Dynamical model of mesoscales in z-coordinates

The seasonality of eddy kinetic energy (EKE) is analyzed in the north Indian Ocean by adopting high-resolution ocean reanalysis data. Significant eddy energy can be mainly spotted in six regions, including the Somali Current (SC) region, the Gulf of Aden, the Laccadive Sea, the east of Sri Lanka, the East Indian Coastal Current (EICC) region, and the northwest of Sumatra. As the most energetic region, the EKE averaged above 200 m could exceed 0.15 m2·s-2 in the SC region, whereas the mean EKE above 200 m is less than 0.04 m2·s-2 in the other regions. The barotropic and baroclinic instabilities are vital to eddy energy, and the contribution of each term in the barotropic/baroclinic equations varies with season and region. In the SC region and EICC region, EKE is primarily generated by barotropic conversion due to the sharp velocity shear caused by the strong SC during the summer monsoon and the EICC from March to June. For the other regions, the leading source of EKE is the eddy potential energy (EPE), which is extracted from available potential energy of mean flow via baroclinic conversion, and then the EPE is converted into EKE through vertical density flux. Once generated, EKE will be redistributed by pressure work and advection via eddy energy flux, which varies in sync with the monthly variation of total EKE, transporting EKE to the adjacent region or deeper layer. From the vertical aspect, eddy energy conversions are more prominent above 200 m. The maximal EKE and barotropic conversion mostly occur at the surface, whereas the EPE and baroclinic conversion may have two peaks, which lie at the surface and in the thermocline. Using the satellite altimeter data and wind data, we further investigate the impact of geostrophic eddy wind work, which reveals a slightly dampening effect to EKE in the north Indian Ocean.

We examine the potential vorticity (PV) flux produced by forced Rossby waves in a two-layer quasigeostrophic model, using a perturbation analysis. Rossby waves are excited by external forcing applied to the upper layer. The southward PV flux is produced in the lower layer by the higher-order Rossby waves that are excited by nonlinear wave–wave interactions, whereas the northward PV flux is produced in the upper layer. The direction of the PV flux is consistent with that obtained by an eddy-resolving model of the wind-driven circulation in previous studies. The southward PV flux is produced in a wide parameter range comparable to the eddy-resolving model. The basic features of the PV flux remain unchanged even in the limit of weak stratification. In this limit, stratification has nearly no effect on the flow, except that it isolates the lower layer from the direct effects of external forcing. The mechanism of the southward PV flux is explained using basic features of the barotropic Rossby waves and does not depend on details of the model. Furthermore, the resonant triad interaction of Rossby waves does not affect the PV flux. Stratification weakens or strengthens the PV flux depending on the horizontal scale of the external forcing.

The surface ocean current’s imprint on the wind stress (known as the current feedback) has a significant influence on the wind power input to the ocean. In this study, we investigate the effect of the current feedback on mesoscale eddy energetics in the Kuroshio extension region using a high-resolution (9 km) coupled regional climate model. We perform three sets of simulations: one calculates the wind stress without the surface current, one includes only the mesoscale eddy’s current and another includes the entire current in the computation. In this way, the mesoscale eddy’s current feedback can be isolated and its contribution to the entire current feedback can be assessed. The simulation results show that the mesoscale eddy’s current feedback results in negative wind power input to mesoscale eddies and reduces the surface eddy kinetic energy (EKE) by ~ 20% in the Kuroshio extension region. This negative wind power is compensated primarily by the enhanced conversion from mean flow kinetic energy (MKE) and eddy potential energy (EPE) to EKE and secondarily by the reduced pressure flux divergence and horizontal dissipation. Compared to the mesoscale eddy’s current feedback, the entire current feedback has a similar impact on EKE and the wind power on mesoscale eddies, while it affects the EKE budget differently. It weakens the MKE to EKE conversion partly due to the reduced kinetic energy input to background flows by wind. Correspondingly, the negative wind power on mesoscale eddies is primarily compensated by the enhanced EPE to EKE conversion.

A model of tidal rectification in a homogeneous ocean (Part I) is extended here to include a front that separates shelf and slope waters. The front is approximated as a density discontinuity, the stratification and anchoring position of which are given, but which otherwise is coupled to the flow field. The dynamical closure is formulated through vorticity balance of the two layers and a parameterization of potential vorticity (PV) flux in terms of local tidal amplitude and the mean field. As an example of the frontal effect on the tidally rectified flow, a solution is calculated for the case of negligible interfacial stress and PV flux in the bottom boundary layer and compared with that of a homogeneous ocean. It is found that the mean along-isobath flow outside the frontal zone remains largely unchanged, but is qualitatively altered in the frontal zone. Specifically, the mean flow above the sloping front—being insulated from bottom friction—is greatly intensified by PV mixing, consistent with observed seasonal change over Georges Bank. The mean flow below the frontal interface on the other hand is weakened by enhanced frictional effect—to nearly zero at the foot of the front. The vanishing Ekman transport would strengthen the front as a barrier to offshore transport of a passive tracer.

