible heat fluxes, cloud liquid water, water vapor content, and rain rate; all of these changes are quantified. Both the linear correlation between wind divergence and downwind sea surface temperature (SST) gradient and the correspondence between vorticity and crosswind SST gradient support the vertical momentum mixing mechanism, which indicates that SST perturbations modify surface winds by changing the vertical turbulent mixing in the marine atmospheric boundary layer (MABL). High‐resolution National Centers for Environmental Prediction Climate Forecast System Reanalysis (CFSR) data can reproduce the atmospheric responses to the oceanic eddies in the MABL albeit with some differences in intensity. In addition, the CFSR data reveal that the atmospheric responses to these oceanic eddies are not confined in the MABL. MABL deepens (shoals) over the warm (cold) eddies; enhanced (reduced) vertical transport of transient zonal momentum occurs over the warm (cold) eddies from the sea surface to about 850 hPa level; vertical velocity anomalies over oceanic eddies penetrate beyond the MABL into free atmosphere; there exists a positive correlated relationship between SST and convective rain rate anomalies, indicative of ocean eddies' impact on the free troposphere. However, the composites of cloud liquid water and rain rate are different from the results based on the satellite data.

Climatology and Ensemble Predictions of Nonconvective High Wind Events in the New York City Metropolitan Region

Abstract Damaging wind events not associated with severe convective storms or tropical cyclones can cause significant problems with transportation, infrastructure, and public safety over the northeastern United States. These nonconvective wind events (NCWEs) are difficult to forecast in New York City and surrounding regions as revealed by the relatively poor probability of detection (POD) and false alarm ratio (FAR) in recent years. This paper investigates the climatology of NCWEs between 15 September and 15 May over 13 cool seasons from 2000/01 through 2012/13. The events are separated into three distinct synoptic patterns: pre-cold-frontal (PRF), post-cold-frontal (POF), and nor’easter/coastal storm (NEC) cases. Relationships between observed winds and some atmospheric parameters such as 900-hPa geopotential height gradient, 3-h mean sea level pressure (MSLP) tendency, low-level wind profile, and stability are also presented. Overall, PRF and NEC have the largest FAR, because several events with a low-level jet at 1–2 km above the surface have relatively strong low-level stability that limits vertical momentum mixing. The POD is lowest for the POF events, which have a strong diurnal influence given the relatively deep mixed layer. Verification is also conducted over the cool seasons from 2009/10 to 2013/14 using the Short Range Ensemble Forecast (SREF) system from the National Centers for Environmental Prediction (NCEP). Both deterministic and probabilistic verification metrics are used to evaluate the performance of the ensemble during NCWEs. Although the SREF has more forecast skill than any of the deterministic SREF control members, it is rather poorly calibrated and exhibits a significant overconfidence given its positive wind speed bias in the lower troposphere.

Submesoscale Cold Filaments in the Gulf Stream

Abstract A set of realistic, very high-resolution simulations is made for the Gulf Stream region using the oceanic model Regional Oceanic Modeling System (ROMS) to study the life cycle of the intense submesoscale cold filaments that form on the subtropical gyre, interior wall of the Gulf Stream. The surface buoyancy gradients and ageostrophic secondary circulations intensify in response to the mesoscale strain field as predicted by the theory of filamentogenesis. It can be understood in terms of a dual frontogenetic process, along the lines understood for a single front. There is, however, a stronger secondary circulation due to the amplification at the center of a cold filament. Filament dynamics in the presence of a mixed layer are not adequately described by the classical thermal wind balance. The effect of vertical mixing of momentum due to turbulence in the surface layer is of the same order of magnitude as the pressure gradient and Coriolis force and contributes equally to a so-called turbulent thermal wind balance. Filamentogenesis is disrupted by vigorous submesoscale instabilities. The cause of the instability is the lateral shear as energy production by the horizontal Reynolds stress is the primary fluctuation source during the process; this contrasts with the usual baroclinic instability of submesoscale surface fronts. The filaments are lines of strong oceanic surface convergence as illustrated by the release of Lagrangian parcels in the Gulf Stream. Diabatic mixing is strong as parcels move across the filaments and downwell into the pycnocline. The life cycle of a filament is typically a few days in duration, from intensification to quasi stationarity to instability to dissipation.

