Joseph A. Biello

Meridional Momentum Flux and Superrotation in the Multiscale IPESD MJO Model

Abstract The derivation of the meridional momentum flux arising from a multiscale horizontal velocity field in the intraseasonal, planetary, equatorial synoptic-scale dynamics (IPESD) multiscale models of the equatorial troposphere is presented. It is shown that, because of the balance dynamics on the synoptic scales, the synoptic-scale component of the meridional momentum flux convergence must always vanish at the equator. Plausible Madden–Julian oscillation (MJO) models are presented along with their planetary-scale meridional momentum fluxes. These models are driven by synoptic-scale heating fluctuations that have vertical and meridional tilts. Irrespective of the sign of the synoptic-scale meridional momentum flux (direction of the tilts) in each of the four MJO examples, the zonal and vertical mean meridional momentum flux convergence from the planetary scales always drives westerly winds near the equator: this is the superrotation characteristic of actual MJOs. The concluding discussion demonstrates...

The Hamiltonian description of incompressible fluid ellipsoids

We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac’s procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, and the moment reduction is applied to this bracket. When the Hamiltonian can be expressed exactly in terms of these moments, a closure is achieved and the resulting finite-dimensional Hamiltonian system provides exact solutions of Euler’s equations. This is shown to be the case for the classical, incompressible Riemann ellipsoids, which have velocities that vary linearly with position and have constant density within an ellipsoidal boundary. The incompressible, noncanonical Poisson bracket differs from its counterpart for the compressible case in that it is not of Lie–Poisson form.

Convective Momentum Transport in a Simple Multicloud Model for Organized Convection

AbstractConvective momentum transport (CMT) is the process of vertical transport of horizontal momentum by convection onto the environmental flow. The significance of CMT from mesoscale to synoptic- and planetary-scale organized cumulus convection has been established by various theoretical and observational studies. A new strategy mimicking the effect of unresolved mesoscale circulation based on the weak temperature gradient (WTG) approximation with a Gaussian profile to redistribute the heating due to parameterized cumulus convection at the subgrid scale is adopted here to construct a CMT parameterization for general circulation models (GCMs). Two main regimes of CMT are considered: an upscale squall-line regime and a downscale non-squall-line regime. An exponential probability distribution is used to select which of these two effects is active, conditional on the state of the large-scale shear. The shear itself is used as a measure of the persistence of mesoscale organized circulation due to the presen...

Double diffusive instability in a tall thin slot

The linear stability of doubly diffusive convection is considered for a two-dimensional, Boussinesq fluid in a tall thin slot. For a variety of boundary conditions on the slot walls, instability sets in through zero wavenumber over a wide range of physical conditions. Long-wave equations governing the nonlinear development of the instability are derived. The form of thc long-wave equations sensitively depends on the thermal and salt boundary conditions; the possible long-wave theories are catalogued. Finite-amplitude solutions and their stability are studied. In some cases the finite-amplitude solutions are not the only possible attractors and numerical solutions presenting the alternatives are given. These reveal temporally complicated dynamics

Competitive effects between stationary chemical reaction centres: A theory based on off-center monopoles

The subject of this paper is competitive effects between multiple reaction sinks. A theory based on off-center monopoles is developed for the steady-state diffusion equation and for the convection-diffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convection-diffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an easy-to-use tool for the calibration of other more complicated models in mass and/or heat transfer.

A Multiscale Model for the Modulation and Rectification of the ITCZ

AbstractThe authors introduce the modulation of the ITCZ equations (M-ITCZ), which describes the multiscale dynamics of the ITCZ on diurnal to monthly time scales in which mesoscale convectively coupled Rossby waves in the ITCZ are modulated by a large-scale gravity wave that is also generated by convection. Westward-propagating disturbances are observed to cause ITCZ breakup over the course of a few days, and the M-ITCZ meso-/planetary-scale coupled waves provide a mechanism for this interaction, thereby providing a framework to study the modulation and rectification of the Hadley circulation over long zonal length scales in the ITCZ.The authors consider examples of zonally symmetric heating profiles in the M-ITCZ system and generate a Hadley circulation consistent with the observed winds. Zonally localized heating creates a wind response throughout the tropics that is carried by a pair of zonally propagating gravity bores driving mean easterlies at the base and mean westerlies at the top of the troposph...

Instabilities of exact, time-periodic solutions of the incompressible Euler equations

We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows

Effect of Overturning Circulation on Long Equatorial Waves: A Low-Frequency Cutoff

AbstractZonally long tropical waves in the presence of a large-scale meridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscale moist dy...

Why do Earth's equatorial waves head east?

Topological effects may direct ocean and atmospheric waves near the equator Equatorial Kelvin waves occur constantly in Earths atmosphere and ocean. They constitute an isolated and powerful component of the observed atmospheric wave spectrum (1), whereas oceanic Kelvin waves drive up- and downwelling in the Pacific Ocean thermocline, which affects the El Niño–Southern Oscillation. In the atmosphere, Kelvin waves are initiated by and coupled to convective activity (storm systems), mostly over the Indian and the western Pacific Oceans, whereas in periods of large-scale convective organization, such as the Madden-Julian Oscillation, equatorial Kelvin wave activity is suppressed. On page 1075 of this issue, Delplace et al. (2) attempt to answer the questions of why there are three equatorially confined waves, and why they all have eastward group velocity. They propose a fascinating perspective on the existence of unidirectional, equatorially confined atmospheric waves by developing an analogy with similar phenomena that occur in electronic materials—in particular, in quantum Hall states and topological insulators.

The Steady-State Convection-Diffusion Equation at High Peclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory

This paper describes an approximate analytical model of competitive effects between members of a dense cluster of absorbing objects, which are modeled as spheres. Neighboring absorbing spheres compete for diffusing species and thereby reduce each others rate of absorption. Levichs well-known asymptotic (high Peclet number) theory of convection-diffusion considers only the inner region of the concentration boundary layer; it does not describe the wake zone accurately. An extension of the Levich model is constructed for the wake zone. This is used to model intersphere competitive effects. The model demonstrates that for two neighboring spheres aligned along the flow direction, the absorption of the downstream sphere is substantially reduced vis-a-vis the upstream sphere. The model is verified by comparison to numerical simulation studies. Both single-sphere simulations (reported in this paper) and multisphere simulations (taken from existing literature) are considered. In the single-sphere case, the discr...