Eddy Generation by Instability of a Highly Ageostrophic Front: Mean Flow Interactions and Potential Vorticity Dynamics

The formation of orographic wakes and vortices is studied within the context of numerically simulated viscous flow with uniform basic-state wind and stability past elongated free-slip ridges. The viscosity and thermal diffusivity are sufficiently large that the onset of small-scale turbulence is suppressed. It is found in Part I of this study that wake formation in the viscous flow is closely tied to the dynamics of a low-level hydraulic-jump-like feature in the lee of the obstacle. Here the role of the hydraulic jump in producing the vorticity and potential vorticity (PV) of the viscous wake is considered. A method for diagnosing vorticity production is developed based on a propagator analysis of the Lagrangian vorticity equation that generalizes Cauchy's formula for the evolution of vorticity in a Lagrangian framework. Application of the method reveals that the vertical vorticity of the wake originates through baroclinic generation and tilting in the mountain wave upstream of the jump. However, upstream of the jump the vertical vorticity is relatively weak. Vertical stretching in the jump then amplifies this vorticity significantly to produce the pronounced vertical vorticity anomalies along the shear lines at the lateral edges of the wake. The PV of the wake is found to result mainly from thermal dissipation in the jump. In particular, thermal diffusion tends to diabatically modify the potential temperature field in the jump so as to create PV from the vertical vorticity already present. From the standpoint of PV conservation, the presence of both diabatic cooling (by thermal diffusion) and vertical vorticity at the base of the jump produces a vertical flux of PV through the lower boundary. The advective fluxes of PV along each side of the wake are then primarily balanced at steady state by fluxes of PV through the obstacle surface.

The three-dimensional structure of temporal mean, variance and covariance fields of the Northern Hemisphere wintertime circulation is documented by making use of twice-daily hemispheric analyses at 10 pressure levels (1000–100 mb) for 11 winters (1965–76). The Northern Hemisphere is partitioned into seven longitudinal sectors which correspond, respectively, to 1) the entrance regions of the two principal jet streams; 2) the two major oceanic storm tracks (areas with pronounced geopotential height variability in the 2.5–6 day period range); 3) the western portions of the North American and Eurasian land masses; and 4) the central part of the Asian continent. Meridional cross sections of various seasonal mean statistics averaged over meridians comprising these individual sectors are displayed. The fields presented in this manner include 1) time-averaged zonal wind and temperature; 2) temporal variance statistics of zonal and meridional wind components, temperature, and geopotential height; 3) meridional fluxes of heat, geopotential energy, westerly momentum and potential vorticity by transient eddies; and 4) poleward component of the time averaged ageostrophic flow. The hemispheric distributions of temperature statistics, meridional heat flux and mean potential vorticity in the vicinity of the tropopause (200 and 300 mb) are also shown. The structure of eddy statistics and the implied energetics in the oceanic storm tracks are in good agreement with the characteristics of developing baroclinic waves. The strongest variability in geopotential height and wind occurs at 300 mb. The geopotential height fluctuations in the 2.5–6 day period range exhibit a secondary maximum at the ground level, so that the 850 mb level corresponds to a relative minimum. Thermal variability is strongest in the middle troposphere and just above the tropopause. The primary maximum for the heat flux statistics is located at 850 mb, with a weaker secondary maximum at 200 mb. The distribution of eddy momentum flux is characterized by strong convergence of westerly momentum into the storm track axis. The western parts of the two major land masses exhibit quite distinct dynamical features in middle latitudes. The upper troposphere is characterized by equatorward heat fluxes, whereas the direction of heat transport in the lower stratosphere is poleward. The momentum fluxes in these regions are strong and poleward at the jet stream level. This configuration of heat and momentum fluxes is consistent with observed strong poleward fluxes of potential vorticity in the vicinity of the tropopause. Strong supergeostrophic winds in the eddies over the western continents are shown to induce conversion from eddy kinetic energy to eddy available potential energy in these regions. The relative importance of the mean flow forcing by the transient eddies is discussed. It is seen that the jet streams in the entrance regions are maintained by strong poleward ageostrophic flows at the tropopause level, while strong equatorward ageostrophic flows over the oceanic storm tracks act to decelerate the jets at these longitudes. The intensity of these local meridional circulations is about an order of magnitude stronger than that of the zonally averaged Ferrel cell in midlatitudes. The local forcing of the mean zonal flow by the Coriolis acceleration accompanying these time-mean ageostrophic flows is shown to be much larger than the forcing due to eddy momentum flux convergence.

