Modulation of Mean Wind and Turbulence in the Atmospheric Boundary Layer by Baroclinicity

This paper investigates the effects of baroclinic pressure gradients on mean flow and turbulence in the diabatic atmospheric boundary layer (ABL). Large-eddy simulations are conducted where the direction of the baroclinicity, its strength, and the surface buoyancy flux are systematically varied to examine their interacting effects. The thermal wind vector, which represents the vertical change in the geostrophic wind vector resulting from horizontal temperature gradients, significantly influences the velocity profiles, the Ekman turning, and the strength and location of the low-level jet (LLJ). For instance, cold advection and positive (negative) geostrophic shear increased (decreased) friction velocity and changed the LLJ elevation. Given the baroclinicity strength and direction under neutral conditions, a simple reduced model is proposed and validated here to predict the general trends of baroclinic mean winds. The baroclinic effects on turbulence intensity and structure are even more intricate, with turbulent kinetic energy (TKE) profiles displaying an increase of TKE magnitude with height for some cases. When a fixed destabilizing surface heat flux is added, a positive geostrophic shear favors streamwise aligned roll-type structures, which are typical of neutral ABLs. Conversely, a negative geostrophic shear promotes cell-type structures, which are typical of strongly unstable ABLs. Furthermore, baroclinicity increases shear in the outer ABL and tends to make the outer flow more neutral by decreasing the Richardson flux number. These findings are consequential for meteorological measurements and the wind-energy industry, among others: baroclinicity alters the mean wind profiles, the TKE, coherent structures, and the stability of the ABL, and its effects need to be considered.

Note on the Rate of Restratification in the Baroclinic Spindown of Fronts

This paper revisits how the restratifying buoyancy flux generated by baroclinic mixed layer instabilities depends on environmental conditions. The frontal spindown is shown to produce buoyancy fluxes that increase significantly beyond the previously proposed and widely used scaling (f is the Coriolis parameter, Λ is the geostrophic shear, and H is the mixed layer depth), irrespective of whether the initial front is broad or narrow. This increase occurs after the initial phase of the nonlinear evolution, when the baroclinic eddies grow in size and develop velocities significantly in excess of the scaling assumption V ~ ΛH. Implications for parameterizing the restratification caused by baroclinic mixed layer instabilities in coarse-resolution models are discussed.

Baroclinic Frontal Instabilities and Turbulent Mixing in the Surface Boundary Layer. Part II: Forced Simulations

Generation of ocean surface boundary layer turbulence and coherent roll structures is examined in the context of wind-driven and geostrophic shear associated with horizontal density gradients using a large-eddy simulation model. Numerical experiments over a range of surface wind forcing and horizontal density gradient strengths, combined with linear stability analysis, indicate that the dominant instability mechanism supporting coherent roll development in these simulations is a mixed instability combining shear instability of the ageostrophic, wind-driven flow with symmetric instability of the frontal geostrophic shear. Disruption of geostrophic balance by vertical mixing induces an inertially rotating ageostrophic current, not forced directly by the wind, that initially strengthens the stratification, damps the instabilities, and reduces vertical mixing, but instability and mixing return when the inertial buoyancy advection reverses. The resulting rolls and instabilities are not aligned with the frontal zone, with an oblique orientation controlled by the Ekman-like instability. Mean turbulence is enhanced when the winds are destabilizing relative to the frontal orientation, but mean Ekman buoyancy advection is found to be relatively unimportant in these simulations. Instead, the mean turbulent kinetic energy balance is dominated by mechanical shear production that is enhanced when the wind-driven shear augments the geostrophic shear, while the resulting vertical mixing nearly eliminates any effective surface buoyancy flux from near-surface, cold-to-warm, Ekman buoyancy advection.

Submesoscale baroclinic instability in the balance equations

Ocean submesoscale baroclinic instability is studied in the framework of the balance equations. These equations are an intermediate model that includes balanced ageostrophic effects with higher accuracy than the quasigeostrophic approximation, but rules out unbalanced wave motions. As such, the balance equations are particularly suited to the study of baroclinic instability in submesoscale ocean dynamics. The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. It is found that non-quasigeostrophic effects appear only for perturbations with cross-front variation, and that perturbation energy can be generated through both baroclinic production and shear production. The Eady problem is solved analytically in the balance equation framework. Ageostrophic effects are shown to increase the range of unstable modes and the growth rate of the instability for perturbations with cross-front variation. The increased level of instability is attributed to both ageostrophic baroclinic production and shear production of perturbation energy; these results are verified in the primitive equations. Finally, submesoscale baroclinic instability is examined in a case where the buoyancy frequency increases rapidly near the bottom boundary, mimicking the increase of stratification at the base of the oceanic mixed layer. The qualitative results of the Eady problem are repeated in this case, with increased growth rates attributed to the production of perturbation energy by the ageostrophic velocity. The results show that submesoscale baroclinic instability acts to reduce lateral buoyancy gradients and their associated geostrophic shear simultaneously through lateral buoyancy fluxes and vertical momentum fluxes.

