The MJO on the equatorial beta-plane: an eastward propagating Rossby wave induced by meridional moisture advection

Linearized wave solutions on the equatorial beta-plane are examined in the presence of a background meridional moisture gradient. Of interest is a slow, eastward propagating n = 1 mode that is unstable at planetary scales and only exists for a small range of zonal wavenumbers (≲ 6). The mode dispersion curve appears as an eastward extension of the westward propagating equatorial Rossby wave solution. This mode is therefore termed the eastward propagating equatorial Rossby wave (ERW). The zonal wavenumber 2 ERW horizontal structure consists of a low-level equatorial convergence center flanked by quadrupole off-equatorial gyres, and resembles the horizontal structure of the observed MJO. An analytic, leading order dispersion relationship for the ERW shows that meridional moisture advection imparts eastward propagation, and that the smallness of a gross moist stability like parameter contributes to the slow phase speed. The ERW is unstable near planetary scales when low-level easterlies moisten the column. This moistening could come from either zonal moisture advection or surface fluxes or a combination thereof. When westerlies instead moisten the column, the ERW is damped and the westward propagating long Rossby wave is unstable. The ERW does not exist when the meridional moisture gradient is too weak. A moist static energy budget analysis shows that the ERW scale selection is partly due to finite timescale convective adjustment and less effective zonal wind-induced moistening at smaller scales. Similarities in the phase speed, preferred scale and horizontal structure suggest that the ERW is a beta-plane analog of the MJO.

Multistability and rare spontaneous transitions in barotropic β-plane turbulence

We demonstrate that turbulent zonal jets, analogous to Jovian ones, which are quasi-stationary, are actually metastable. After extremely long times, they randomly switch to new configurations with a different number of jets. The genericity of this phenomenon suggests that most quasi-stationary turbulent planetary atmospheres might have many climates and attractors for fixed values of the external forcing parameters. A key message is that this situation will usually not be detected by simply running the numerical models, because of the extremely long mean transition time to change from one climate to another. In order to study such phenomena, we need to use specific tools: rare event algorithms and large deviation theory. With these tools, we make a full statistical mechanics study of a classical barotropic beta-plane quasigeostrophic model. It exhibits robust bimodality with abrupt transitions. We show that new jets spontaneously nucleate from westward jets. The numerically computed mean transition time is consistent with an Arrhenius law showing an exponential decrease of the probability as the Ekman dissipation decreases. This phenomenology is controlled by rare noise-driven paths called instantons. Moreover, we compute the saddles of the corresponding effective dynamics. For the dynamics of states with three alternating jets, we uncover an unexpectedly rich dynamics governed by the symmetric group of permutations, with two distinct families of instantons, which is a surprise for a system where everything seemed stationary in the hundreds of previous simulations of this model. We discuss the future generalization of our approach to more realistic models.

Equilibrium statistical mechanics of barotropic quasi-geostrophic equations

We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to the first integrals energy and enstrophy are Gaussian measures supported by distributional spaces. We define a suitable weak formulation for barotropic equations, and prove existence of a solution preserving Gibbsian measures, thus providing a rigorous infinite-dimensional framework for the equilibrium statistical mechanics of the model.

Rossby wave energy: a local Eulerian isotropic invariant

<p>Conservation laws relate the local<span>  </span>time-rate-of-change of the spatial integral of a density function to the divergence of its<span>  </span>flux through the boundaries of the integration domain. These provide integral constraints on the spatio-temporal development<span>  </span>of a field. Here we show<span>  </span>that<span>  </span>a new type of conserved quantity exists, that does not require integration over a particular domain but which holds locally,<span>  </span>at any point in the field.<span>  </span>This is derived for the pseudo-energy density of<span>  </span>nondivergent Rossby waves where<span>  </span>local invariance is obtained for (1) a single plane wave, and (2) waves produced by an impulsive point-source of vorticity.<span> </span></p><p>The definition of pseudo-energy used here<span>  </span>consists of a conventional kinetic part, as well as an unconventional pseudo-potential part, proposed by<span>  </span>Buchwald (1973).<span>  </span>The anisotropic nature of the nondivergent energy flux that appears in response to the point source further clarifies the role of the beta plane in the<span>  </span>observed western intensification of ocean currents.<span> </span></p>

Steady radiating baroclinic vortices in vertically sheared flows

<p>Baroclinic vortices embedded in a large-scale vertical shear are examined. We describe a new class of steady propagating vortices that radiate Rossby waves but yet do not decay. This is possible since they can extract available potential energy (APE) from a large-scale vertically sheared flow, even though this flow is linearly stable. The vortices generate Rossby waves which induce a meridional vortex drift and an associated heat flux explained by an analysis of pseudomomentum and pseudoenergy. An analytical steady solution is considered for a marginally stable flow in a two-layer model on the beta-plane, where the beta-effect is compensated by the potential vorticity gradient (PVG) associated with the meridional slope of the density interface. The compensation occurs in the upper layer for an upper layer westward flow (an easterly shear) and in the lower layer for an upper layer eastward flow (the westerly shear). The theory is confirmed by numerical simulations indicating that for westward flows in subtropical oceans, the reduced PVG in the upper layer provides favorable conditions for eddy persistence and long-range propagation. The drifting and radiating vortex is an alternative mechanism besides baroclinic instability for converting background APE to mesoscale energy. </p>

Quasi-Equilibrium and Weak Temperature Gradient Balances in an Equatorial Beta-Plane Model

Convective quasi-equilibrium (QE) and weak temperature gradient (WTG) balances are frequently employed to study the tropical atmosphere. This study uses linearized equatorial beta-plane solutions to examine the relevant regimes for these balances. Wave solutions are characterized by moisture–temperature ratio (q–T ratio) and dominant thermodynamic balances. An empirically constrained precipitation closure assigns different sensitivities of convection to temperature (εt) and moisture (εq). Longwave equatorial Kelvin and Rossby waves tend toward the QE balance with q–T ratios of εt:εq that can be ~1–3. Departures from strict QE, essential to both precipitation and wave dynamics, grow with wavenumber. The propagating QE modes have reduced phase speeds because of the effective gross moist stability meff, with a further reduction when εt > 0. Moisture modes obeying the WTG balance and with large q–T ratios (>10) emerge in the shortwave regime; these modes exist with both Kelvin and Rossby wave meridional structures. In the υ = 0 case, long propagating gravity waves are absent and only emerge beyond a cutoff wavenumber. Two bifurcations in the wave solutions are identified and used to locate the spatial scales for QE–WTG transition and gravity wave emergence. These scales are governed by the competition between the convection and gravity wave adjustment times and are modulated by meff. Near-zero values of meff shift the QE–WTG transition wavenumber toward zero. Continuous transitions replace the bifurcations when meff < 0 or moisture advection/WISHE mechanisms are included, but the wavenumber-dependent QE and WTG balances remain qualitatively unaltered. Rapidly decaying convective/gravity wave modes adjust to the slowly evolving QE/WTG state in the longwave/shortwave regimes, respectively.