An analytical theory of distributed axisymmetric barotropic vortices on the β-plane

1994 ◽  
Vol 269 ◽  
pp. 301-321 ◽  
Author(s):  
G. M. Reznik ◽  
W. K. Dewar
Keyword(s):  
Radiation Effects ◽  
Planetary Wave ◽  
Complete Solution ◽  
Asymptotic Series ◽  
Vortex Motion ◽  
Present Theory ◽  
Analytical Theory ◽  
Wave Radiation ◽  
Initial Value ◽  
Numerical Predictions

An analytical theory of barotropic β-plane vortices is presented in the form of an asymptotic series based on the inverse of vortex nonlinearity. In particular, a solution of the initial value problem is given, in which the vortex is idealized as a radially symmetric function of arbitrary structure. Motion of the vortex is initiated by its interaction with the so-called ‘β-gyres’ which, in turn, are generated by the vortex circulation. Comparisons of analytical and numerical predictions for vortex motion are presented and demonstrate the utility of the present theory for times comparable to the ‘wave’ timescale. The latter exceeds the temporal limit derived from formal considerations. The properties of the far-field planetary wave radiation are also computed.This theory differs from previous calculations by considering more general initial vortex profiles and by obtaining a more complete solution for the perturbation fields. Vortex trajectory predictions accrue error systematically by integrating vortex propagation rates which are too strong. This appears to be connected to higher-order planetary wave radiation effects.

Intense vortex motion in a stratified fluid on the beta-plane: an analytical theory and its validation

1997 ◽  
Vol 336 ◽  
pp. 203-220 ◽  
Author(s):  
GEORGI G. SUTYRIN ◽  
YVES G. MOREL
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Vortex Core ◽  
Vortex Motion ◽  
Relative Displacement ◽  
Analytical Theory ◽  
Wave Radiation ◽  
Layer Model ◽  
Beta Plane ◽  
Constant Potential

This paper deals with the self-induced translation of intense vortices on the β-plane in the framework of the multi-layer quasi-geostrophic approximation. An analytical theory is presented and compared to numerical experiments. To predict the vortex trajectories, we consider initially monopolar vortices, with a core of piecewise-constant potential vorticity, and calculate the evolution of the dipolar circulation which advects the vortex core. This multi-layer model yields analytical solutions for a period while the Rossby wave radiation is small.The development of the dipolar circulation and corresponding vortex translation are described as the results of three effects. The first and second are similar to what was found in earlier studies with a one-layer model: advection of the planetary vorticity by the symmetric vortex circulation, and horizonal deformations of the vortex core. In addition, when stratification is taken into account, the vertical tilting of the vortex core also plays a role. This third effect is here represented by the relative displacement of potential vorticity contours in different layers.Examples are given for one-, two- and three-layer models and compared with numerical simulations. It is found that the analytical predictions are good for several Rossby wave periods.

A Simple Analytical Theory for Interpreting Measured Total Pressure in Multiphase Flows

1998 ◽  
Vol 120 (2) ◽  
pp. 385-389 ◽  
Author(s):  
Abhijit Guha
Keyword(s):  
Total Pressure ◽  
Multiphase Flows ◽  
Practical Importance ◽  
Present Theory ◽  
Vapour Phase ◽  
Solid Particles ◽  
Analytical Theory ◽  
Nonequilibrium Processes ◽  
Measuring Device ◽  
Wide Range

This paper presents a simple, analytical theory for determining total pressure in multiphase flows, a subject of theoretical interest as well as of practical importance. It is shown here that the nonequilibrium processes occurring in the vicinity of a measuring device have a significant influence on the magnitude of flow velocity inferred from Pitot measurements. The present theory predicts that, depending on the size of the particles or droplets, the total pressure varies monotonically between the two limiting values: the frozen total pressure (when there is no interphase mass, momentum, and energy transfer in the decelerating flow toward the stagnation point) and the equilibrium total pressure (when the dispersed phase, either liquid droplets, or solid particles, is always at inertial and thermodynamic equilibrium with the continuous vapour phase). The presented analytical theory is a relation between nondimensional total pressure and Stokes number, representing particle size or inertia, and specifies the total pressure under different nonequilibrium conditions. One simple equation applies to diverse multiphase mixtures, solid particle laden gas as well as vapour-droplet mixtures, and at a wide range of flow conditions, both subsonic and supersonic. The associated issue of interpreting total temperature, and the relation between measured total pressure and entropy production in multiphase flows have been discussed at length by Guha (1998).

