Gamma distributions represent particle size distributions (SDs) in mesoscale and cloud-resolving models that predict one, two, or three moments of hydrometeor species. They are characterized by intercept (N0), slope (λ), and shape (μ) parameters prognosed by such schemes or diagnosed based on fits to SDs measured in situ in clouds. Here, ice crystal SDs acquired in arctic cirrus during the Indirect and Semi-Direct Aerosol Campaign (ISDAC) and in hurricanes during the National Aeronautic and Space Administration (NASA) African Monsoon Multidisciplinary Analyses (NAMMA) are fit to gamma distributions using multiple algorithms. It is shown that N0, λ, and μ are not independent parameters but rather exhibit mutual dependence. Although N0, λ, and μ are not highly dependent on choice of fitting routine, they are sensitive to the tolerance permitted by fitting algorithms, meaning a three-dimensional volume in N0–λ–μ phase space is required to represent a single SD. Depending on the uncertainty in the measured SD and on how well a gamma distribution matches the SD, parameters within this volume of equally realizable solutions can vary substantially, with N0, in particular, spanning several orders of magnitude. A method to characterize a family of SDs as an ellipsoid in N0–λ–μ phase space is described, with the associated scatter in N0–λ–μ for such families comparable to scatter in N0, λ, and μ observed in prior field campaigns conducted in different conditions. Ramifications for the development of cloud parameterization schemes and associated calculations of microphysical process rates are discussed.

A diagnostic framework is developed to explain the response of tropical cyclones (TCs) to climate in high-resolution global atmospheric models having different complexity of boundary conditions. The framework uses vortex dynamics to identify the large-scale control on the evolution of TC precursors—first non-rotating convective clusters and then weakly rotating seeds. In experiments with perturbed sea surface temperature (SST) and $$\hbox {CO}_2$$ CO 2 concentration from the historical values, the response of TCs follows the response of seeds. The distribution of seeds is explained by the distribution of the non-rotating convective clusters multiplied by a probability that they transition to seeds. The distribution of convective clusters is constrained by the large-scale vertical velocity and is verified in aquaplanet experiments with shifting Inter tropical Convergence Zones. The probability of transition to seeds is constrained by the large-scale vorticity via an analytical function, representing the relative importance between vortex stretching and vorticity advection, and is verified in aquaplanet experiments with uniform SST. The consistency between seed and TC responses breaks down substantially when the realistic SST is perturbed such that the spatial gradient is significantly enhanced or reduced. In such cases, the difference between the responses is explained by a change in the ventilation index, which influences the fraction of seeds that develop into TCs. The proposed TC-climate relationship serves as a framework to explain the diversity of TC projection across models and forcing scenarios.

The mechanisms and universality class underlying the remarkable phenomena at the transition to turbulence remain a puzzle 130 years after their discovery . The statistical behaviour is thought to be related to directed percolation (DP; refs 6,11-13). Attempts to understand transitional turbulence dynamically invoke periodic orbits and streamwise vortices [14][15][16][17][18][19] , the dynamics of long-lived chaotic transients 20, and model equations based on analogies to excitable media 21. Here we report direct numerical simulations of transitional pipe flow, showing that a zonal flow emerges at large scales, activated by anisotropic turbulent fluctuations; in turn, the zonal flow suppresses the small-scale turbulence leading to stochastic predator-prey dynamics. We show that this ecological model of transitional turbulence, which is asymptotically equivalent to DP at the transition 22, reproduces the lifetime statistics and phenomenology of pipe flow experiments. Our work demonstrates that a fluid on the edge of turbulence exhibits the same transitional scaling behaviour as a predator-prey ecosystem on the edge of extinction, and establishes a precise connection with the DP universality class.Turbulent fluids are ubiquitous in nature, arising for sufficiently large characteristic speeds U , depending on the kinematic viscosity ν and a characteristic system scale, such as the diameter of a pipe D. Turbulent flows are complex, stochastic, and unpredictable in detail, but transition at lower velocities to a laminar flow, which is simple, deterministic and predictable. This transition is controlled by the dimensionless parameter known as the Reynolds number, which in the pipe geometry of interest here is given by Re ≡ UD/ν, and occurs in the range 1,700 Re 2,300. The laminar-turbulence transition has presented a challenge to experiment and theory since Osborne Reynolds' original observation of intermittent 'flashes' of turbulence 1 . To explore this transitional regime, we have performed direct numerical simulations of the Navier-Stokes equations in a pipe of length L = 10D, using the open-source code 'Open Pipe Flow' 23 , as described in Supplementary Methods. The Reynolds number at which transitional turbulence occurs is higher for short pipes 23 , and the simulations reported here for L = 10D were performed at a nominal value Re = 2,600, which we estimate to be equivalent to Re 2,200 in long pipe data 7 based on estimates of when puff decay transitions to puff splitting. We confirmed that our results did not qualitatively change for a longer pipe with L = 20D. We denote the time-dependent velocity deviation from the Hagen-Poiseuille flow by u = (u z , u θ , u r ). Because we were interested in transitional behaviour, we looked for a decomposition 2,6,24,25 of large-scale modes that would indicate some form of collective behaviour, as well as small-scale modes that would be representative of turbulent dynamics. In particular, we report here the behaviour of the velocity field (u z , u θ , u r ), where the bar de...

The purpose of this paper is to present a 2D depth-averaged model for simulating and examining flow patterns in channel bends. In particular, this paper proposes a 2D depth-averaged model that takes into account the influence of the secondary flow phenomenon through the calculation of the dispersion stresses arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. The proposed model uses an orthogonal curvilinear coordinate system to efficiently and accurately simulate the flow field with irregular boundaries. As for the numerical solution procedure, the two-step split-operator approach consisting of the dispersion step and the propagation step with the staggered grid is used to numerically solve the flow governing equations. Two sets of experimental data from de Vriend and Koch and from Rozovskii were used to demonstrate the model's capabilities. The former data set was from a mildly curved channel, whereas the latter was from a sharply curved channel. The simulations considering the secondary flow effect agree well with the measured data. Furthermore, an examination of the dispersion stress terms shows that the dispersion stresses play a major role in the transverse convection of the momentum shifting from the inner bank to the outer bank for flows in both mild and sharp bends.