Near-Surface Shear Flow in the Tropical Pacific Cold Tongue Front*

Near-surface shear in the Pacific cold tongue front at 2°N, 140°W was measured using a set of five moored current meters between 5 and 25 m for nine months during 2004–05. Mean near-surface currents were strongly westward and only weakly northward (∼3 cm s−1). Mean near-surface shear was primarily westward and, thus, oriented to the left of the southeasterly trades. When the southwestward geostrophic shear was subtracted from the observed shear, the residual ageostrophic currents relative to 25 m were northward and had an Ekman-like spiral, in qualitative agreement with an Ekman model modified for regions with a vertically uniform front. According to this “frontal Ekman” model, the ageostrophic Ekman spiral is forced by the portion of the wind stress that is not balanced by the surface geostrophic shear. Analysis of a composite tropical instability wave (TIW) confirms that ageostrophic shear is minimized when winds blow along the front, and strengthens when winds blow oblique to the front. Furthermore, the magnitude of the near-surface shear, both in the TIW and diurnal composites, was sensitive to near-surface stratification and mixing. A diurnal jet was observed that was on average 12 cm s−1 stronger at 5 m than at 25 m, even though daytime stratification was weak. The resulting Richardson number indicates that turbulent viscosity is larger at night than daytime and decreases with depth. A “generalized Ekman” model is also developed that assumes that viscosity becomes zero below a defined frictional layer. The generalized model reproduces many of the features of the observed mean shear and is valid both in frontal regions and at the equator.

Friction, Frontogenesis, and the Stratification of the Surface Mixed Layer

The generation and destruction of stratification in the surface mixed layer of the ocean is understood to result from vertical turbulent transport of buoyancy and momentum driven by air–sea fluxes and stresses. In this paper, it is shown that the magnitude and penetration of vertical fluxes are strongly modified by horizontal gradients in buoyancy and momentum. A classic example is the strong restratification resulting from frontogenesis in regions of confluent flow. Frictional forces acting on a baroclinic current either imposed externally by a wind stress or caused by the spindown of the current itself also modify the stratification by driving Ekman flows that differentially advect density. Ekman flow induced during spindown always tends to restratify the fluid, while wind-driven Ekman currents will restratify or destratify the mixed layer if the wind stress has a component up or down front (i.e., directed against or with the geostrophic shear), respectively. Scalings are constructed for the relative importance of friction versus frontogenesis in the restratification of the mixed layer and are tested using numerical experiments of mixed layer fronts forced by both winds and a strain field. The scalings suggest and the numerical experiments confirm that for wind stress magnitudes, mixed layer depths, and cross-front density gradients typical of the ocean, wind-induced friction often dominates frontogenesis in the modification of the stratification of the upper ocean. The experiments reveal that wind-induced destratification is weaker in magnitude than restratification because the stratification generated by up-front winds confines the turbulent stress to a depth shallower than the Ekman layer, which enhances the frictional force, Ekman flow, and differential advection of density. Frictional destratification is further reduced over restratification because the stress associated with the geostrophic shear at the surface tends to compensate a down-front wind stress.

Deep Cyclonic Circulation in the Gulf of Mexico

The anticyclonic Loop Current dominates the upper-layer flow in the eastern Gulf of Mexico, with a weaker mean anticyclonic pattern in the western gulf. There are reasons, however, to suspect that the deep mean flow should actually be cyclonic. Topographic wave rectification and vortex stretching contribute to this cyclonic tendency, as will the supply of cold incoming deep water at the edges of the basin. The authors find that the deep mean flow is cyclonic both in the eastern and western gulf, with speeds on the order of 1–2 cm s−1 at 2000 m. Historical current-meter mooring data, as well as profiling autonomous Lagrangian circulation explorer (PALACE) floats (at 900 m), suggest that vertical geostrophic shear relative to 1000 m gives a surprisingly accurate result in the interior of the basin. The temperature around the edges of the basin at 2000 m is coldest near the Yucatan Channel, where Caribbean Sea water is colder by ∼0.1°C. The temperature increases steadily with distance in the counterclockwise direction from the Yucatan, consistent with a deep mean cyclonic boundary flow.

An Advanced Method to Estimate Deep Currents from Profiling Floats

Subsurface ocean currents can be estimated from the positions of drifting profiling floats that are being widely deployed for the international Argo program. The calculation of subsurface velocity depends on how the trajectory of the float while on the surface is treated. The following three aspects of the calculation of drift velocities are addressed: the accurate determination of surfacing and dive times, a new method for extrapolating surface and dive positions from the set of discrete Argos position fixes, and a discussion of the errors in the method. In the new method described herein, the mean drift velocity and the phase and amplitude of inertial motions are derived explicitly from a least squares fit to the set of Argos position fixes for each surface cycle separately. The new method differs from previous methods that include prior assumptions about the statistics of inertial motions. It is concluded that the endpoints of the subsurface trajectory can be estimated with accuracy better than 1.7 km (East Sea/Sea of Japan) and 0.8 km (Indian Ocean). All errors, combined with the error that results from geostrophic shear and extrapolation, should result in individual subsurface velocity estimates with uncertainty of the order of 0.2 cm s−1.

Numerical study of the motions within a slowly precessing sphere at low Ekman number

A geostrophic circulation and a pair of oblique oscillating shear layers arise in a spherical uid cavity contained in a slowly precessing rigid body. Both are caused by the breakdown of the Ekman boundary layer at two critical circles. We rely on numerical modelling to characterize these motions for very small Ekman numbers. Both the O(E1/5) amplitude of the velocity in the oscillating shear layer and the width (also O(E1/5)) of these oblique layers are the result of in ux into the interior from the regions where the Ekman layer breaks down. The oscillating motions are confined to narrow shear layers and their amplitude decays exponentially away from the characteristic surfaces. Nonlinear interactions inside the boundary layer drive the geostrophic shear layer attached to the critical circles. This steady layer, again of O(E1/5) thickness, contains O(E−3/10) velocities. Our results are in good agreement with the experimental measurement by Malkus of the geostrophic velocity arising in a slowly precessing spheroid.