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Author: Sandipan Banerjee
Publisher:
ISBN: 9781369353464
Category :
Languages : en
Pages : 57
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Book Description
Collisions of sedimenting droplets in a turbulent flow is of great importance in cloud physics. Collision efficiency and collision enhancement over gravitational collision by air turbulence govern the growth of the cloud droplets leading to warm rain initiation and precipitation dynamics. In this thesis we present direct numerical simulation (DNS) results for collision statistics of droplets in turbulent flows of low dissipation rates (in the range of 3 cm2/s3--100 cm2/s3) relevant to strato-cumulus clouds. First, we revisit the case of gravitational collision in still fluid to validate the details of the collision detection algorithm used in our code. We compare the collision statistics with either new analytical predictions regarding the percentages of different collision types, or results from published papers. The effect of initial conditions on the collision statistics and statistical uncertainties are analyzed both analytically and through the simulation data. Second, we consider the case of weak turbulence (as in strato-cumulus clouds). In this case the particle motion is mainly driven by gravity. The standard deviation (or the uncertainty) of the average collision statistics is examined analytically in terms of time correlation function of the data. We then report new DNS results of collision statistics in a turbulent flow, showing how air turbulence increases the geometric colli- sion statistics and the collision efficiency. We find that the collision-rate enhancement due to turbulence depends nonlinearly on the flow dissipation rate. This result calls for a more careful parameterization of the collision statistics in strato-cumulus clouds. Due to the low flow dissipation rate in stratocumulus clouds, a related challenge is low droplet Stokes number. Here the Stokes number is the ratio of droplet inertial response time to the flow Kolmogorov time. A very low Stokes number implies that the numerical integration time step is now governed by the droplet inertial response time, rather than the time step necessary for the flow simulation. This situation makes the simulations very expensive to perform. With the motivation to speed up the simulations, we implement the asymptotic expansion approach (as in Maxey, 1987) for particle tracking as this method is suitable for low particle Stokes number and avoids the numerical integration of the stiff equation of motion of droplets. We first validate our implementation using the simpler 2-D cellular flow. Next, we compare the collision statistics of the newly implemented asymptotic approach with our existing approach of particle tracking as well as with published results from journal papers. Finally, we provide the run time comparison for both methods.
Author: Sandipan Banerjee
Publisher:
ISBN: 9781369353464
Category :
Languages : en
Pages : 57
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Book Description
Collisions of sedimenting droplets in a turbulent flow is of great importance in cloud physics. Collision efficiency and collision enhancement over gravitational collision by air turbulence govern the growth of the cloud droplets leading to warm rain initiation and precipitation dynamics. In this thesis we present direct numerical simulation (DNS) results for collision statistics of droplets in turbulent flows of low dissipation rates (in the range of 3 cm2/s3--100 cm2/s3) relevant to strato-cumulus clouds. First, we revisit the case of gravitational collision in still fluid to validate the details of the collision detection algorithm used in our code. We compare the collision statistics with either new analytical predictions regarding the percentages of different collision types, or results from published papers. The effect of initial conditions on the collision statistics and statistical uncertainties are analyzed both analytically and through the simulation data. Second, we consider the case of weak turbulence (as in strato-cumulus clouds). In this case the particle motion is mainly driven by gravity. The standard deviation (or the uncertainty) of the average collision statistics is examined analytically in terms of time correlation function of the data. We then report new DNS results of collision statistics in a turbulent flow, showing how air turbulence increases the geometric colli- sion statistics and the collision efficiency. We find that the collision-rate enhancement due to turbulence depends nonlinearly on the flow dissipation rate. This result calls for a more careful parameterization of the collision statistics in strato-cumulus clouds. Due to the low flow dissipation rate in stratocumulus clouds, a related challenge is low droplet Stokes number. Here the Stokes number is the ratio of droplet inertial response time to the flow Kolmogorov time. A very low Stokes number implies that the numerical integration time step is now governed by the droplet inertial response time, rather than the time step necessary for the flow simulation. This situation makes the simulations very expensive to perform. With the motivation to speed up the simulations, we implement the asymptotic expansion approach (as in Maxey, 1987) for particle tracking as this method is suitable for low particle Stokes number and avoids the numerical integration of the stiff equation of motion of droplets. We first validate our implementation using the simpler 2-D cellular flow. Next, we compare the collision statistics of the newly implemented asymptotic approach with our existing approach of particle tracking as well as with published results from journal papers. Finally, we provide the run time comparison for both methods.
