scholarly journals Generation of Localised Vertical Streams in Unstable Stratified Atmosphere

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 454
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Istvan Ballai ◽  
Aleksandr Kryshtal ◽  
Gary Verth
Keyword(s):  
Bessel Functions ◽  
Vertical Direction ◽  
Azimuthal Velocity ◽  
Internal Gravity Waves ◽  
Growth Time ◽  
Axially Symmetric ◽  
Structure And Dynamics ◽  
Vorticity Component ◽  
Nonlinear Analytical Model ◽  
Characteristic Growth

A new model of axially symmetric concentrated vortex generation was developed herein. In this work, the solution of a nonlinear equation for internal gravity waves in an unstable stratified atmosphere was obtained and analysed in the framework of ideal hydrodynamics. The related expressions for the velocities in the inner and outer regions of the vortex were described by Bessel functions and modified zeroth-order Bessel functions. The proposed new nonlinear analytical model allows the study of the structure and dynamics of vortices in the radial region. The formation of jets (i.e., structures elongated in the vertical direction with finite components of the poloidal (radial and vertical) velocities that grow exponentially in time in an unstable stratified atmosphere) was also analysed. The characteristic growth time was determined by the inverse growth rate of instability. It is shown that a seed vertical vorticity component may be responsible for the formation of vortices with a finite azimuthal velocity.

scholarly journals The Stationary Concentrated Vortex Model

Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  
Keyword(s):  
Vortex Structure ◽  
Radial Direction ◽  
Symmetry Axis ◽  
Outer Part ◽  
Vertical Direction ◽  
Axially Symmetric ◽  
New Model ◽  
Vortex Model ◽  
Axis Of Symmetry ◽  
Good Agreement

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.

Synthesis of ZnO Nanowires by Hydrothermal Technique for Integration Into Chalcopyrite Thin Films

2012 ◽  
Vol 1406 ◽  
Author(s):  
H. Karaagac ◽  
M. Parlak ◽  
M. Saif Islam
Keyword(s):  
Thin Film ◽  
Solar Cell ◽  
Seed Layer ◽  
Growth Parameters ◽  
Vertical Direction ◽  
Zno Nanowires ◽  
Growth Time ◽  
Silicon Substrates ◽  
Transmission Measurement ◽  
Hydrothermal Technique

ABSTRACTVertically oriented, highly dense ZnO nanowires (NWs) array was successfully grown on both glass and silicon substrates using hydrothermal technique. A systematic study was carried out to investigate the effects of growth parameters including growth time and thickness of ZnO seed layer on the quality of ZnO NWs in terms of their homogeneity and orientation in the vertical direction. The diameter as well as the length of grown ZnO NWs was found to be closely dependent on the thickness of the pre-coated ZnO seed layer. The structures of ZnO NWs and electron-beam evaporated AgGa0.5In0.5Se2 (AGIS) thin film have been characterized by X-ray diffraction measurements and optical properties were measured by transmission measurement. The optic band gap of AGIS thin film was found to be almost optimum (1.56 eV) to match the abundant part of solar cell spectrum. AGIS thin film was deposited on the synthesized ZnO NWs to form p-n heterojunction based inorganic solar cell, which exhibited photovoltaic behavior with a power conversion efficiency of 0.37 % under A.M (1.5) illumination.

scholarly journals RANS Simulations of Supercavity Flows

2010 ◽  
Vol 54 (03) ◽  
pp. 161-173
Author(s):  
C. Pellone ◽  
T. Maître ◽  
J. P Franc
Keyword(s):  
Nonlinear Boundary ◽  
Source Term ◽  
Cavity Length ◽  
Computational Grid ◽  
Variable Density ◽  
Navier Stokes ◽  
Growth Time ◽  
Two Phases ◽  
Characteristic Growth ◽  
Unsteady Conditions

This work aims at evaluating the capacity and limitations of conventional Reynolds-averaged Navier-Stokes (RANS) techniques to numerically simulate supercavity flows. The configuration is that of a two-dimensional (2D) symmetrical supercavitating wedge investigated experimentally by Michel (1974). Mesh effect is studied in detail under noncavitating conditions. The computational grid is refined in the region where cavitation develops in order to accurately track the supercavity. The effect of tunnel height is also analyzed, and the height finally chosen was large enough to simulate an infinite flow-field. The cavitating flow is treated as a homogeneous mixture of variable density. To account for vaporization and condensation, an additional continuity equation for the vapor (or the liquid) is solved with an appropriate source term expressing mass transfer between the two phases. The effect of nuclei concentration on the vaporization rate and then on the development of the supercavity is investigated. Results obtained using two different RANS codes are compared. They are also compared with experimental data and with inviscid solutions including a nonlinear boundary element method. They concern in particular cavity length and shape, pressure distribution, and drag coefficient. Under unsteady conditions, a special attention is paid to the characteristic growth time of the supercavity following a sudden pressure drop, from noncavitating conditions.

A simple method of summing Bessel series

1968 ◽  
Vol 64 (3) ◽  
pp. 705-710 ◽  
Author(s):  
J. A. Greenwood
Keyword(s):  
Simple Formula ◽  
Bessel Functions ◽  
Convergent Series ◽  
Axially Symmetric ◽  
Simple Method ◽  
Symmetric Potential ◽  
Potential Problems ◽  
Direct Substitution

AbstractA simple formula is derived for transforming the slowly convergent series involving Bessel functions which arise in axially symmetric potential problems into more rapidly convergent series. Using it, sums of series previously found by elaborate special methods may be obtained by direct substitution. The necessary numerical coefficients are given.

scholarly journals Derivative-type ascent formulas for kernels of some half-space Dirichlet problems

2000 ◽  
Vol 42 (2) ◽  
pp. 185-194
Author(s):  
L. R. Bragg
Keyword(s):  
Potential Theory ◽  
Half Space ◽  
Laplace Equation ◽  
Bessel Functions ◽  
Axially Symmetric ◽  
Dirichlet Problems ◽  
Symmetric Potential ◽  
Derivative Type ◽  
Differentiation Formulas

AbstractDerivative-type ascent formulas are deduced for the kernels of certain half-space Dirichlet problems. These have the character of differentiation formulas for the Bessel functions but involve modifying variables after completing the differentiations. The Laplace equation and the equation of generalized axially-symmetric potential theory (GASPT) are considered in these. The methods employed also permit treating abstract versions of Dirichlet problems.