A Numerical Simulation Study of the Effects of Anvil Shading on Quasi-Linear Convective Systems

Abstract Numerical simulations are used to investigate how the attenuation of solar radiation by the intervening cumulonimbus cloud, particularly its large anvil, affects the structure, intensity, and evolution of quasi-linear convective systems and the sensitivity of the effects of this “anvil shading” to the ambient wind profile. Shading of the pre-gust-front inflow environment (as opposed to shading of the cold pool) has the most important impact on the convective systems. The magnitude of the low-level cooling, associated baroclinicity, and stabilization of the pre-gust-front environment due to anvil shading generally increases as the duration of the shading increases. Thus, for a given leading anvil length, a slow-moving convective system tends to be affected more by anvil shading than does a fast-moving convective system. Differences in the forward speeds of the convective systems simulated in this study are largely attributable to differences in the mean environmental wind speed over the depth of the troposphere. Anvil shading reduces the buoyancy realized by the air parcels that ascend through the updrafts. As a result, anvil shading contributes to weaker updrafts relative to control simulations in which clouds are transparent to solar radiation. Anvil shading also affects the convective systems by modifying the low-level (nominally 0–2.5 km AGL) vertical wind shear in the pre-gust-front environment. The shear modifications affect the slope of the updraft region and system-relative rear-to-front flow, and the sign of the modifications is sensitive to the ground-relative vertical wind profile in the far-field environment. The vertical wind shear changes are brought about by baroclinic vorticity generation associated with the horizontal buoyancy gradient that develops in the shaded boundary layer (which makes the pre-gust-front, low-level vertical wind shear less westerly) and by a reduction of the vertical mixing of momentum due to the near-surface (nominally 0–300 m AGL) stabilization that accompanies the shading-induced cooling. The reduced mixing makes the pre-gust-front, low-level vertical shear more (less) westerly if the ambient, near-surface wind and wind shear are westerly (easterly).

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.

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.

On the critical Richardson number in stably stratified turbulence

AbstractThe critical Richardson number, Ric, is used in studies of stably stratified turbulence as a measure of flow laminarization. The accepted range of Ric is between 0.2 and 1. A growing body of experimental and observational data indicates, however, that turbulence survives for Ri ≫ 1. This result is supported by a new spectral theory of turbulence that accounts for strong anisotropy and waves. The anisotropization results in the enhanced horizontal mixing of both momentum and scalar. Internal wave contribution preserves vertical momentum mixing above its molecular level. In the absence of laminarization, Ric becomes devoid of its conventional meaning. Copyright © 2007 Royal Meteorological Society

Tidal currents in the northwestern Adriatic: High‐frequency radio observations and numerical model predictions

A 2‐year deployment of high‐frequency radio current meters along the Italian coast of the northwestern Adriatic is used to characterize the surface tidal currents. In the middle of the basin, the M2 and K1 currents oscillate along the basin axis, but become more circular toward the Italian coast. Comparisons with a 3‐D finite‐element nonlinear numerical model of the tides show a good agreement for phases in the middle of the basin, although modeled currents amplitudes are overestimated. However, modeled phases lag observed phases by up to 50° (1.7 hours) for M2 and 100° (6.7 hours) for K1, and modeled amplitudes are underestimated, in a 10–20 km wide strip along the Italian coast. This shallow (< 30 m deep) region is stratified by low‐salinity surface water from the Po, and laterally sheared by the Western Adriatic Current, both absent from the model but possibly affecting tidal propagation. The model may also incompletely parameterize the combined effects of bottom friction and vertical mixing of momentum.