Author:
Publisher:
ISBN: 9780542227769
Category : Atmospheric turbulence
Languages : en
Pages :
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Book Description
This dissertation concerns effects of air turbulence on the collision rate of atmospheric cloud droplets. This research was motivated by the speculation that air turbulence could enhance the collision rate thereby help transform cloud droplets to rain droplets in a short time as observed in nature. The air turbulence within clouds is assumed to be homogeneous and isotropic, and its small-scale motion (1 mm to 10 cm scales) is computationally generated by direct numerical integration of the full Navier-Stokes equations. Typical droplet and turbulence parameters of convective warm clouds are used to determine the Stokes numbers (St) and the nondimensional terminal velocities (Sv) which characterize droplet relative inertia and gravitational settling, respectively. A novel and efficient methodology for conducting direct numerical simulations (DNS) of hydrodynamically-interacting droplets in the context of cloud microphysics has been developed. This numerical approach solves the turbulent flow by the pseudo-spectral method with a large-scale forcing, and utilizes an improved superposition method to embed analytically the local, small-scale (10 & mu;m to 1 mm) disturbance flows induced by the droplets. This hybrid representation of background turbulent air motion and the induced disturbance flows is then used to study the combined effects of hydrodynamic interactions and airflow turbulence on the motion and collisions of cloud droplets. Hybrid DNS results show that turbulence can increase the geometric collision kernel relative to the gravitational geometric kernel by as much as 42% due to enhanced radial relative motion and preferential concentration of droplets. The exact level of enhancements depends on the Taylor-microscale Reynolds number, turbulent dissipation rate, and droplet pair size ratio. One important finding is that turbulence has a relatively dominant effect on the collision process between droplets close in size as the gravitational collision mechanism diminishes. A theory was developed to predict the radial relative velocity between droplets at contact. The theory agrees with our DNS results to within 5% for cloud droplets with strong settling. In addition, an empirical model is developed to quantify the radial distribution function.
Author: Dennis Lamb
Publisher: Cambridge University Press
ISBN: 1139500945
Category : Science
Languages : en
Pages : 599
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Book Description
Clouds affect our daily weather and play key roles in the global climate. Through their ability to precipitate, clouds provide virtually all of the fresh water on Earth and are a crucial link in the hydrologic cycle. With ever-increasing importance being placed on quantifiable predictions - from forecasting the local weather to anticipating climate change - we must understand how clouds operate in the real atmosphere, where interactions with natural and anthropogenic pollutants are common. This textbook provides students - whether seasoned or new to the atmospheric sciences - with a quantitative yet approachable path to learning the inner workings of clouds. Developed over many years of the authors' teaching at Pennsylvania State University, Physics and Chemistry of Clouds is an invaluable textbook for advanced students in atmospheric science, meteorology, environmental sciences/engineering and atmospheric chemistry. It is also a very useful reference text for researchers and professionals.
Author: David Collins
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We propose a mathematical procedure to derive a stochastic parameterization for the bulk warm cloud micro-physical properties of collision and coalescence. Unlike previous bulk parameterizations, the stochastic parameterization does not assume any particular droplet size distribution, all parameters have physical meanings which are recoverable from data, all equations are independently derived making conservation of mass intrinsic, the auto conversion parameter is finely controllable, and the resultant parameterization has the flexibility to utilize a variety of collision kernels. This new approach to modelling the kinetic collection equation (KCE) decouples the choice of a droplet size distribution and a collision kernel from a cloud microphysical parameterization employed by the governing climate model. In essence, a climate model utilizing this new parameterization of cloud microphysics could have different distributions and different kernels in different climate model cells, yet employ a single parameterization scheme.This stochastic bulk model is validated theoretically and empirically against an existing bulk model that contains a simple enough (toy) collision kernel such that the KCE can be solved analytically. Theoretically, the stochastic model reproduces all the terms of each equation in the existing model and precisely reproduces the power law dependence for all of the evolving cloud properties. Empirically, values of stochastic parameters can be chosen graphically which will precisely reproduce the coefficients of the existing model, save for some ad-hoc non-dimensional time functions. Furthermore values of stochastic parameters are chosen graphically. The values selected for the stochastic parameters effect the conversion rate of mass cloud to rain. This conversion rate is compared against (i) an existing bulk model, and (ii) a detailed solution that is used as a benchmark.The utility of the stochastic bulk model is extended to include hydrodynamic and turbulent collision kernels for both clean and polluted clouds. The validation and extension compares the time required to convert 50\% of cloud mass to rain mass, compares the mean rain radius at that time, and used detailed simulations as benchmarks. Stochastic parameters can be chosen graphically to replicate the 50\% conversion time in all cases. The curves showing the evolution of mass conversion that are generated by the stochastic model with realistic kernels do not match corresponding benchmark curves at all times during the evolution for constant parameter values. The degree to which the benchmark curves represent ground truth, i.e. atmospheric observations, is unknown. Finally, among alternate methods of acquiring parameter values, getting a set of sequential values for a single parameter has a stronger physical foundation than getting one value per parameter, and a stochastic simulation is preferable to a higher order detailed method due to the presence of bias in the latter.
