Horizontal Eddy Flux Research Articles

The Response of the Water Surface Layer to Internal Turbulence and Surface Forcing

We have carried out an experimental study of the turbulence kinetic energy dissipation rate (ϵ), temperature dissipation rate (χ), and turbulent heat flux (THF) within the water surface layer in the presence of non-breaking wave, surface convection, and horizontal heat and eddy fluxes that play a prominent role in the front. We noted that the non-breaking wave dominates ϵ values within the surface layer. While analyzing the vertical ϵ variability, the presence of a wave-affected layer from the water surface to a depth of z≈1.25λw is observed, where λw is the wavelength. ϵ associated with non-breaking waves ranged to 4.9×10−6–7×10−6 m2/s3 for the wavelength range of 0.038 m < λw < 0.098 m categorized as the gravity and gravity-capillary wave regimes. ϵ values increase for longer λw and non-breaking wave ϵ values represent their significant contribution to the ocean energy budget and dynamic of surface layer considering that the non-breaking wave covers the large fraction of ocean surface. We also found that the surface mean square slope (MSS) and wave generated ϵ have the same order of magnitude, i.e., MSS ∼ϵ. Besides, we have documented that the small-scale temperature fluctuation change (i.e., χ) is consistent with the large-scale temperature gradient change (i.e., d<T>/dz). The value of the THF is approximately constant within the surface layer. It represents that the measured THF near the water surface can be considered a surface water THF, challenging to measure directly.

Oxygen Variability During ENSO in the Tropical South Eastern Pacific

The Oxygen Minimum Zone (OMZ) of the Tropical South Eastern Pacific (TSEP) is one of the most intensely deoxygenated water masses of the global ocean. It is strongly affected at interannual time scales by El Nino (EN) and La Nina (LN) due to its proximity to the equatorial Pacific. In this work, the physical and biogeochemical processes associated with the subsurface oxygen variability during EN and LN in the period 1958 – 2008 were studied using a regional coupled physical-biogeochemical model and in situ observations. The passage of intense remotely forced coastal trapped waves caused a strong deepening (shoaling) of the OMZ upper limit during EN (LN). A close correlation between the OMZ upper limit and thermocline depths was found close to the coast, highlighting the role of physical processes. The subsurface waters over the shelf and slope off central Peru had different origins depending on ENSO conditions. Offshore of the upwelling region (near 88°W), negative and positive oxygen subsurface anomalies were caused by Equatorial zonal circulation changes during LN and EN, respectively. The altered properties were then transported to the shelf and slope (above 200 m) by the Peru-Chile undercurrent. The source of nearshore oxygenated waters was located at 3°S – 4°S during neutral periods, further north (1°S – 1°N) during EN and further south (4°S – 5°S) during LN. The offshore deeper (< 200 – 300 m) OMZ was ventilated by waters originating from ~ 8°S during EN and LN. Enhanced mesoscale variability during EN also impacted OMZ ventilation through horizontal and vertical eddy fluxes. The vertical eddy flux decreased due to the reduced vertical gradient of oxygen in the surface layer, whereas horizontal eddy fluxes injected more oxygen into the OMZ through its meridional boundaries. In subsurface layers, remineralization of organic matter, the main biogeochemical sink of oxygen, was higher during EN than during LN due to oxygenation of the surface layer and in spite of a reduced primary production. Sensitivity experiments highlighted the larger impact of equatorial remote forcing with respect to local wind forcing during EN and LN.

Seasonal and Interannual Variabilities of the Central Indian Ocean Mode

The central Indian Ocean (CIO) mode, an intrinsic coupled mode, plays an important role in the intraseasonal variabilities over the Indian monsoon region. Besides the intraseasonal variabilities, the CIO mode also has pronounced seasonal and interannual variabilities. The CIO mode is active during boreal summer but suppressed during boreal winter. The seasonality is mainly attributable to the barotropic instability, which is caused by the large meridional shear of zonal winds. By decomposing the temporal tendency of the meridional gradient of zonal winds, it is found that the zonal wind shear mainly follows the variation of the horizontal eddy flux, which indicates the importance of the multiscale interaction in tropical dynamics. The interannual variability of the CIO mode also depends on the energy transfer associated with the barotropic instability. The influences of El Niño or La Niña and Indian Ocean dipole–zonal mode (IODZM) on the CIO mode are analyzed. El Niño and La Niña have moderate impacts on the CIO mode. El Niño weakens the CIO mode and La Niña strengthens it via the changes in the low-level zonal wind shear. IODZM does not significantly change the amplitude of the CIO mode but can shift its latitudinal position by modifying the meridional shear of the zonal winds. The low-frequency variabilities of the CIO mode at seasonal and interannual time scales unveil the impacts of the background circulations at the intraseasonal variabilities during the Indian summer monsoon in a multiscale framework. While the low-frequency variabilities of this mode will clearly have an implication for monsoon variability and prediction, further studies are needed to quantify the impacts.