The flux form of the potential vorticity (PV) equation in isentropic coordinates is used to examine the effects of advection and the effects of parameterized mechanical and thermal forcing on the PV budget of the second generation Canadian Climate Centre general circulation model (CCC GCM). Model data corresponding to Northern Hemisphere winter are used. The simulated PV flux contains significant nonadvective contributions in the planetary boundary layer, in the gravity wave drag regions of the Northern Hemisphere, and in the tropical midtroposphere in regions of intense latent heat release associated with persistent moist convection. The model advective PV flux is compared to the advective PV flux calculated from a National Centers for Environmental Prediction observational dataset. Large discrepancies are seen where parameterized gravity wave drag dominates the mechanical forcing field in the model. The zonally averaged model PV flux in the upper troposphere and lower stratosphere is characteri...

On the conversion between mean and eddy components of potential and kinetic energy in isentropic and isopycnic coordinates

Oceanic boundary currents over the continental slope exhibit variability with a range of time scales. Numerical studies of steady, along-slope currents over a sloping bathymetry have shown that cross-slope Ekman transport can advect buoyancy surfaces in a bottom boundary layer (BBL) so as to produce vertically sheared geostrophic flows that bring the total flow to rest: a process known as buoyancy shutdown of Ekman transport or Ekman arrest. This study considers the generation and evolution of near-bottom flows due to a barotropic, oscillating, and laterally sheared flow over a slope. The sensitivity of the boundary circulation to changes in oscillation frequency ω, background flow amplitude, bottom slope, and background stratification is explored. When ω/f ≪ 1, where f is the Coriolis frequency, oscillations allow the system to escape from the steady buoyancy shutdown scenario. The BBL is responsible for generating a secondary overturning circulation that produces vertical velocities that, combined with the potential vorticity (PV) anomalies of the imposed barotropic flow, give rise to a time-mean, rectified, vertical eddy PV flux into the ocean interior: a “PV pump.” In these idealized simulations, the PV anomalies in the BBL make a secondary contribution to the time-averaged PV flux. Numerical results show the domain-averaged eddy PV flux increases nonlinearly with ω with a peak near the inertial frequency, followed by a sharp decay for ω/f > 1. Different physical mechanisms are discussed that could give rise to the temporal variability of boundary currents.

This paper is a study of the transport properties of large‐scale quasi‐geostrophic flow, when it is forced by an unstable shear of much greater horizontal scale than the scale of the resultant eddies. One of the purposes is thereby to test certain phenomenological parametrization schemes which predict the transport of potential vorticity or heat, or which predict the time‐mean state of the zonally averaged atmosphere. Models used are highly nonlinear spectral quasi‐geostrophic models, with sufficient resolution to resolve the energy‐containing scales and partially resolve an enstrophy inertial range. A scale separation is enforced between the mean and eddy flow, this being a necessary condition for transfer theories to work. An expression is derived for the rate of change of the mean flow in such cases. As a quantitative predictor of the time‐mean state of the zonal flow, baroclinic adjustment is found to work only when nonlinear wave‐wave interaction between eddies is small. In such cases, the amplitude of the eddy flow is determined by the forcing on the zonal flow, which itself equilibrates close to the critical value for linear instability. In fully nonlinear models if the zonal flow is strongly forced the mean flow can be highly supercritical. The flux of potential vorticity is found to depend strongly and monotonically on the mean shear, although no obvious simple relationship is found relating it to potential vorticity gradient. In part because potential vorticity is not a passive scalar, using phenomenological transfer coefficients is by no means straightforward. Such transfer relationships are seen to be in some ways unsatisfactory.