Vortex Motion Behind a Circular Cylinder

1925 ◽  
Vol 29 (172) ◽  
pp. 189-195
Author(s):  
R. C. J. Howland
Keyword(s):  
Circular Cylinder ◽  
Single Case ◽  
Complete Solution ◽  
Vortex Motion ◽  
Theory And Practice ◽  
Turbulent Motion ◽  
Applied Mathematician

The study of aerodynamics is still largely empirical, and there seems little hope at present that the gap between theory and practice will be sensibly diminished by any means at present known to the applied mathematician. Yet the light that would, in all likelihood, be thrown on a number of practical problems by the complete solution of even a single case of turbulent motion would be very great. Of the problems that can be attempted, that of the flow of a fluid past a circular cylinder is likely to prove the least intractable.

scholarly journals Initial value problems in water wave theory

1963 ◽  
Vol 3 (3) ◽  
pp. 340-350 ◽  
Author(s):  
A. G. Mackie
Keyword(s):  
Initial Value Problems ◽  
Complete Solution ◽  
Wave Theory ◽  
Minor Role ◽  
Axially Symmetric ◽  
Initial Value ◽  
Hydrodynamic Impact ◽  
Linearized Theory ◽  
A Minor ◽  
Thin Wedge

The work described in this paper grew out of an attempt to generalize some results obtained in an earlier paper [4] on the water entry problem of a thin wedge or cone into an incompressible fluid. The object of the generalization was to include the effect of gravity terms. In most papers on hydrodynamic impact it is considered permissible to neglect this effect since gravity terms might be expected to play a minor role in the initial stages of the motion. However, it seems desirable to investigate the effect of including gravity terms in order both to examine the later stages of the motion and to estimate to what extent their neglect is justified in the early stages. It will be seen that it is possible to develop a fairly complete solution for the normal entry of a thin symmetric body, both for two-dimensional and axially symmetric cases, on the basis of a linearized theory. The restriction to a linearized theory means that the whole field of analysis associated with the theory of surface waves of small amplitude becomes available. Most of the problems considered in this paper are initial value problems in which the whole fluid is at rest at t = 0.

Comparison of Ultrasonic Wave Radiation Effects on Asphaltene Aggregation in Toluene–Pentane Mixture Between Heavy and Extra Heavy Crude Oils

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
S. M. R. Mousavi ◽  
I. Najafi ◽  
M. H. Ghazanfari ◽  
M. Amani
Keyword(s):  
Crude Oil ◽  
Ultrasonic Wave ◽  
Radiation Effects ◽  
American Petroleum Institute ◽  
Wave Radiation ◽  
Crude Oils ◽  
Heavy Crude Oil ◽  
Heavy Crude ◽  
Radiation Time ◽  
Flocculation Rate

In this study, it is aimed to compare the efficiency of ultrasonic wave technology on asphaltene flocculation inhibition of crude oils with different American Petroleum Institute (API) gravities. A set of confocal microscopy test is performed and a series of statistical analysis is done. According to the results of this study, there is an optimum radiation time for both crudes at which the viscosity and the flocculation rate of asphaltenic crude oils reduces to its minimum. This optimum appears at later times of radiation for extra heavy oil. Also, it is shown that the rate of changes in the properties measured in this study is sharper for extra heavy crude oil. It could be concluded that the alternations caused by this technology is more significant for Kouh-e-Mond, which is heavier oil than Sarvak crude oil. Derjaguin–Ladau–Verwey–Overbeek (DLVO) kinetic model was also studied and it was understood that this model cannot be a validate model for radiated samples.

Laminar Flame Speeds and Strain Sensitivities of Mixtures of H2 With CO, CO2and N2 at Elevated Temperatures

2007 ◽  
Author(s):  
J. Natarajan ◽  
T. Lieuwen ◽  
J. Seitzman
Keyword(s):  
Radiation Effects ◽  
Equivalence Ratio ◽  
Elevated Temperatures ◽  
Laminar Flame ◽  
Flame Speed ◽  
Bunsen Flame ◽  
Clear Trend ◽  
Numerical Predictions ◽  
Fuel Mixtures ◽  
Lean Conditions

Laminar flame speed and strain sensitivities have been measured for mixtures of H2/CO/CO2/N2/O2 with a wall stagnation flame technique at high preheat temperature (700 K) and lean conditions. The measurements are compared with numerical predictions based on two reaction mechanisms: GRI Mech 3.0 and a H2/CO mechanism (Davis et al.). For H2:CO 50:50 fuel mixtures, both models tend to over predict the temperature dependence of the flame speed especially at very lean conditions, which confirms the trend found in an earlier study employing a Bunsen flame technique. The predicted strain sensitivities are in good agreement with the measurements. For 50:50 H2:CO fuel mixtures diluted with 40% CO2, the amount of over prediction by the models is about the same as in the undiluted case, which suggests that radiation effects associated with CO2 addition are not important for this mixture at highly preheated lean condition. For low H2 content (5 to 20%) H2/CO fuel mixtures at 5 atm and fuel lean condition, the predicted unstrained flame speeds are in excellent agreement with the measurements, but the models fail to predicted the strain sensitivity as the amount of H2 increases to 20%. Results are also presented for pure H2 with N2 diluted air (O2:N2 1:9) over a range of equivalence ratios. At lean conditions, the models over predict the measured flame speed by as much as 30%, and the amount of over prediction decreases as the equivalence ratio increases to stoichiometric and rich condition. The measured strain sensitivities are three times higher than the model predictions at lean conditions. More importantly, the predicted strain sensitivities do not change with equivalence ratio for both models, while the measurements reveal a clear trend (decreasing and then increasing) as the fuel-air ratio changes from lean to rich.