Evaluating Different Parameterizations for Mixed Layer Eddy Fluxes induced by Baroclinic Instability

AbstractIn this study, the authors discuss two different parameterizations for the effect of mixed layer eddies, one based on ageostrophic linear stability analysis (ALS) and the other one based on a scaling of the potential energy release by eddies (PER). Both parameterizations contradict each other in two aspects. First, they predict different functional relationships between the magnitude of the eddy fluxes and the Richardson number (Ri) related to the background state. Second, they also predict different vertical structure functions for the horizontal eddy fluxes. Numerical simulations for two different configurations and for a large range of different background conditions are used to evaluate the parameterizations. It turns out that PER is better suited to capture the Ri dependency of the magnitude of the eddy fluxes. On the other hand, the vertical structure of the meridional eddy fluxes predicted by ALS is more accurate than that of PER, while the vertical structure of the vertical eddy fluxes is well predicted by both parameterizations. Therefore, this study suggests the use of the magnitude of PER and the vertical structure functions of ALS for an improved parameterization of mixed layer eddy fluxes.

Isopycnal Averaging at Constant Height. Part II: Relating to the Residual Streamfunction in Eulerian Space

Abstract In Part I, the “vertical” transport streamfunction was defined as resulting from isopycnic averaging at constant height in the same way that the meridional streamfunction results from averaging at constant latitude. Part II here discusses the relationship between these two isopycnic streamfunctions and the Eulerian residual streamfunction that arises from the transformed Eulerian mean (TEM). It is known that the meridional isopycnic streamfunction can be approximated by a Taylor expansion to give an Eulerian residual streamfunction involving the horizontal eddy flux. This Taylor expansion approximation works well in the interior, removing the spurious mixing associated with the simple Eulerian-averaged streamfunction. However, it fails near the surface where isopycnals outcrop to the surface. It can be shown in a similar way that the vertical isopycnic streamfunction can formally be approximated by a residual streamfunction involving the vertical eddy flux. However, if horizontal isopycnal displacements are large, this approximation fails even in the ocean interior. Inspired by the two different residual streamfunctions, a more general form of TEM formulation is explored. It is shown that the different TEM residual streamfunctions arise from decomposing the eddy flux into a component along isopycnals, which leads to advective flow, and a remaining diffusive component, which is oriented either vertically or horizontally. In theory the diffusive flux can be oriented in any direction, although in practice the orientation should be such that neither the advective flow nor the diffusive flux cross any boundary (surface, sidewalls, and bottom). However, it is not clear how to merge the continuously changing orientation in a physically meaningful way. A variety of approaches are discussed.

On advection and diffusion in the mesosphere and lower thermosphere: The role of rotational fluxes

A formalism to describe the advective and diffusive eddy transport in terms of the mean tracer is presented. It is based on Eulerian averaging, the flux‐gradient relation, and the decomposition of the eddy flux of a tracer into advective, diffusive, and rotational components. The rotational (nondivergent) flux arises because the conservation equation for the mean tracer contains only a divergence of the eddy flux of the tracer. To provide a closure, a modification to the flux separation technique based on the eddy variance equation is introduced. The “eddy‐induced” advective velocity is represented as the sum of two velocities v1 and v2. Velocity v1 is similar to that in the Transformed Eulerian Mean (TEM) formulation but is generalized to account for both horizontal and vertical eddy fluxes and mean gradients. The velocity v2 depends on the flux of eddy variance of the tracer. The diffusion coefficient is represented as a sum of K1, which may serve as a diagnostic of an irreversible mixing, and K2, which describes up‐ or down‐gradient eddy fluxes of the tracer due to local transformations of the eddy variance. Both v2 and K2 arise from taking account of the rotational fluxes. The scheme is applied to output from a global circulation model of the middle atmosphere. It is shown that in the meridional plane the correction v2 to the TEM velocity is small in the mesosphere and lower thermosphere. For the diffusion coefficient, however, the correction K2 must be accounted for above approximately 110 km.