On Boundary Layer Separation in the Lee of Mesoscale Topography

Abstract The onset of boundary layer separation (BLS) forced by gravity waves in the lee of mesoscale topography is investigated based on a series of numerical simulations and analytical formulations. It is demonstrated that BLS forced by trapped waves is governed by a normalized ratio of the vertical velocity maximum to the surface wind speed; other factors such as the mountain height, mountain slope, or the leeside speedup factor are less relevant. The onset of BLS is sensitive to the surface sensible heat flux—a positive heat flux tends to increase the surface wind speed through enhancing the vertical momentum mixing and accordingly inhibits the occurrence of BLS, and a negative heat flux does the opposite. The wave forcing required to cause BLS decreases with an increase of the aerodynamical roughness zo; a larger zo generates larger surface stress and weaker surface winds and therefore promotes BLS. In addition, BLS shows some sensitivity to the terrain geometry, which modulates the wave characteristics. For a wider ridge, a higher mountain is required to generate trapped waves with a wave amplitude comparable to that generated by a lower but narrower ridge. The stronger hydrostatic waves associated with the wider and higher ridge play only a minor role in the onset of BLS. It has been demonstrated that although hydrostatic waves generally do not directly induce BLS, undular bores may form associated with wave breaking in the lower troposphere, which in turn induce BLS. In addition, BLS could occur underneath undular jump heads or associate with trapped waves downstream of a jump head in the presence of a low-level inversion.

Turbulent structure of high‐density suspensions formed under waves

We performed a series of laboratory experiments on the interactions between turbulent wave boundary layers and a predominantly silt‐sized sediment bed. Under a wide range of wave conditions similar to those observed on storm‐dominated midshelf environments we produced quasi‐steady high‐density benthic suspensions. These suspensions were turbulent, while containing large near‐bed concentrations of suspended sediment (17–80 g/L), and were separated from the upper water column by a lutocline. Detailed measurements of the vertical structure of velocity, turbulence, and sediment concentration revealed that the wave boundary layer, while typically >1 cm thick in sediment‐free conditions, was reduced substantially in size, often to <3 mm, with the addition of suspendible sediment. This likely resulted from sediment‐induced stratification that limited vertical mixing of momentum. Despite boundary layer reduction the flows were able to support high‐density suspensions as thick as 8 cm because turbulent energy was transported upward from this thin but highly energetic near‐bed region. Standard formulations of the Richardson number for shear flows are not applicable to our experiments since the suspensions were supported from transported rather than locally produced turbulence.

Seasonal and Interannual Variations in the Daily Cycle of Winds over the Galápagos

Abstract While the daily cycle of near-surface winds over the equatorial east Pacific has been studied in some detail, little is known about the daily cycle above the surface layer. Furthermore, the causes of the observed near-surface daily cycle are not well understood. A better understanding of the structure and forcing mechanisms at work on the lower-tropospheric winds over this region may increase our appreciation for the varying importance of local and remote atmospheric and oceanic processes. This study documents the daily cycle of lower-tropospheric winds over one of the Galápagos Islands during the late 1990s, as well as how it varied seasonally and interannually, using half-hourly profiler winds. The well-known zonal semidiurnal tide is evident in the data, as is a diurnal cycle that is predominantly meridional and may be driven by the results of convection over the Andes. In addition, the high vertical resolution of the wind profiles reveals a decoupling of the daily cycle of winds below ∼500 m from those aloft during periods of cold (<23°C) SSTs. This decoupling, which is not evident in long-term mean profiles that effectively filter the daily cycle, may inhibit the vertical mixing of momentum or vertical propagation of tidal or wave signatures over the region.

Can large wind farms affect local meteorology?

The RAMS model was used to explore the possible impacts of a large wind farm in the Great Plains region on the local meteorology over synoptic timescales under typical summertime conditions. A wind turbine was approximated as a sink of energy and source of turbulence. The wind farm was created by assuming an array of such turbines. Results show that the wind farm significantly slows down the wind at the turbine hub‐height level. Additionally, turbulence generated by rotors create eddies that can enhance vertical mixing of momentum, heat, and scalars, usually leading to a warming and drying of the surface air and reduced surface sensible heat flux. This effect is most intense in the early morning hours when the boundary layer is stably stratified and the hub‐height level wind speed is the strongest due to the nocturnal low‐level jet. The impact on evapotranspiration is small.

