Linear Baroclinic Waves Research Articles

Observed intra-seasonal to interannual variability of the upper ocean thermal structure in the southeastern Arabian Sea during 2002–2008

The southeastern Arabian Sea (SEAS), located in the Indian Ocean warm pool, is a key-region of the regional climate system. It is suspected to play an important role in the dynamics of the Asian summer monsoon system. The present study reports the salient features derived from a newly harvested observational dataset consisting of repeated fortnightly XBT transects in the SEAS over the period 2002–2008. The fortnightly resolution of such a multi-year record duration is unprecedented in this part of the world ocean and provides a unique opportunity to examine the observed variability of the near-surface thermal structure over a wide spectrum, from intra-seasonal to interannual timescales. We find that most of the variability is trapped in the thermocline, taking the form of upwelling and downwelling motions of the thermal stratification. The seasonal variations are consistent with past studies and confirm the role of the monsoonal wind forcing through linear baroclinic waves (coastally-trapped Kelvin and planetary Rossby waves). Sub-seasonal variability takes the form of anomalous events lasting a few weeks to a few months and occurs at two preferred timescales: in the 30–110 day band, within the frequency domain of the Madden–Julian oscillation and in the 120–180 day band. While this sub-seasonal variability appears fairly barotropic in the offshore region, the sign of the anomaly in the upper thermocline is opposite to that in its lower part on many occasions along the coast. Our dataset also reveals relatively large interannual temperature variations of about 1 °C from 50 to 200 m depth that reflect a considerable year-to-year variability of the magnitude of both upwelling and downwelling events. This study clearly demonstrates the necessity for sustained long-term temperature measurements in the SEAS.

Piecewise Potential Vorticity Inversion: Elementary Tests

Abstract Piecewise potential vorticity inversion (PPVI) is widely accepted as a useful tool in atmospheric diagnostics. This method is thought to quantify the instantaneous interaction at a distance of anomalies of potential vorticity (PV) separated horizontally and/or vertically. Doubts with respect to the dynamical justification of PPVI are formulated. In particular, it is argued that the tendency of the inverted streamfunction must be determined in order to quantify far-field effects. Elementary tests of PPVI are conducted to clarify these points. First, PPVI is performed for the textbook case of linear Rossby waves in a one-dimensional barotropic fluid. Analytic solutions are presented for PPVI and the related tendency problem. It is found that PPVI does not contribute to an understanding of Rossby wave dynamics. On the other hand, PPVI turns out to be more useful when applied to confined PV extrema. Neither the application of PPVI to linear baroclinic waves in zonal shear flow nor the inversions of the related temperature anomalies at the boundaries help to better understand the wave development. It is concluded that PPVI with additional tendency calculations poses and solves a specific problem by retaining observed PV anomalies in one subdomain and removing them in others. The usefulness of the results with regard to the diagnosis of the observed state depends strongly on the flows considered and on the partitions chosen, which must comply with a simple rule.

Nonlinear Midlatitude Ocean Adjustment

Ocean adjustment on annual to interdecadal scales to variable forcing is considered for a more nonlinear general circulation than has previously been studied. The nature of the response is a strong function of forcing frequency and importantly involves the inertial recirculations rather than linear baroclinic waves. The spatial expression of this variability is concentrated near the separation latitudes of the Gulf Stream extension, a model region corresponding to an area in the real ocean of well-known strong ocean–atmosphere buoyancy exchange. “Turn-on” cases, periodically forced cases, and stochastically forced cases are considered. The first set of experiments clarifies the adjustment timescales and dynamics of a nonlinear circulation. The second set examines modifications to that adjustment rendered by time-dependent forcing. The last set is perhaps the most realistic in terms of the atmospheric forcing of the ocean, because wind spectra are not strongly peaked beyond a few weeks. Multidecadal forcing is argued both to excite a novel, rapid mode of adjustment and to resonate with a considerably slower, nonlinear mode. Stochastic forcing seems clearly to excite the fast mode and to contribute to the slower mode, although the latter also derives considerable variance from intrinsic sources. These conclusions are based on a suite of distinct spatial and temporal characteristics of the dominant ocean variability patterns under various forcing scenarios and comment on the ocean dynamics likely to be important to decadal timescale midlatitude climate variability.