Numerical Prediction of Wind Flow Around Irregular Models

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
D. Y. Wang ◽  
Y. Zhou ◽  
Y. Zhu ◽  
Tim K. T. Tse
Keyword(s):  
Bluff Body ◽  
Numerical Models ◽  
Vortex Motion ◽  
Velocity Profiles ◽  
Wind Flow ◽  
Lateral Velocity ◽  
Fluctuating Pressure ◽  
Pressure Coefficients ◽  
Numerical Predictions ◽  
Building Models

This paper presents numerical predictions of flow around irregular-plan buildings (S-, R-, L- and U-shaped models) in high Reynolds number. The adopted computational approach and numerical models are described firstly. Then comparative analysis with the numerical and experimental data has been conducted to verify the reliability of the numerical predictions. Finally, characteristics of mean and fluctuating pressure distributions and vertical and lateral velocity profiles of the flow around the four models have been investigated and assessed thoroughly. The study shows that satisfactory results can be obtained by large eddy simulation (LES), especially when fluctuating wind velocity is considered in the inflow boundary. Distribution of mean pressure coefficients on front faces is relatively regular. Large fluctuating pressure coefficients are induced by strong vortex motion. Velocity profiles of wind flow are disturbed obviously among the four building models, especially in weak flow. The disturbed intensity decreases with increasing of the distance away from bluff body. The suggested MDS (Maximum Disturbance Scopes) away from bluff body are generally 0.25H in inflow zones, 0.4H in roof zones, 0.5H in both side zones and 3H in weak zones.

A Systematic Evaluation of NOx Formation Pathways and Subgrid Scale Models in Turbulent Nonpremixed CO/H2/N2 Jet Flame Predictions

2004 ◽  
Author(s):  
Padmabhushana R. Desam ◽  
Philip J. Smith
Keyword(s):  
Radiation Effects ◽  
High Sensitivity ◽  
Systematic Evaluation ◽  
Oh Radicals ◽  
Subgrid Scale ◽  
Jet Flame ◽  
No Formation ◽  
Numerical Predictions ◽  
Scale Models ◽  
Turbulent Nonpremixed

Numerical prediction of Nitrogen Oxides (NOx) from combustion processes has been a challenging task to the combustion community, yet necessary to reduce environmental impact. Turbulent nonpremixed combustion is characterized by wide ranges of overlapping length and time scales associated with the mixing and chemical reaction processes. In practice, averaged governing equations are solved with subgrid scale models to account for the unresolved scales and interactions among them. A validation study of subgrid scale models is made for a turbulent nonpremixed CO/H2/N2 jet flame. Numerical predictions of Nitric Oxide (NO) quantities are compared with experimental data to evaluate the accuracy of subgrid scale models. Factors significantly affect NO formation are identified and studied thoroughly. In addition to thermal NO pathway, N2O-intermediate pathway is also dominant for this fuel composition. Even though this flame has a very low radiant fraction, the heat loss has a significant effect on NO formation because of the highly temperature dependent NO formation rates. Superequilibrium O-atom & OH radical levels showed high sensitivity to the thermal NO formation in high-temperature zones. An order of magnitude differences are observed in thermal NO by neglecting subgrid scale fluctuations on NO formation with some what less sensitivity to NO formation by the N2O pathway. For reliable and accurate NO numerical predictions, the following should be accounted for; NO formation pathways, radiation effects, nonequilibrium O-atom & OH-radicals and subgrid scale turbulence effects. Overall, the Zeldovich mechanism predicted thermal NO very closely and overpredictions resulted from the N2O-intermediate pathway.

Numerical Predictions on the Soil Thermal Effect Under Surface Fire Conditions

1997 ◽  
Vol 7 (1) ◽  
pp. 51 ◽  
Author(s):  
LA Oliveira ◽  
DX Viegas ◽  
AM Raimundo
Keyword(s):  
Temperature Distribution ◽  
Flame Front ◽  
Radiation Effects ◽  
Control Volume ◽  
Ground Surface ◽  
Soil Surface ◽  
Heat Transfer Process ◽  
Maximum Temperature ◽  
Transient Temperature ◽  
Numerical Predictions

A control volume numerical method is used to predict the temperature distribution inside a soil extent, the surface of which has been swept by a two-dimensional flame front with pre-defined velocity and temperature distributions. Natural and forced convection, as well as radiation effects are included in the specification of the soil surface thermal boundary condition. The flame residence time and maximum temperature are identified as two major parameters to characterize the flame front. As expected, the heat penetration depth is confined to the near vicinity of the soil surface. Moreover, horizontal heat conduction throughout the soil has not always a significant effect on its global, transient temperature distribution. The influence of wind velocity and of soil thermal diffusivity upon its temperature distribution are analysed. Radiation is the dominant contribution in the whole heat transfer process between flame and ground surface.

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