On the thermohaline circulation in flat bottom marginal seas

The thermohaline circulation in an idealized marginal sea is studied using both numerical and analytical models. The circulation is forced by repeating an annual cycle of cooling in the interior of the marginal sea for 2 months and turning off the surface forcing for 10 months. The marginal sea is connected to an open ocean through a narrow strait, thus providing a means to equilibrate the cooling within the marginal sea by exchange with the open ocean. The resulting upper ocean circulation consists of a warm boundary current that flows into the marginal sea through the strait that is gradually eroded as it circulates cyclonically around the marginal sea. The interior of the marginal sea is relatively cold and has a closed cyclonic circulation. The mean downwelling is concentrated within a narrow boundary layer that for a Laplacian parameterization of subgridscale mixing of density and momentum, has a width of L d σ 1/2 and an along-boundary decay scale of L d σ 3/2 D -1 , where L d is the internal deformation radius, σ is the horizontal Prandtl number, and E is a horizontal Ekman number. The net downwelling outside of this boundary layer is very small at all times. The heat balance near the boundary is between vertical advection and horizontal diffusion at scales smaller than the mesoscale. In the interior, cooling by surface forcing and vertical convection is balanced by horizontal eddy fluxes. For some configurations, these eddy fluxes are characterized by very low frequency oscillations (periods of 1-10 years) in the gyre-scale circulation. One of the main results of this study is that the downwelling in the marginal sea is concentrated near the boundaries and depends on details of the mixing of momentum and density on scales smaller than the mesoscale. The basin-scale stratification and circulation also depend on how momentum and density mix within this boundary layer. This suggests that, in addition to resolving the mesoscale eddy field, improved parameterizations of submesoscale mixing are needed to properly represent the circulation in marginal seas and the downwelling limb of the thermohaline circulation.

Diagnoses of an Eddy-Resolving Atlantic Ocean Model Simulation in the Vicinity of the Gulf Stream. Part II: Eddy Potential Enstrophy and Eddy Potential Vorticity Fluxes

Abstract Output of an eddy-resolving model of the North Atlantic is diagnosed in the vicinity of the Gulf Stream (GS), using quasigeostrophic potential vorticity (QGPV), quasigeostrophic potential enstrophy (QGPE), and modified divergent eddy potential vorticity flux, (V′hq′*)d. A tongue or an elongated island of large mean QGPV along the model GS in the top 1000 m is associated with predominantly downgradient (V′hq′*)d, suggesting that the horizontal eddy fluxes are balancing a sink of eddy QGPE in most of the tongue or island by converting the mean QGPE into eddy QGPE. Some large upgradient (V′hq′*)d is observed to the north of the center of the tongue or island, however, suggesting that some of the eddy fluxes in the northern half of the tongue or island of high QGPV are balancing a source of eddy QGPE there by converting eddy QGPE into the mean QGPE. At the intermediate levels of the model, under the GS, eddy QGPE is small, and the role of eddies appears to be mixed; they are forcing the mean to some ...

Potential Vorticity Asymmetries and Tropical Cyclone Evolution in a Moist Three-Layer Model

Abstract The role of potential vorticity (PV) asymmetries in the evolution of a tropical cyclone is investigated using a three-layer model that includes boundary layer friction, surface moisture fluxes, and a convergence-based convective parameterization. In a benchmark experiment, a symmetric vortex is first spun up on an f plane for 24 h. The symmetric vortex has a realistic structure, including a local PV maximum inside its radius of maximum wind (RMW). A weak azimuthal-wavenumber 2 PV asymmetry confined to the lower two layers of the model is then added to the vortex near the RMW. After an additional 2 h (for a total 26-h simulation), the asymmetric PV anomaly produces changes in the symmetric vortex that have significant differences from those in dry experiments with the present model or previous barotropic studies. A diagnosis of the contributions to changes in the symmetric wind tendency due to the asymmetry confirm the dominance of horizontal eddy fluxes at early times. The barotropic eddy kick pr...