Simulation of eddy-driven deep circulation in the East/Japan Sea by using a three-layer model with wind, throughflow and deep water formation forcings

Extremely persistent, equivalent barotropic zonal jets are observed in statistically steady quasigeostrophic two-layer beta-plane turbulence. Flows are forced by an imposed unstable vertical shear, horizontally uniform over domains several tens of Rossby radii wide. Damping is by surface drag, small-scale mixing, and for some runs, radiative relaxation. When dissipation is weak, zonal jets emerge with a meridional scale related to beta and the equilibrated eddy energy level as suggested by Rhines. Spinup behavior suggests a priori prediction of this level will be difficult. The scale of energy conversion also cannot be determined a priori, and while upscale energy transfer is important, (reverse) energy cascading ranges of any significant extent do not occur. Time scales considerably longer than those simply related to model parameters are prominent. The choices of doubly periodic boundary conditions and spatially homogeneous forcing and dissipation emphasize that the low-frequency behavior is due to internal dynamics. When the domain size is an integral multiple of the jet scale, jets evolve rather independently of each other, meandering on relatively long time scales. Jet interactions are predominantly pairwise when the implicit quantization is violated. Eddy fluxes occur in intermittent bursts asymmetric about jet axes, producing momentum flux convergences to maintain the jets against surface drag. Heat fluxes are everywhere downgradient, reaching local maxima in jet cores. Potential vorticity homogenization is not seen in these forced-dissipative equilibria. Zonally averaged potential vorticity gradients are bounded away from zero when forcing is strong, and zero crossings occur only in the lower layer at weak forcing (when they may be anticipated from the form of the forcing). The relation between potential vorticity fluxes and their gradients is determined by details of the dissipation rather than by any general principle. As seen earlier with a “one-dimensional” model, baroclinic adjustment parameterizations are inappropriate in wide domains.

The sensitivity of the midlatitude storm track and eddy-driven wind to the sea surface temperature (SST) boundary forcing is studied over a wide range of perturbations using both simple and comprehensive general circulation models over aquaplanet lower boundary conditions. Under the single-jet circulation regime similar to the conditions of the present climate in the Northern Hemisphere winter or the Southern Hemisphere summer, the eddy-driven jet shifts monotonically poleward with both the global mean and the equator-to-pole gradient of the SST. The eddy-driven jet can have a reverse relationship to the gradient if it is well separated from the subtropical jet and Hadley cell boundary in a double-jet circulation regime. A simple scaling is put forward to interpret the simulated sensitivity of the storm-track/eddy-driven westerly wind position within the single-jet regime in both models. The rationale for the scaling is based on the notion that the wave activity flux can propagate horizontally away from the source region, resulting in a broader distribution of eddy potential vorticity (PV) flux in the upper troposphere than that of the flux in the opposite direction in the lower troposphere. As a consequence, the position of the maximum of the eddy-driven westerlies tends to be controlled by the profile of the relatively sharp-peaked low-level PV flux, which is dominated by the eddy heat flux component of the Eliassen–Palm (EP) flux. Thus, the position of the eddy-driven surface westerlies may be inferred from the vertical EP flux coming out of the lower troposphere. The vertical EP flux can be parameterized by a measure of baroclinicity, whose latitudinal variations show a linear relationship with the meridional displacement of the eddy-driven westerlies and the storm track. This relationship still holds well within the single-jet regime, even when only the variation of static stability is taken into consideration in estimating the baroclinicity (the temperature gradient component of which is fixed). To the extent that the static stability is deterministically constrained by and hence can be predicted from the given SST conditions through a moist scaling for the midlatitude stratification, one may, given SST perturbations, predict which way the storm track and eddy-driven wind should shift with respect to a chosen reference climate state. The resultant anomaly-wise scaling turns out to be valid for both the idealized and comprehensive models, regardless of the details in the model physics. By corollary, it can be argued that the poleward shift of storm track found in the global warming simulations by fully coupled climate models may be attributed, at least partially, to the increase in the subtropical and midlatitude static stability with global warming.

The formation of three Loop Current Eddies, Ekman, Franklin, and Hadal, during the period April 2009 through November 2011 was observed by an array of moored current meters and bottom mounted pressure equipped inverted echo sounders. The array design, areal extent nominally 89°W to 85°W, 25°N to 27°N with 30–50km mesoscale resolution, permits quantitative mapping of the regional circulation at all depths. During Loop Current Eddy detachment and formation events, a marked increase in deep eddy kinetic energy occurs coincident with the growth of a large-scale meander along the northern and eastern parts of the Loop Current. Deep eddies develop in a pattern where the deep fields were offset and leading upper meanders consistent with developing baroclinic instability. The interaction between the upper and deep fields is quantified by evaluating the mean eddy potential energy budget. Largest down-gradient heat fluxes are found along the eastern side of the Loop Current. Where strong, the horizontal down-gradient eddy heat flux (baroclinic conversion rate) nearly balances the vertical down-gradient eddy heat flux indicating that eddies extract available potential energy from the mean field and convert eddy potential energy to eddy kinetic energy.