The Square Root Approximation to the Dispersion Relation of the Axially-symmetric Electron Wave on a Cylindrical Plasma

1997 ◽  
Vol 52 (10) ◽  
pp. 709-712
Author(s):  
V.M. Babović ◽  
B.A. Aničin ◽  
D. M. Davidović
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Gravity Waves ◽  
Water Surface ◽  
Bessel Functions ◽  
Exact Expression ◽  
Square Root ◽  
Axially Symmetric ◽  
Electron Wave ◽  
Surface Gravity Waves

Abstract This paper suggests the use of a simple square root approximation to the dispersion relation of axially-symmetric electron surface waves on cylindrical plasmas. The point is not merely to substitute the exact expression for the dispersion relation which involves a number of Bessel functions with a more tractable analytical approximant, but to cast the dispersion relation in a form useful in the comparison with other waves, such as water surface gravity waves and the associated tide-rip effect. The square root form of the dispersion relation is also of help in the analysis of surfactron plasmas, as it directly predicts a linear roll-off of electron density in the discharge.

Coupling of surface and internal gravity waves: a mode coupling model

1976 ◽  
Vol 77 (1) ◽  
pp. 185-208 ◽  
Author(s):  
Kenneth M. Watson ◽  
Bruce J. West ◽  
Bruce I. Cohen
Keyword(s):  
Energy Transfer ◽  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Wave Field ◽  
Internal Waves ◽  
Wave Spectrum ◽  
Coupled Model ◽  
Internal Gravity Waves ◽  
Growth Time

A surface-wave/internal-wave mode coupled model is constructed to describe the energy transfer from a linear surface wave field on the ocean to a linear internal wave field. Expressed in terms of action-angle variables the dynamic equations have a particularly useful form and are solved both numerically and in some analytic approximations. The growth time for internal waves generated by the resonant interaction of surface waves is calculated for an equilibrium spectrum of surface waves and for both the Garrett-Munk and two-layer models of the undersea environment. We find energy transfer rates as a function of undersea parameters which are much faster than those based on the constant Brunt-ViiisSila model used by Kenyon (1968) and which are consistent with the experiments of Joyce (1974). The modulation of the surface-wave spectrum by internal waves is also calculated, yielding a ‘mottled’ appearance of the ocean surface similar to that observed in photographs taken from an ERTS1 satellite (Ape1 et al. 1975b).

Introduction to Modeling Convection in Planets and Stars

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Magnetic Field ◽  
Numerical Methods ◽  
Teaching Method ◽  
Vertical Direction ◽  
Internal Gravity Waves ◽  
Three Dimensions ◽  
Magnetic Field Generation ◽  
Computer Codes ◽  
Essential Resource ◽  
Realistic Geometries

This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, the book begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a 2D box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. It then describes how to implement more efficient a nd accurate numerical methods and more realistic geometries in two and three dimensions. The third part of the book demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation. The book features numerous exercises throughout, and is an ideal textbook for students and an essential resource for researchers. It explains how to create codes that simulate the internal dynamics of planets and stars, and builds on basic concepts and simple methods. The book shows how to improve the efficiency and accuracy of the numerical methods. It considers more relevant geometries and boundary conditions.

Rapid simulation of borehole electromagnetic response in axially symmetric and transversely isotropic formations

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. E245-E257 ◽  
Author(s):  
Gong Li Wang ◽  
Aria Abubakar
Keyword(s):  
Plane Waves ◽  
Vertical Direction ◽  
Transversely Isotropic ◽  
Data Interpretation ◽  
Fourier Series Expansion ◽  
Electromagnetic Response ◽  
Axially Symmetric ◽  
Conductivity Anisotropy ◽  
Transverse Isotropic ◽  
1D Model

Downhole well-logging data acquired by modern electromagnetic (EM) tools enables determining not only conductivity but also conductivity anisotropy of reservoirs. The most popular anisotropic model for EM data interpretation is a horizontally layered model with transverse isotropic conductivity in each layer. Such a model ignores the conductivity change caused by the mud-filtrate invasion that often occurs in a permeable layer. The invasion effect can be so strong that the conductivity derived using the 1D model can be substantially affected. We have developed an efficient forward-modeling approach that includes the invasion in the formation model so that the invasion effect can be properly accounted for in data interpretation and inversion. The approach uses a Fourier series expansion for the electric field in the azimuthal direction to take advantage of the invariance of conductivity in this direction. Each harmonic in the expansion is expressed in terms of numerical eigenmodes in the radial direction and exponential functions in the vertical direction. Physically, the latter describes a set of plane waves propagating upward or downward in the vertical direction. This property allows us to use reflection and transmission matrices to couple EM fields from layer to layer, making it highly efficient to simulate EM logging response because the two matrices are computed only once for all logging points. The approach is best suited for a multilayer and transversely isotropic formation in which each layer can have an arbitrary number of radial discontinuities. Numerical experiments demonstrate that the new approach can accurately model the response of induction and propagation tools in various formations. A speedup of two orders of magnitude is obtained in a multilayer case compared with a previous 2D method using a different hybridization strategy.

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