Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres

Binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of the particles. The spheres on these new trajectories do not pass each other (as they would in free space) but instead they swap their cross-streamline positions. To determine the significance of the wall-induced particle migration, we have evaluated the hydrodynamic self-diffusion coefficient associated with a sequence of uncorrelated particle displacements due to binary particle encounters. The results of our calculations quantitatively agree with the experimental value obtained by \cite{Zarraga-Leighton:2002} for the self-diffusivity in a dilute suspension of spheres undergoing shear flow in a Couette device. We thus show that the wall-induced cross-streamline particle migration is the source of the anomalously large self-diffusivity revealed by their experiments.Comment: submited to JF

Fractal-like aggregates: Relation between morphology and physical properties

A number of modern technological applications require a detailed calculation of the physical properties of aggregated aerosol particles. For example, in probing soot aerosols by the method called laser-induced incandescence (LII), the soot clusters are suddenly heated by a short, powerful laser pulse and then cool down to the temperature of the carrier gas. LII sizing is based on rigorous calculation of the soot aggregate heat-up and cooling and involves prediction of laser light absorption and energy and mass transfer between aggregated particles and the ambient gas. This paper describes results of numerical simulations of the mass or energy transfer between the gas and fractal-like aggregates of N spherical particles in either the free-molecular or continuum regime, as well as the light scattering properties of random fractal-like aggregates, based on Rayleigh–Debye–Gans (RDG) theory. The aggregate geometries are generated numerically using specially developed algorithms allowing “tuning” of the fractal dimension and prefactor values. Our results are presented in the form of easily applicable scaling laws, with special attention paid to relations between the aggregate gyration radius and the effective radius describing various transport processes between the aggregates and the carrier gas

Westward-propagating Rossby modes in idealized GCMs

This work investigates the characteristics of westward-propagating Rossby modes in idealized global general circulation models. Using a nonlinear smoothing algorithm to estimate the background spectrum and an objective method to extract the spectral peaks, the four leading meridional modes can be identified for each of the first three zonal wavenumbers, with frequencies close to the predictions from the Hough modes obtained by linearizing about a state of rest. Variations in peak amplitude for different modes, both within a simulation and across simulations, may be understood under the assumption that the forcing of the modes scales with the background spectrum. Surface friction affects the amplitude and width of the peaks but both remain finite as friction goes to zero, which implies that some other mechanism, arguably nonlinear, must also contribute to the damping of the modes. Although spectral peaks are also observed for the precipitation field with idealized moist physics, there is no evidence of mode enhancement by the convective heating. Subject to the same friction, the amplitude of the peaks are very similar in the dry and moist models when both are normalized by the background spectra

The sensitivity of superrotation to the satitude of baroclinic forcing in a terrestrial dry dynamical core

Previous studies have shown that Kelvin-Rossby instability is a viable mechanism for producing equatorial superrotation in small and/or slowly rotating planets. It is shown in this paper that this mechanism can also produce superrotation with terrestrial parameters when the baroclinic forcing moves to low latitudes, explaining previous results by Williams. The transition between superrotating and subrotating flow occurs abruptly as the baroclinic forcing moves poleward. Although Kelvin-Rossby instability weakens when the baroclinic zone moves away from the equator, the key factor explaining the abrupt transition is the change in the baroclinic eddies. When differential heating is contained within the tropics, baroclinic eddies do not decelerate the subtropical jet and the upper-tropospheric flow approximately conserves angular momentum, providing conditions favorable for Kelvin-Rossby instability. In contrast, when baroclinic eddies are generated in the extratropics, they decelerate the subtropical jet and prevent the Kelvin-Rossby coupling. Due to this sensitivity to baroclinic eddies the system exhibits hysteresis: near the transition parameter, extratropical eddies can prevent superrotation when they are initially present

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

We present an experimental study of flows in a cylindrical rotating annulus convectively forced by local heating in an annular ring at the bottom near the external wall and via a cooled circular disk near the axis at the top surface of the annulus. This new configuration is distinct from the classical thermally-driven annulus analogue of the atmosphere circulation, in which thermal forcing is applied uniformly on the sidewalls, but with a similar aim to investigate the baroclinic instability of a rotating, stratified flow subject to zonally symmetric forcing. Two vertically and horizontally displaced heat sources/sinks are arranged so that, in the absence of background rotation, statically unstable Rayleigh-Bénard convection would be induced above the source and beneath the sink, thereby relaxing strong constraints placed on background temperature gradients in previous experimental configurations based on the conventional rotating annulus. This better emulates local vigorous convection in the tropics and polar regions of the atmosphere whilst also allowing stably-stratified baroclinic motion in the central zone of the annulus, as in midlatitude regions in the Earth’s atmosphere. Regimes of flow are identified, depending mainly upon control parameters that in turn depend on rotation rate and the strength of differential heating. Several regimes exhibit baroclinically unstable flows which are qualitatively similar to those previously observed in the classical thermally-driven annulus, However, in contrast to the classical configuration, they typically exhibit more spatiotemporal complexity. Thus, several regimes of flow demonstrate the equilibrated co-existence of, and interaction between, free convection and baroclinic wave modes. These new features were not previously observed in the classical annulus and validate the new setup as a tool for exploring fundamental atmosphere-like dynamics in a more realistic framework. Thermal structure in the fluid is investigated and found to be qualitatively consistent with previous numerical results, with nearly isothermal conditions respectively above and below the heat source and sink, and stably-stratified, sloping isotherms in the near-adiabatic interior

Applying the Fluctuation–Dissipation Theorem to a Two-Layer Model of Quasigeostrophic Turbulence

The fluctuation–dissipation theorem (FDT) provides a means of calculating the response of a dynamical system to a small force by constructing a linear operator that depends only on data from the internal variability of the unperturbed system. Here the FDT is used to estimate the response of a two-layer quasigeostrophic model to two zonally symmetric torques, both barotropic, with the same sign of the forcing in the two layers, and baroclinic, with opposite sign forcing in the two layers. The supercriticality of the model is also varied to test how the FDT fares, as this parameter is varied. To perform the FDT calculations the data are decomposed onto empirical orthogonal functions (EOFs) and only those EOFs that are well resolved are retained in the FDT calculations. In the barotropic case good qualitative estimates are obtained for all values of the supercriticality, though the FDT consistently overestimates the response, perhaps because of significant non-Gaussian behavior present in the model. Nevertheless, this adds to the evidence that the annular-mode time scale plays an important role in determining the response of the midlatitudes to small perturbations. The baroclinic case is more challenging for the FDT. However, by constructing different bases with which to calculate the EOFs, it is shown that the issue in this case is that the baroclinic variability is poorly sampled, not that the FDT fails. The strategies developed in order to generate these estimates may be applicable to situations in which the FDT is applied to larger systems.Peer reviewe

The Finite-Amplitude Evolution of Mixed Kelvin–Rossby Wave Instability and Equatorial Superrotation in a Shallow-Water Model and an Idealized GCM

An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring.P. Z.-G. acknowledges financial support by Grant CGL2015-72259-EXP by the Ministry of Economy and Competitivity of Spain. This work has been partly done during P. Z.-G.’s visit to Princeton, funded by NSF Grant AGS-1733818.Peer reviewe