Equatorial Kelvin waves as revealed by EOS Microwave Limb Sounder observations and European Centre for Medium-Range Weather Forecasts analyses: Evidence for slow Kelvin waves of zonal wave number 3

[1] Temperature and ozone observations from the Microwave Limb Sounder (MLS) on the EOS Aura satellite are used to study equatorial wave activity in the autumn of 2005. In contrast to previous observations for the same season in other years, the temperature anomalies in the middle and lower tropical stratosphere are found to be characterized by a strong wave-like eastward progression with zonal wave number equal to 3. Extended empirical orthogonal function (EOF) analysis reveals that the wave 3 components detected in the temperature anomalies correspond to a slow Kelvin wave with a period of 8 days and a phase speed of 19 m/s. Fluctuations associated with this Kelvin wave mode are also apparent in ozone profiles. Moreover, as expected by linear theory, the ozone fluctuations observed in the lower stratosphere are in phase with the temperature perturbations, and peak around 20–30 hPa where the mean ozone mixing ratios have the steepest vertical gradient. A search for other Kelvin wave modes has also been made using both the MLS observations and the analyses from one experiment where MLS ozone profiles are assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) data assimilation system via a 6-hourly 3D var scheme. Our results show that the characteristics of the wave activity detected in the ECMWF temperature and ozone analyses are in good agreement with MLS data.

Life-cycle simulations of shallow frontal waves and the impact of deformation strain

The life-cycle of shallow frontal waves and the impact of deformation strain on their development is investigated using the idealised version of the Met Office non-hydrostatic Unified Model which includes the same physics and dynamics as the operational forecast model. Frontal wave development occurs in two stages; first, a deformation strain is applied to a front and a positive potential vorticity (PV) strip forms, generated by latent heat release in the frontal updraft; second, as the deformation strain is reduced the PV strip breaks up into individual anomalies. The circulations associated with the PV anomalies cause shallow frontal waves to form. The structure of the simulated frontal waves is consistent with the conceptual model of a frontal cyclone. Deeper frontal waves are simulated if the stability of the atmosphere is reduced. Deformation strain rates of different strengths are applied to the PV strip to determine whether a deformation strain threshold exists above which frontal wave development is suppressed. An objective method of frontal wave activity is defined and frontal wave development was found to be suppressed by deformation strain rates $\ge 0.4\times10^{-5}\mbox{s}^{-1}$. This value compares well with observed deformation strain rate thresholds and the analytical solution for the minimum deformation strain rate needed to suppress barotropic frontal wave development. The deformation strain rate threshold is dependent on the strength of the PV strip with strong PV strips able to overcome stronger deformation strain rates (leading to frontal wave development) than weaker PV strips.

Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer

The influence of surface waves and an applied wind stress is studied in an ensemble of large eddy simulations to investigate the nature of deeply penetrating jets into an unstratified mixed layer. The influence of a steady monochromatic surface wave propagating parallel to the wind direction is parameterized using the wave-filtered Craik-Leibovich equations. Tracer trajectories and instantaneous downwelling velocities reveal classic counterrotating Langmuir rolls. The associated downwelling jets penetrate to depths in excess of the wave's Stokes depth scale, δs. Qualitative evidence suggests the depth of the jets is controlled by the Ekman depth scale. Analysis of turbulent kinetic energy (tke) budgets reveals a dynamical distinction between Langmuir turbulence and shear-driven turbulence. In the former, tke production is dominated by Stokes shear and a vertical flux term transports tke to a depth where it is dissipated. In the latter, tke production is from the mean shear and is locally balanced by dissipation. We define the turbulent Langmuir number Lat = (v*/Us)0.5 (v* is the ocean's friction velocity and Us is the surface Stokes drift velocity) and a turbulent anisotropy coefficient Rt = /( + ). The transition between shear-driven and Langmuir turbulence is investigated by varying external wave parameters δs and Lat and by diagnosing Rt and the Eulerian mean and Stokes shears. When either Lat or δs are sufficiently small the Stokes shear dominates the mean shear and the flow is preconditioned to Langmuir turbulence and the associated deeply penetrating jets.

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

Analysis of convectively-generated gravity waves in mesoscale model simulations and wind profiler observations

The characteristics of convectively-generated gravity waves during an episode of deep convection near the coast of Wales are examined in both high resolution mesoscale simulations [with the (UK) Met Oce Unified Model] and in observations from a Mesosphere-Stratosphere-Troposphere (MST) wind profiling Doppler radar. Deep convection reached the tropopause and generated vertically propagating, high frequency waves in the lower stratosphere that produced vertical velocity perturbations O(1 m/s). Wavelet analysis is applied in order to determine the characteristic periods and wavelengths of the waves. In both the simulations and observations, the wavelet spectra contain several distinct preferred scales indicated by multiple spectral peaks. The peaks are most pronounced in the horizontal spectra at several wavelengths less than 50 km. Although these peaks are most clear and of largest amplitude in the highest resolution simulations (with 1 km horizontal grid length), they are also evident in coarser simulations (with 4 km horizontal grid length). Peaks also exist in the vertical and temporal spectra (between approximately 2.5 and 4.5 km, and 10 to 30 minutes, respectively) with good agreement between simulation and observation. Two-dimensional (wavenumber-frequency) spectra demonstrate that each of the selected horizontal scales contains peaks at each of preferred temporal scales revealed by the one- dimensional spectra alone.

Inertia-Gravity Waves Emitted from Balanced Flow: Observations, Properties, and Consequences

This paper describes laboratory observations of inertia–gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia–gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05–0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia–gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia–gravity waves at the peak of their generation. The findings of this study imply an inevitable emission of inertia–gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia–gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia–gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

The influence of bottom topography on the decay of modeled Agulhas rings

The influence of a large meridional submarine ridge on the decay of Agulhas rings is investigated with a 1 and 2-layer setup of the isopycnic primitive-equation ocean model MICOM. In the single-layer case we show that the SSH decay of the ring is primarily governed by bottom friction and secondly by the radiation of Rossby waves. When a topographic ridge is present, the effect of the ridge on SSH decay and loss of tracer from the ring is negligible. However, the barotropic ring cannot pass the ridge due to energy and vorticity constraints. In the case of a two-layer ring the initial SSH decay is governed by a mixed barotropic–baroclinic instability of the ring. Again, radiation of barotropic Rossby waves is present. When the ring passes the topographic ridge, it shows a small but significant stagnation of SSH decay, agreeing with satellite altimetry observations. This is found to be due to a reduction of the growth rate of the m = 2 instability, to conversions of kinetic energy to the upper layer, and to a decrease in Rossby-wave radiation. The energy transfer is related to the fact that coherent structures in the lower layer cannot pass the steep ridge due to energy constraints. Furthermore, the loss of tracer from the ring through filamentation is less than for a ring moving over a flat bottom, related to a decrease in propagation speed of the ring. We conclude that ridges like the Walvis Ridge tend to stabilize a multi-layer ring and reduce its decay.