Satellite Observations of Cool Ocean–Atmosphere Interaction

Over most of the World Ocean, sea surface temperature (SST) is below 26°C and atmospheric deep convection rarely takes place. Cool ocean–atmosphere interaction is poorly understood and this lack of understanding is a stumbling block in the current effort to study non-ENSO climate variability. Using new satellite observations, the response of surface wind and low clouds to changes in SST is investigated over cool oceans, where the planetary boundary layer (PBL) is often capped by a temperature inversion. While one-way atmospheric forcing is a major mechanism for basinscale SST variability in the extratropics, clear wind response is detected in regions of strong ocean currents. In particular, SST modulation of vertical momentum mixing emerges as the dominant mechanism for SST-induced wind variability near oceanic fronts around the world, which is characterized by a positive SST–wind speed correlation. Several types of boundary layer cloud response are found, whose correlation with SST varies from positive to negative, depending on the role of surface moisture convergence. Noting that the surface moisture convergence is strongly scale dependent, it is proposed that horizontal scale is important for setting the sign of this SST–cloud correlation. Finally, the processes by which a shallow PBL response might lead to a deep, tropospheric-scale response and the implications for the study of extratropical basin-scale air–sea interaction are discussed.

Reynolds Stresses and Secondary Circulation in a Stratified Rotating Shear Flow

Abstract A transverse secondary circulation should result from vertical mixing of momentum in a stratified shear flow influenced by the earth's rotation. A rigidly mounted acoustic Doppler current profiler was deployed at the bottom of Juan de Fuca Strait, a stratified estuary on the west coast of North America, for 21 days, to examine this dynamical process and its variation over a spring–neap tidal cycle. The data demonstrate a significant fortnightly modulation of the estuarine exchange flow, with stronger along-channel flow, less dynamic stability, and much greater cross-strait currents at neap tide than at spring tide. Reliable estimates of the Reynolds stresses in the stratified shear flow away from boundaries were also obtained. They were small except for several days around neap tide when they were associated with times of reduced Richardson number. These stresses are not related in any simple way (such as with a smooth, positive, eddy viscosity) to the shear of the mean flow but do have a pattern...

Entrainment, Rayleigh Friction, and Boundary Layer Winds over the Tropical Pacific

Abstract Winds over the tropical Pacific are interpreted using mixed-layer theory. The theory—which posits that the surface winds can be derived in terms of a force balance among surface drag, pressure gradients, Coriolis forces, and the vertical mixing of momentum into the boundary layer (entrainment)—is very successful in predicting the seasonal climatology of the surface winds. The model is also used as a basis for interpreting previous results. In particular the model illustrates why studies that model the momentum flux divergence as a Rayleigh damping find optimal damping coefficients that are anisotropic. A linear variant of the model, which also incorporates entrainment but neglects the quadratic relation between the wind speed and the surface stress, is also found to predict the surface winds skillfully. In addition to improving the representation of the winds, it leads to realistic representations of the divergence of the vector wind. If the key parameters of the model (the entrainment rate and t...

