Peter Bartello

Geostrophic adjustment and inverse cascades in rotating stratified turbulence

Abstract Rotating stratified turbulence is examined both numerically and analytically, guided by energy and potential enstrophy conservation as well as resonant interaction theory, in order to investigate the cascade properties of rotational and wave modes at Froude numbers of order one or below, over a range of Rossby numbers. As Ro → 0, rotational modes are only weakly coupled to wave modes, and there are only weak rotational wave energy exchanges when initial conditions are random. A catalytic interaction involving two waves and a rotational mode, leaving the rotational mode unchanged, then provides the mechanism for geostrophic adjustment via a downscale cascade of wave energy. When simulations are initially balanced, gravity modes act to damp large-scale rotational modes through a transfer into intermediate-scale gravity modes and a subsequent downscale wave cascade involving the catalytic interaction. At larger Ro transfer from rotational to wave modes is important at any Froude number, and geostrop...

Stratified turbulence dominated by vortical motion

We present numerical simulations of stably stratified, vortically forced turbulence at a wide range of Froude numbers. Large-scale vortical forcing was chosen to represent geophysical vortices which break down at small scales where Coriolis effects are weak. The resulting vortical energy spectra are much steeper in the horizontal direction and shallower in the vertical than typical observations in the atmosphere and ocean, as noted in previous studies. We interpret these spectra in terms of the vertical decoupling which emerges in the strongly stratified limit. We show that this decoupling breaks down at a vertical scale of U/N, where N is the Brunt-Vaisala frequency and U is a characteristic horizontal velocity, confirming previous scaling arguments. The transfer of vortical energy to wave energy is most efficient at this vertical scale; vertical spectra of wave energy are correspondingly peaked at small scales, as observed in past work. The equilibrium statistical mechanics of the inviscid unforced truncated problem qualitatively predicts the nature of the forced-dissipative solutions, and confirms the lack of an inverse cascade of vortical energy.

Collision Rates of Cloud Droplets in Turbulent Flow

Direct numerical simulations of an evolving turbulent flow field have been performed to explore how turbulence affects the motion and collisions of cloud droplets. Large numbers of droplets are tracked through the flow field and their positions, velocities, and collision rates have been found to depend on the eddy dissipation rate of turbulent kinetic energy. The radial distribution function, which is a measure of the preferential concentration of droplets, increases with eddy dissipation rate. When droplets are clustered there is an increased probability of finding two droplets closely separated; thus, there is an increase in the collision kernel. For the flow fields explored in this study, the clustering effect accounts for an increase in the collision kernel of 8%–42%, as compared to the gravitational collision kernel. The spherical collision kernel is also a function of the radial relative velocities among droplets and these velocities increase from 1.008 to 1.488 times the corresponding gravitational value. For an eddy dissipation rate of about 100 cm 2 s 3 , the turbulent collision kernel is 1.06 times the magnitude of the gravitational value, while for an eddy dissipation rate of 1500 cm 2 s 3 , this increases to 2.08 times. Therefore, these results demonstrate that turbulence could play an important role in the broadening and evolution of the droplet size distribution and the onset of precipitation.

Microscopic Approach to Cloud Droplet Growth by Condensation. Part II: Turbulence, Clustering, and Condensational Growth

The goal of this work is to answer the question of whether nonuniformity in the spatial distribution of sizes and positions of cloud droplets and/or variable vertical velocity in a turbulent medium can contribute to the broadening of the droplet size distribution. A numerical approach to simulate the growth and trajectory of several tens of thousands of cloud droplets in a turbulent environment whose properties vary from droplet to droplet is used. The finite inertia of particles in a turbulent fluid causes particles to diverge from regions of high vorticity and to converge preferentially in regions of low vorticity, thus creating strong deviations in particle concentration. As a first step, the inertia effect was examined in the context of nongrowing, sedimenting, or nonsedimenting droplets. It was found that statistically significant preferential concentration is possible in conditions typical of cloud droplets in cumulus clouds. In the absence of sedimentation, preferential concentration increases as a function of the Stokes number St. Allowing the droplets to sediment decreases preferential concentration to a degree that increases with the velocity ratio Sy. A series of experiments including condensational growth of droplets was then performed. It was found that while the increasing preferential concentration of droplets, as a result of increasing eddy dissipation rate, does result in increases in the instantaneous dispersion of the supersaturation perturbation distribution, the width of the size distribution of droplets, which is a function of the dispersion in the time integral of the supersaturation perturbations, decreases. This result is a consequence of the decrease in decorrelation time of the supersaturation perturbations as the turbulence intensity increases. Comparison of the results herein with the observations made in quasi-adiabatic cloud cores leads one to the conclusion that the microscopic approach, even under the most favorable condition of no turbulence, produces too little broadening to explain the observations.

The transition from geostrophic to stratified turbulence

We present numerical simulations of forced rotating stratified turbulence dominated by vortical motion (i.e. with potential vorticity). Strong stratification and various rotation rates are considered, corresponding to a small Froude number and a wide range of Rossby numbers

The cost-effectiveness of semi-lagrangian advection

\hbox{\it Ro}

Stratified turbulence generated by internal gravity waves

spanning the regimes of stratified turbulence (

The intermediate Rossby number range and two-dimensional-three-dimensional transfers in rotating decaying homogeneous turbulence

\hbox{\it Ro}\,{=}\,\infty

Sampling Errors in Ensemble Kalman Filtering. Part I: Theory

) to quasi-geostrophic turbulence (

Geostrophic versus Wave Eddy Viscosities in Atmospheric Models

\hbox{\it Ro}\,{\ll}\,1