Causes of Atlantic Ocean Climate Variability between 1958 and 1998*

Numerical experiments are performed to examine the causes of variability of Atlantic Ocean SST during the period covered by the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis (1958-98). Three ocean models are used. Two are mixed layer models: one with a 75-m-deep mixed layer and the other with a variable depth mixed layer. For both mixed layer models the ocean heat transports are assumed to remain at their diagnosed climatological values. The third model is a full dynamical ocean general circulation model (GCM). All models are coupled to a model of the subcloud atmospheric mixed layer (AML). The AML model computes the air temperature and humidity by balancing surface fluxes, radiative cooling, entrainment at cloud base, advection and eddy heat, and moisture transports. The models are forced with NCEP-NCAR monthly mean winds from 1958 to 1998. The ocean mixed layer models adequately reproduce the dominant pattern of Atlantic Ocean climate variability in both its spatial pattern and time dependence. This pattern is the familiar tripole of alternating zonal bands of SST anomalies stretching between the subpolar gyre and the subtropics. This SST pattern goes along with a wind pattern that corresponds to the North Atlantic Oscillation (NAO). Analysis of the results reveals that changes in wind speed create the subtropical SST anomalies while at higher latitudes changes in advection of temperature and humidity and changes in atmospheric eddy fluxes are important. An observational analysis of the boundary layer energy balance is also performed. Anomalous atmospheric eddy heat fluxes are very closely tied to the SST anomalies. Anomalous horizontal eddy fluxes damp the SST anomalies while anomalous vertical eddy fluxes tend to cool the entire midlatitude North Atlantic during the NAO's high-index phase with the maximum cooling exactly where the SST gradient is strengthened the most. The SSTs simulated by the ocean mixed layer model are compared with those simulated by the dynamic ocean GCM. In the far North Atlantic Ocean anomalous ocean heat transports are equally important as surface fluxes in generating SST anomalies and they act constructively. The anomalous heat transports are associated with anomalous Ekman drifts and are consequently in phase with the changing surface fluxes. Elsewhere changes in surface fluxes dominate over changes in ocean heat transport. These results suggest that almost all of the variability of the North Atlantic SST in the last four decades can be explained as a response to changes in surface fluxes caused by changes in the atmospheric circulation. Changes in the mean atmospheric circulation force the SST while atmospheric eddy fluxes dampen the SST. Both the interannual variability and the longer timescale changes can be explained in this way. While the authors were unable to find evidence for changes in ocean heat transport systematically leading or lagging development of SST anomalies, this leaves open the problem of explaining the causes of the low-frequency variability. Possible causes are discussed with reference to the modeling results.

Estimates of the seasonal cycle of mass and ozone transport at high northern latitudes

Zonally averaged transport of mass and ozone into high northern latitudes exhibits a pronounced annual cycle. During summer, downwelling is at a minimum, and horizontal bulk advection and eddy fluxes of ozone and mass are found to be significant. This study examines in detail the ozone budget between 58 and 67 hPa in a meridional annulus ranging from 60° to 70°N during summer. The area of the study was chosen to correspond with the Photochemistry of Ozone Loss in the Arctic Region in Summer high‐altitude aircraft experiment based in Fairbanks, Alaska, from April to September, 1997. It is found that the seasonal cycle in transport is an important contributor to the resultant seasonal march of ozone at high latitudes. The horizontal eddy contribution to the ozone tendency at high latitudes in the lower stratosphere is found to be large and negative (reducing ozone) during middle and late summer, where it more than offsets the increasing ozone tendency due to advection by the residual circulation. During early summer, the high‐latitude air mass appears to be relatively isolated, with in situ chemical processes driving the ozone tendency.

Three‐dimensional simulation of stratospheric trace gas distributions measured by CRISTA

The Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) experiment has been flown on two space shuttle missions (STS 66 and STS 85). During these missions, global trace gas distributions have been measured with high spatial resolution. The first flight was performed in early November 1994 during a period of disturbed dynamical conditions characterized by relatively large wave activity and associated exchange of tropical and extratropical air. As a result, numerous small‐ and medium‐scale structures were present in the trace gas distributions measured by CRISTA. The detailed structure of the constituent distributions has been modeled with the National Center for Atmospheric Research Research on Ozone in the Stratosphere and Its Evolution (ROSE) model, which is driven by assimilated winds and temperatures provided by the U.K. Meteorological Office. The modeled trace gas distributions capture much of the measured structures. Very good agreement is found in the lower stratosphere of the northern hemisphere, with the exception of unrealisticly high variability of the modeled trace gas fields at equatorial and subtropical latitudes. In this paper, model results of two specific tracers, CFC‐11 and N2O, are compared to respective CRISTA measurements. For quantitative comparisons of trace gas transport in the ROSE model and trace gas transport associated with the measurements, CRISTA version 1 (level 2) data have been assimilated into the model by using a simple sequential technique. The trace gas assimilation system interpolated the measured distributions of long‐lived tracers onto the model grid and yields synoptic fields that are consistent with the CRISTA measurements, at each time step of the model (20 min). Horizontal eddy fluxes of CFC‐11 (31.6 mbar) calculated from the assimilated trace gas concentrations are in reasonable agreement with respective fluxes calculated from modeled trace gas fields without data assimilation. Both data sets indicate a large degree of temporal cancellation of eddy transport during the time period of the CRISTA measurements. The assimilated trace gas distributions represent a value‐added level 3 product, which has been used for transport and budget studies of CFC‐11 (31.6 mbar) and CH4 (4.6 mbar). The study indicates that irreversible transport processes are rather important at the 4.6 mbar pressure level during the time period of the CRISTA measurements. Most interesting is a pronounced mixing event from midlatitudes into the tropics, which is also evident in measured and calculated zonal mean CH4 mixing ratio tendencies.

