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This study introduces a two-degree-of-freedom piezoelectric energy harvester designed to harness rotational motion as an energy source. The harvester is built using a cut-out beam, which enables the first two resonant frequencies to be closely located in the low-frequency range. A distributed continuous model is developed and validated with experimental results. As the beam undergoes significant displacement due to rotational excitations, the geometric nonlinearity arising from longitudinal displacement is considered in the model to enhance its accuracy. It is observed that as the rotating speed increases, the increased centrifugal force causes the first resonant frequency to rise while the second resonant frequency decreases. The rotation-specific mode veering and the interchange of the first two modes are discussed. This study explores the potential to expand the bandwidth of the harvester using two types of nonlinear external force, namely mechanical stoppers and magnetic force. The results indicate that the proposed harvester can broaden the bandwidth of the first and second resonant frequencies. This research addresses the gap of combining multimodal and nonlinear force methods in rotation-al piezoelectric energy harvesting.

Aerosol-cloud interactions (ACI) pose the largest uncertainty for climate projections. Among many challenges of understanding ACI, the question of whether ACI is deterministic or stochastic has not been explicitly formulated and asked. Here we attempt to answer this question by predicting cloud droplet number concentration Nc from aerosol number concentration Na and ambient conditions. We use aerosol properties, vertical velocity fluctuation w', and meteorological states (temperature T and water vapor mixing ratio q_v) from the ACTIVATE field observations (2020 to 2022) as predictor variables to estimate Nc. We show that the climatological Nc can be successfully predicted using a machine learning model despite the strongly nonlinear and multi-scale nature of ACI. However, the observation-trained machine learning model fails to predict Nc in individual cases while it successfully predicts Nc of randomly selected data points that cover a broad spatiotemporal scale, suggesting the stochastic nature of ACI at fine spatiotemporal scales.

Aerosol effects on micro-/macro-physical properties of marine stratocumulus clouds over the Western North Atlantic Ocean (WNAO) are investigated using in-situ measurements and large-eddy simulations (LES) for two cold air outbreak (CAO) cases (February 28 and March 1, 2020) during the Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). The LES is able to reproduce the vertical profiles of liquid water content (LWC), effective radius r_eff and the cloud droplet number concentration Nc from fast cloud droplet probe (FCDP) in-situ measurements for both cases. Furthermore, we show that aerosols affect cloud properties (Nc, r_eff, and LWC) via the prescribed bulk hygroscopicity of aerosols and aerosol size distributions characteristics. Nc, r_eff, and liquid water path (LWP) are positively correlated to the bulk hygroscopicity of aerosols and aerosol number concentration (Na) while cloud fractional cover (CFC) is insensitive to the bulk hygroscopicity of aerosols and aerosol size distributions for the two cases. The changes to aerosol size distribution (number concentration, width, and the geometrical diameter) allow us to disentangle aerosol effects on cloud properties from the meteorological effects. We also use the LES results to evaluate cloud properties from two reanalysis products, ERA5 and MERRA-2. Comparing to LES, the ERA5 reanalysis is able to capture the time evolution of LWP and total cloud coverage within the study domain during both CAO cases while MERRA-2 underestimates them.

Large-eddy simulation (LES) is able to capture key boundary-layer (BL) turbulence and cloud processes. Yet, large-scale forcing and surface turbulent fluxes of sensible and latent heat are often poorly prescribed for LES simulations. We derive these quantities from measurements and reanalysis obtained for two cold air outbreak (CAO) events during Phase I of the Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE) in February-March 2020. We study the two contrasting CAO cases by performing LES and test the sensitivity of BL structure and clouds to large-scale forcings and turbulent heat fluxes. Profiles of atmospheric state and large-scale divergence and surface turbulent heat fluxes obtained from the reanalysis data ERA5 agree reasonably well with those derived from ACTIVATE field measurements for both cases at the sampling time and location. Therefore, we adopt the time evolving heat fluxes, wind and advective tendencies profiles from ERA5 reanalysis data to drive the LES. We find that large-scale thermodynamic advective tendencies and wind relaxations are important for the LES to capture the evolving observed BL meteorological states characterized by the hourly ERA5 reanalysis data and validated by the observations. We show that the divergence (or vertical velocity) is important in regulating the BL growth driven by surface heat fluxes in LES simulations. The evolution of liquid water path is largely affected by the evolution of surface heat fluxes. The liquid water path simulated in LES agrees reasonably well with the ACTIVATE measurements.This study paves the path to investigate aerosol-cloud-meteorology interactions using LES informed and evaluated by ACTIVATE field measurements., Comment: Accepted for publication in Journal of the Atmospheric Sciences

We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high resolution (10243) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves towards a shape which is a reflection of the gas-density distribution, regardless of the initial distribution. That is, in case of isothermal, rotationally forced turbulence, the GSD tends to be a lognormal distribution. We also show that in hypersonic turbulence, decoupling of gas and dust becomes important and that this leads to an even further accelerated grain growth.

Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium (ISM) for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and the effects on the size distribution and coagulation rate due to increasing Mach number is explored. We show that the time evolution of particle size distribution mainly depends on the compressibility (Mach number). We find that the average coagulation kernel $\langle C_{ij}\rangle$ scales linearly with the average Mach number $\mathcal{M}_{\rm rms}$ multiplied by the combined size of the colliding particles, that is, $\langle C_{ij}\rangle \sim \langle (a_i + a_j)^3\rangle\, \mathcal{M}_{\rm rms}\tau_\eta^{-1}$, which is qualitatively consistent with expectations from analytical estimates. A quantitative correction $\langle C_{ij}\rangle \sim \langle(a_i + a_j)^3\rangle(v_{\rm p,rms}/c_{\rm s})\tau_\eta^{-1}$ is proposed and can serve as a benchmark for future studies. We argue that the coagulation rate $\langle R_c\rangle$ is also enhanced by compressibility-induced compaction of particles.

It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space ('lucky droplet model'). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water-vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet-size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation fluctuation-induced broadening of droplet-size distributions enhances the collisional growth. This is contrary to classical (non-turbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet-size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation., Comment: revised version, 17 pages, 1 table, 13 figures

Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets being modeled as Lagrangian particles. The supersaturation field is calculated directly by simulating the temperature and water vapor fields instead of being treated as a passive scalar. Thermodynamic feedbacks to the fields due to condensation are also included for completeness. We find that the width of droplet size distributions increases with time, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower size distributions. Nevertheless, in agreement with earlier Lagrangian stochastic models of the condensational growth, the standard deviation of the surface area of droplets increases as $t^{1/2}$. Also, for the first time, we explicitly demonstrate that the time evolution of the size distribution is sensitive to the Reynolds number, but insensitive to the mean energy dissipation rate. This is shown to be due to the fact that temperature fluctuations and water vapor mixing ratio fluctuations increases with increasing Reynolds number, therefore the resulting supersaturation fluctuations are enhanced with increasing Reynolds number. Our simulations may explain the broadening of the size distribution in stratiform clouds qualitatively, where the mean updraft velocity is almost zero., Comment: 17 pages, 2 tables, 4 figures, submitted to Atmosph. Chem. Phys

Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed., Comment: 8 pages, 5 figures, MNRAS, resubmitted

We investigate the effect of turbulence on the collisional growth of um-sized droplets through high- resolution numerical simulations with well resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate, but only weakly on the Reynolds number. This can be explained through the energy dissipation rate dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as the square root of the energy dissipation rate even when coalescence is invoked. The size distribution exhibits power law behavior with a slope of -3.7 between a maximum at approximately 10 um up to about 40 um. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is due to the fact that turbulence enhances the collisional growth between similar sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.