Author: C. L. Olson
Publisher:
ISBN:
Category : Cloud physics
Languages : en
Pages : 37
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Book Description
The formation of precipitation in warm cumulus clouds is most simply modeled by a uniform distribution of droplets falling at their terminal velocities in still air. However, it is known that storm clouds possess a large updraft and are turbulent in general. This memorandum discusses the possible mechanisms by which turbulence could affect the growth rate of droplets and reviews present research on this subject. (Author).
Author: Fausto Carlos de Almeida
Publisher:
ISBN:
Category : Aerosols
Languages : en
Pages : 428
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Book Description
Author: Pao K. Wang
Publisher: Cambridge University Press
ISBN: 1107005566
Category : Science
Languages : en
Pages : 469
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Book Description
New textbook on microphysics, thermodynamics and cloud-scale dynamics of clouds and precipitation, for graduate and advanced undergraduate students, researchers and professionals.
Author: Shankar Subramaniam
Publisher: Academic Press
ISBN: 0323901344
Category : Technology & Engineering
Languages : en
Pages : 588
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Book Description
Modelling Approaches and Computational Methods for Particle-laden Turbulent Flows introduces the principal phenomena observed in applications where turbulence in particle-laden flow is encountered while also analyzing the main methods for analyzing numerically. The book takes a practical approach, providing advice on how to select and apply the correct model or tool by drawing on the latest research. Sections provide scales of particle-laden turbulence and the principal analytical frameworks and computational approaches used to simulate particles in turbulent flow. Each chapter opens with a section on fundamental concepts and theory before describing the applications of the modelling approach or numerical method. Featuring explanations of key concepts, definitions, and fundamental physics and equations, as well as recent research advances and detailed simulation methods, this book is the ideal starting point for students new to this subject, as well as an essential reference for experienced researchers. - Provides a comprehensive introduction to the phenomena of particle laden turbulent flow - Explains a wide range of numerical methods, including Eulerian-Eulerian, Eulerian-Lagrange, and volume-filtered computation - Describes a wide range of innovative applications of these models
Author: M.K. Yau
Publisher: Elsevier
ISBN: 0080570941
Category : Science
Languages : en
Pages : 308
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Book Description
Covers essential parts of cloud and precipitation physics and has been extensively rewritten with over 60 new illustrations and many new and up to date references. Many current topics are covered such as mesoscale meteorology, radar cloud studies and numerical cloud modelling, and topics from the second edition, such as severe storms, precipitation processes and large scale aspects of cloud physics, have been revised. Problems are included as examples and to supplement the text.
Author: Sisi Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"In shallow cloud systems, such as cumulus or stratocumulus clouds, broad droplet size spectra and fast rain formation times are frequently observed using radar and in-situ measurements. However, these observations cannot be represented by classical condensational growth theory. Turbulence has been hypothesized to accelerate the formation of raindrops by enhancing the cloud droplet collision-coalescence process. In this thesis, the direct numerical simulation (DNS) approach is used to investigate the role of turbulence in cloud microphysics processes during warm-rain initiation and to quantify the effect of turbulence on the collision rate between droplets. We developed an accurate and sophisticated modeling framework that couples dynamics and thermodynamics, thus allowing the incorporation of droplet growth by simultaneous condensational and collisional processes under various turbulent conditions. Throughout the thesis, three sets of numerical experiments are conducted to study the turbulence impact on various droplet growth processes: 1) the droplet geometric collision, i.e., collisions without considering the disturbance flow induced by the presence of droplets, 2) the droplet hydrodynamic collisions, by including the disturbance flow, and 3) the interactions between condensational growth and collisional growth by further including the thermodynamic fields. The results of the first two sets of experiments demonstrate that for droplet pairs with different sizes (r1/r20.8), turbulence plays a dominant role in modifying the droplet hydrodynamic response to the local disturbance flow, weakly increasing the droplet relative velocity and creating the clustering of droplets in space. Consequentially, a significant enhancement of the collision efficiency and a mild enhancement of geometric collision kernel resulted. On the other hand, for droplet pairs with similar sizes (r1/r20.8), the turbulence enhancement in geometric collision and droplet hydrodynamic interactions is strong. Since droplet condensational growth produces a narrow droplet size distribution (DSD), we hypothesize that turbulence effectively widens the narrow spectrum by boosting similar-sized collisions. This hypothesis is further verified by conducting simulations of DSD evolution through collision-coalescence at various flow conditions. It is found that turbulence significantly broadens the DSD, and similar-sized collisions contribute to 21-24% of the total collisions compared to only 9% in the still-air experiments. Finally, we study the interaction of thermodynamics and dynamics and its impact on droplet growth by allowing droplets to simultaneously grow by condensation and collision in turbulent and non-turbulent environments. The results show that the condensational process promotes collisions in a turbulent environment while it reduces the collisions when in still air, indicating a positive impact of dynamics (turbulence) on the interaction of condensation and collision.In addition, we investigate the relative importance of different scales of turbulent flow on the collision statistics by varying the computational domain size. It is found that for small droplets (r