224Ra distribution in surface and deep water of Long Island Sound: sources and horizontal transport rates

Measurements of surface water and deep water 224Ra (half-life 3.64 days) distributions in Long Island Sound (LIS) were conducted in July 1991. Because the pycnocline structure of LIS had been in place for about 50 days in July (long compared to the half-life of 224Ra), 224Ra in the surface water and the deep water operate as separate systems. In the surface water, the fine-grain sediments of nearshore and saltmarsh environments provide a strong source of 224Ra, which is horizontally mixed away from the shore to central LIS. A one-dimensional model of 224Ra distribution suggests across-LIS horizontal eddy dispersivity of 5–50 m 2 s −1. In the deep water, the mid-LIS sediment flux of 224Ra is enhanced by ∼2x relative to the periphery, and the horizontal eddy flux is from central LIS to the periphery. A second one-dimensional model suggests a cross-LIS horizontal eddy dispersivity below the thermocline of 5–50 m 2 s −1. 224Ra fluxes into the deep water of the central LIS are likely enhanced by (1) inhomogeneous sediment or (2) a reduced scavenging of 224Ra in the sediments of central LIS brought about by low oxygen conditions (hypoxia) and the loss of the MnO 2 scavenging layer in the sediments. These rates of horizontal eddy dispersivity are significantly less than the estimate of 100–650 m 2 s −1 (Riley, 1967) but are consistent with the transport necessary to explain the dynamics of oxygen depletion in summer LIS. These results demonstrate the use of 224Ra for quantifying the parameters needed to describe estuarine mixing and transport.

Numerical Simulation of Flow around a Tall Isolated Seamount. Part II: Resonant Generation of Trapped Waves

A sigma-coordinate, primitive equation ocean circulation model is used to explore the problem of the remnant generation of trapped waves about a tall, circular, isolated seamount by an incident oscillatory barotropic current. The numerical solutions are used to extend prior studies into the fully nonlinear regime, and in particular to quantify and interpret the occurrence of residual circulation. Specific attention is also devoted to the dependence of the resonance and rectification mechanisms on stratification, forcing frequency, and choice of subgrid-scale viscous closure. Resonantly generated trapped waves of significant amplitude are found to occur broadly in parameter space; a precise match between the frequency of the imposed incident current and the frequency of the trapped free wave is not necessary to produce substantial excitation of the trapped wave. The maximum amplification factors produced in these numerical solutions, O(100) times the strength of the incident current, are consistent with previous studies. In the presence of nonlinear advection, strong residual currents are produced. The time-mean circulation about the seamount is dominated by a strong bottom-intensified, anticyclonic circulation closely trapped to the seamount. Maximum local time-mean current amplitudes are found to be as large as 37% of the magnitude of the propagating waves. In addition to the strong anticyclonic residual flow, there is a weaker secondary circulation in the vertical-radial plane characterized by downwelling over the top of the seamount at all depths. Maximum vertical downwelling rates of several tens of meters per day occur at the summit of the seamount. The vertical mass flux implied by this systematic downwelling is balanced by a slow radial flux of mass directed outward along the flanks of the seamount. Time-mean budgets for the radial and azimuthal components of momentum show that horizontal eddy fluxes of momentum are responsible for transporting net radial and azimuthal momentum from the far field to the upper flanks of the seamount. There, Coriolis and pressure gradient forces provide the dominant balances in the radial direction. However, the Coriolis force and viscous effects provide the primary balance for the azimuthal component.