On Ocean Dynamics in Midlatitude Climate

Several recent models of midlatitude climate have speculated on the role of the North Atlantic Ocean in modulating the North Atlantic oscillation (NAO). Here this role is examined by means of numerical experimentation with a quasigeostrophic ocean model underneath a highly idealized atmosphere. It is argued that the dominant midlatitude oceanic influence is due to the so-called inertial recirculations, rather than linear baroclinic waves, as have previously been studied. In these experiments, the forced response of the inertial recirculations dominates the leading-order ocean spatial mode, but that mode is energized by oceanic intrinsic variability. The oceanic signals are amplified relative to those predicted by wave models. The primary oceanic role of the coupling is to damp sea surface temperature (SST) at longer timescales, and the interdecadal atmospheric variability is placed under the control of the ocean. The SST damping reflects competition between intrinsically driven intergyre heat flux and an opposing feedback-driven advective heat flux. Spectral SST extrema can result near the transition point where the feedback heat flux approaches equilibrium, although these are secondary phenomena. The picture of midlatitude climate variability painted here has qualitative similarities to that obtained from the linear waves models, but differs fundamentally from them both dynamically and philosophically. Most important, ocean variability is a dominant, rather than passive, partner in all aspects of the coupled system.

Baroclinic instability of semi‐geostrophic fronts with uniform potential vorticity. II: Comparison of analytic and numerical solutions

AbstractThe structure of an asymptotic analytic solution for linear baroclinic waves on a frontal basic state is analysed and compared with finite‐difference solutions. The accuracy of the geostrophic fields is good for fronts with widths less than about 400 km. There is direct cancellation between along‐front advection of the disturbance by the strong frontal jet, and disturbance cross‐front advection of the sharp basic‐state gradients. This cancellation of small‐scale effects leaves the larger scales to control the evolution of the disturbance. It follows that the structure is very similar to that of the classic, meridionally uniform, Eady model. Secondary features, such as the ageostrophic circulation, are more sensitive to the frontal width and hence less accurately reproduced in the asymptotic solution. The analysis illustrates significant differences between the ageostrophic circulation associated with deformation frontogenesis and that which occurs in the linear stage of the instability, forced by along‐front curvature. In the latter case, the horizontal ageostrophic wind associated with the rising motion is characterized by along‐front convergence and cross‐front divergence (i.e. ageostrophic frontolysis).

Baroclinic instability of semi-geostrophic fronts with uniform potential vorticity. II: Comparison of analytic and numerical solutions

The structure of an asymptotic analytic solution for linear baroclinic waves on a frontal basic state is analysed and compared with finite-difference solutions. The accuracy of the geostrophic fields is good for fronts with widths less than about 400 km. There is direct cancellation between along-front advection of the disturbance by the strong frontal jet, and disturbance cross-front advection of the sharp basic-state gradients. This cancellation of small-scale effects leaves the larger scales to control the evolution of the disturbance. It follows that the structure is very similar to that of the classic, meridionally uniform, Eady model. Secondary features, such as the ageostrophic circulation, are more sensitive to the frontal width and hence less accurately reproduced in the asymptotic solution. The analysis illustrates significant differences between the ageostrophic circulation associated with deformation frontogenesis and that which occurs in the linear stage of the instability, forced by along-front curvature. In the latter case, the horizontal ageostrophic wind associated with the rising motion is characterized by along-front convergence and cross-front divergence (i.e. ageostrophic frontolysis).