On the potential influence of ice nuclei on surface‐forced marine stratocumulus cloud dynamics

The mixed phase cloudy boundary layer that occurs during off‐ice flow in the marine Arctic was simulated in an environment with a strong surface heat flux (nearly 800 W m−2). A two‐dimensional, eddy‐resolving model coupled to a detailed cloud microphysical model was used to study both liquid phase and mixed phase stratocumulus clouds and boundary layer (BL) dynamics in this environment. Since ice precipitation may be important to BL dynamics, and ice nuclei (IN) concentrations modulate ice precipitation rates, the role of IN in cloud and BL development was explored. The results of several simulations illustrate how mixed phase microphysical processes affect the evolution of the cloudy BL in this environment. In agreement with past studies, BLs with mixed phase clouds had weaker convection, shallower BL depths, and smaller cloud fractions than BLs with clouds restricted to the liquid phase only. It is shown that the weaker BL convection is due to strong ice precipitation. Ice precipitation reduces convective strength directly by stabilizing downdrafts and more indirectly by sensibly heating the BL and inhibiting vertical mixing of momentum thereby reducing surface heat fluxes by as much as 80 W m−2. This feedback between precipitation and surface fluxes was found to have a significant impact on cloud/BL morphology, producing oscillations in convective strength and cloud fraction that did not occur if surface fluxes were fixed at constant values. Increases in IN concentrations in mixed phase clouds caused a more rapid Bergeron‐Findeisen process leading to larger precipitation fluxes, reduced convection and lower cloud fraction. When IN were removed from the BL through precipitation, fewer crystals were nucleated at later simulation times leading to progressively weaker precipitation rates, greater cloud fraction, and stronger convective BL eddies.

A Two-Layer Model of Shelfbreak Jets with Application to the Labrador Current

Abstract The role played by bottom friction, bottom slope, β effect, and density mixing in exchange between the shelf and a frontal jet is examined in the light of a two-layer model. The model uses linear dynamics and bottom and interfacial friction to parameterize vertical momentum mixing, and Newtonian cooling to parameterize density mixing. It is assumed that the dynamics approximately obey Csanady’s diffusion equations in both shelf and frontal regions. Assuming a velocity profile appropriate to a shelfbreak jet, the authors examine how the various dynamical factors can affect cross-shelf exchange in the frontal region and derive some front solutions by assuming a simple torque balance. It is shown that the β effect and density mixing both produce onshore geostrophic fluxes and counteract the offshore flux due to the frictional torque. Consideration of the conditions at the intersection point of the front with the bottom shows an important role of the JEBAR effect in changing the cross-shelf circulati...

Application of a range of turbulence energy models to the computation of the internal tide

SUMMARY A non-linear, three dimensional, baroclinic model with a range of turbulence energy submodels and algebraic models for the vertical mixing of momentum and density, is used in a cross shelf form to examine the spatial variation of vertical mixing due to the internal tide at the shelf edge off the west coast of Scotland. Particular emphasis is placed on the sensitivity of the mixing to the form of the parameterization of the subgrid scale processes. Calculations using a fine finite difference grid in the horizontal of the order of 0.6 km with 50 sigma levels in the vertical and a typical winter time stratification, show that the model can reproduce the major features of the internal tide with the range of parameterizations considered here, although there are some differences in the magnitude of both the velocity and mixing intensity of the internal tide, depending upon the parameterization of the mixing. In particular, the turbulence energy models show regions of intense mixing at the sea bed where the internal tide is generated and at the sea surface above the shelf break associated with the shear production of turbulence. These differences suggest that detailed measurements of current, internal displacement of density fields and turbulence dissipation rate may be able to assess the accuracy of the various mixing models. Calculations, however, show that the internal tide is particularly sensitive to small perturbations in the initial density field, suggesting that besides detailed measurements to validate the model, a detailed synoptic data set is required for model initialization. © 1998 John Wiley & Sons, Ltd.

On the Net Cyclonic Circulation in Large Stratified Lakes*

Schwab et al. have investigated a possible cause of long-term cyclonic circulation often observed in stratified lakes. They conclude that the adiabatic boundary condition applied to the bottom boundary leads to cyclonic circulation. In this note the authors emphasize that it is the combination of vertical mixing of density, the associated bottom and surface boundary conditions, and variable bottom topography that is important. The authors demonstrate the mechanism using a numerical model. Results also demonstrate the important role of the cross-shore flow (driven by vertical mixing of momentum) in setting the maximum azimuthal flow speed and the cross-shore structure of the azimuthal flow.