Non—Acceleration theorem in a primitive equation system: I. Acceleration of zonal mean flow

Non—acceleration theorem in a primitive equation system is developed to investigate the influences of waves on the mean flow variation against external forcing. Numerical results show that mechanical forcing overwhelms thermal forcing in maintaining the mean flow in which the internal mechanical forcing associated with horizontal eddy flux of momentum plays the most important roles. Both internal forcing and external forcing are shown to be active and at the first place for the mean flow variations, whereas the forcing-induced mean meridional circulation is passive and secondary. It is also shown that the effects on mean flow of external mechanical forcing are concentrated in the lower troposphere, whereas those due to wave-mean flow interaction are more important in the upper troposphere. These act together and result in the vertically easterly shear in low latitudes and westerly shear in mid-latitudes. This vertical shear of mean flow is to some extent weakened by thermal forcing.

The Maintenance Mechanisms of Transient Large-Scale Variations in the Atmosphere. Part 1: Potential Temperature and Moisture

The budget equations for the transient variance of a scalar s (s′2¯) and its squared time mean (s2¯) are derived for a hydrostatic fluid. They are discussed and illustrated with two alternative box diagrams. The 10 yr rawinsonde global data of Oort are used in presenting and discussing the observed atmospheric variance budgets of potential temperature and moisture in the DJF season, excluding year-to-year variations. The results indicate that the daily variances (θ′2¯ and q′2¯) are maintained largely by the downgradient heat and moisture horizontal transient eddy (TE) fluxes which are strong in the midlatitude baroclinic zones (storm tracks) in both hemispheres. The flux convergence (advection of existing variance by the time-mean wind) is small and so the production must be compensated by the damping net effect of upgradient vertical potential temperature fluxes, third order flux divergences and time correlations between eddies and forcing. In contrast, the budgets of the squared means (θ′2¯ and q2¯) are governed by the time-mean sources with compensating large advections by the mean wind and a smaller smoothing effeect from the transient eddies.

Diagnosis of the Net Cloud Mass Flux in Gate

Abstract A diagnostic analysis of the net cloud mass flux for the mean state of Phase III is presented. In the upper troposphere, the environmental mass flux is shown to be slightly larger than the adiabatic sinking motion required by radiative cooling. At the outflow layer of tall clouds, if the moistening effect due to detrainments is balanced primarily by the drying caused by adiabatic sinking in the environment, the computed net detrainment rate would be underestimated. It is hypothesized that a considerable portion of the moisture detrained from tall clouds is transported horizontally toward higher latitudes by horizontal eddy fluxes. The diagnosed environmental subsidence has a maximum in the midtroposphere and is less than 1.5 times the sinking motion required by the radiative cooling in low levels. The vertical profile of the diagnosed net detrainment rate suggests three primary detrainment layers: below 800 mb, between 700 and 500 mb, and above 300 mb. It is shown that overprediction of the cloud...

On the Interpretation of Eddy Fluxes During a Blocking Episode

Abstract Using twice daily synoptic charts, objectively analyzed at the National Meteorological Centre, horizontal eddy fluxes of temperature and quasi-geostrophic potential vorticity are computed for the month Of July 1976, when a blocking anticyclone was centered over western Europe. The local time-averaged eddy variance equations are used to provide a dynamical basis for interpreting the spatial pattern of eddy fluxes, and their relation to mean gradients. It is shown that a rotational non-divergent flux can be identified, the cross-gradient component of which balances the mean flow advection of eddy variance. The remaining flux is the dynamically significant one which helps maintain the block and can be understood in terms of a response to sources and sinks of eddy variance.

On the Direction of the Eddy Momentum Flux in Baroclinic Instability

Abstract The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potenti...

The Transport of Trace Chemicals by Planetary Waves in the Stratosphere Part 2: Transport of O3and N2O by Transient Waves

Abstract The transport of ozone and nitrous oxide by transient planetary wave in the stratosphere is studied on a midlatitude β-plane with Newtonian cooling. The transport is found for chemically-inert traces when the mean-zonal state is forced from equilibrium by an initial switch-on of the wave at the lower boundary and returned to the initial state by radiative damping. In the absence of a critical level the net change in the tracer was due almost entirely to horizontal eddy flux convergence. However, this net change could also be described in terms of a one-ell Lagrangian-mean circulation. In the critical level case the net transport resulted from the superposition of the one-cell Legragian-mean circulation and the critical level circulation of Matsuno and Nakamura, as well as from particle mixing. It is concluded that transient waves are more important in tracer transport than steady waves because of the nonlinear dependence of transport on wave amplitude and Doppler-shifted frequency. Critical level...