Mass and Angular Momentum Diagnostics of Cyclones within Numerically Simulated Linear Baroclinic Waves

The mass and angular momentum budgets of extratropical cyclones within three numerically simulated adiabatic linear baroclinic waves are investigated through quasi-Lagrangian diagnostics. The waves analyzed, wavenumbers 5, 11 and 17, were chosen to represent a range of baroclinically active horizontal scales observed in the atmosphere within which cyclonic circulations develop. Results are compared with diagnostics of an observed atmospheric cyclone in order to examine the extent to which linear baroclinic instability theory explains extratropical cyclone development in the real atmosphere. Diagnostics are computed in both isobaric and isentropic coordinates. In the isobaric framework, inward mass and angular momentum transport occurs in the lower troposphere of the linear cyclones while the transport is outward in the upper troposphere Upward transport of these quantities throughout the troposphere redistributes these quantities vertically. Within isobaric coordinates the mass and angular momentum budgets of the cyclones within linear waves resemble results from actual cyclones. Analysis of these linear model cyclones in isentropic coordinates shows that the mass and angular momentum transport is inward in upper isentropic layers and outward below. Angular momentum is transferred from upper to lower isentrople layers by pressure and inertial torques within the baroclinic structure. The vertical distribution of transport process and torques within linear baroclinic wave is in general agreement with the results occurring during the dry-baroclinic phase of development in a 1971 Alberta cyclone but differs markedly from the distribution observed during the moist-baroclinic phase. The major dissimilarity between the development of the model cyclones and leeside dry-baroclinic cyclogenesis is the existence of a much stronger eddy component of horizontal angular momentum transport in the model cyclones. A strong eddy transport is required for the cyclones to simultaneously deepen and spin-up over the flat terrain in the linear model, while such a transfer is not necessary for development over sloped topography.

The Effect of the Meridional Circulation on the Baroclinic Instability of the Winter Zonal Flow

Abstract The linear instability of the observed winter zonal mean flow, with and without the inclusion of the meridional circulation, is presented. The purpose of this note is to determine whether the meridional circulation has an important effect on the growth-rate spectrum and structure of the linear baroclinic waves. It is found that the inclusion of the meridional circulation produced only slight changes in the growth-rate spectrum, as compared to the case where the meridional flow is neglected. The presence of the meridional flow destabilized all wavenumbers greater than 5, although the change was less than 7% for all wavenumbers. The maximum growth rate, with or without considering meridional circulation, occurred between wavenumbers 12 and 15. The wave structures were also very similar in the two cases. The maximum amplitude of the geopotential perturbation for wavenumbers 5–7 remains at the earth’s surface when the meridional circulation is included; however, the position of the maximum geopotenti...

Some Non-Quasigeostrophic Effects in Linear Baroclinic Waves

Abstract Non-quasigeostrophic effects in unstable baroclinic waves, defined as differences between solutions in primitive equation and quasigeostrophic models due to terms in the governing equations that are neglected in the quasigeostrophic model, are examined. It is determined that these non-quasigeostrophic effects produce significant asymmetries in a baroclinic wave, as compared to the symmetry that would be expected if that wave were governed by the quasigeostrophic equations, even when the Rossby number is relatively small. These asymmetries result in significant differences in some of the eddy fluxes in a primitive equation model as compared to a quasigeostrophic model. This was found to be especially true for u′v&prime, where even the sign was different in certain regions.

Two Similarities Between Atmospheric Eddies and Linear Baroclinic Waves

Abstract Very good agreement is shown to exist between the meridional distributions of the zonal wavenumber n of rapidly amplifying baroclinic waves on a sphere and of an average wavenumber n of “grid-scale” atmospheric eddies. As a consequence, the zonal wavelength of both baroclinic and atmospheric eddies remains virtually constant, i.e., within a factor of 2, over the extratropics. The values of n at different latitudes have been obtained by using linearized baroclinic theory on different meridional profiles of the unperturbed zonal wind (MPUZW). Since they agree with n, atmospheric eddies are, in relation to linear baroclinic waves, independent of MPUZW. In this senses n is controlled locally rather than globally. The mutual dependence of the upward and poleward transports of (sensible) heat in baroclinic wave theory is correctly formulated-as compared to a direct analysis of the first law of thermodynamics.