A Unified Perspective on the Dynamics of Axisymmetric Hurricanes and Monsoons

2006 ◽  
Vol 63 (10) ◽  
pp. 2529-2547 ◽  
Author(s):  
Volkmar Wirth ◽  
Timothy J. Dunkerton
Keyword(s):  
Numerical Solutions ◽  
Surface Wind ◽  
Thermal Relaxation ◽  
General System ◽  
Surface Friction ◽  
Secondary Circulation ◽  
Scaling Analysis ◽  
Vortex Center ◽  
Surface Winds ◽  
Wide Range

Abstract This paper provides a unified perspective on the dynamics of hurricane- and monsoonlike vortices by identifying them as specific limiting cases of a more general flow system. This more general system is defined as stationary axisymmetric balanced flow of a stably stratified non-Boussinesq atmosphere on the f plane. The model is based on the primitive equations assuming gradient wind balance in the radial momentum equation. The flow is forced by heating in the vortex center, which is implemented as relaxation toward a specified equilibrium temperature Te. The flow is dissipated through surface friction, and it is assumed to be almost inviscid in the interior. The heating is assumed supercritical, which means that Te does not allow a regular thermal equilibrium solution with zero surface wind, and which gives rise to a cross-vortex secondary circulation. Numerical solutions are obtained using time stepping to a steady state, where at each step the Eliassen secondary circulation is diagnosed as part of the solution strategy. Reality and regularity of the solution is discussed, putting this work in relation to previous work. Scaling analysis suggests that for a given geometry, essential vortex properties are controlled by the ratio ℱ = αT/cD, where αT is the rate of thermal relaxation and cD quantifies the strength of surface friction for a given surface wind. For large ℱ, the temperature is close to Te and the vortex shows properties that can be associated with a hurricane including strong cyclonic surface winds. On the other hand, for small ℱ, the vortex shows properties that can be associated with a monsoon; that is, the surface winds are small and the secondary circulation keeps the temperature significantly away from Te. The scaling analysis is verified by numerical solutions spanning a wide range of the parameter space. It is shown how the two limiting cases correspond with the respective approximate semianalytical theories presented previously. The results imply an important role of αT for hurricane formation.

Submesoscale surface fronts and filaments: secondary circulation, buoyancy flux, and frontogenesis

2017 ◽  
Vol 823 ◽  
pp. 391-432 ◽  
Author(s):  
James C. McWilliams
Keyword(s):  
Surface Wind ◽  
Circulation Pattern ◽  
Solution Procedure ◽  
Secondary Circulation ◽  
Buoyancy Flux ◽  
Momentum Balance ◽  
Rossby Number ◽  
Surface Wind Stress ◽  
Wide Range ◽  
Ageostrophic Circulation

Problems are posed and solved for upper-ocean submesoscale density fronts and filaments in the presence of surface wind stress and the associated boundary-layer turbulent mixing, their associated geostrophic and secondary circulations and their instantaneous buoyancy fluxes and frontogenetic evolutionary tendencies in both velocity and buoyancy gradients. The analysis is diagnostic rather than prognostic, and it is based on a momentum-balanced approximation that assumes the ageostrophic acceleration is negligible, although the Rossby number is finite and ageostrophic advection is included, justified by the quasi-steady, coherent-structure flow configurations of fronts and filaments. Across a wide range of wind and buoyancy-gradient parameters, the ageostrophic secondary circulation for a front is a single overturning cell with downwelling on the dense side, hence with a positive (restratifying) vertical buoyancy flux. For a dense filament the circulation is a double cell with central downwelling and again positive vertical buoyancy flux. The primary explanation for these secondary-circulation cells is a ‘turbulent thermal wind’ linear momentum balance. These circulation patterns, and their associated frontogenetic tendencies in both the velocity and buoyancy gradients, are qualitatively similar to those due to the ‘classical’ mechanism of strain-induced frontogenesis. For linear solutions, the secondary circulation and frontogenesis are essentially independent of wind direction, but in nonlinear solutions ageostrophic advection provides a strong intensification of the peak vertical velocity, while generally preserving the ageostrophic circulation pattern, when the Rossby number is order one and the wind orientation relative to the frontal axis is favourable. At large Rossby number the solution procedure fails to converge, with an implication of a failure of existence of wholly balanced circulations.

scholarly journals An Assessment of NASA’s GMAO MERRA-2 Reanalysis Surface Winds

2019 ◽  
Vol 32 (23) ◽  
pp. 8261-8281 ◽  
Author(s):  
D. Carvalho
Keyword(s):  
Surface Wind ◽  
The Other ◽  
Surface Winds ◽  
Wind Fields ◽  
Near Surface ◽  
Wind Speeds ◽  
Wide Range ◽  
Ocean Surface Winds ◽  
The Tropics ◽  
Global Surface

Abstract The quality of MERRA-2 surface wind fields was assessed by comparing them with 10 years of measurements from a wide range of surface wind observing platforms. This assessment includes a comparison of MERRA-2 global surface wind fields with the ones from its predecessor, MERRA, to assess if GMAO’s latest reanalyses improved the representation of the global surface winds. At the same time, surface wind fields from other modern reanalyses—NCEP-CFSR, ERA-Interim, and JRA-55—were also included in the comparisons to evaluate MERRA-2 global surface wind fields in the context of its contemporary reanalyses. Results show that MERRA-2, CFSR, ERA-Interim, and JRA-55 show similar error metrics while MERRA consistently shows the highest errors. Thus, when compared with wind observations, the accuracy of MERRA-2 surface wind fields represents a clear improvement over its predecessor MERRA and is in line with the other contemporary reanalyses in terms of the representation of global near-surface wind fields. All reanalyses showed a tendency to underestimate ocean surface winds (particularly in the tropics) and, oppositely, to overestimate inland surface winds (except JRA-55, which showed a global tendency to underestimate the wind speeds); to represent the wind direction rotated clockwise in the Northern Hemisphere (positive bias) and anticlockwise in the Southern Hemisphere (negative bias), with the exception of JRA-55; and to show higher errors near the poles and in the ITCZ, particularly in the equatorial western coasts of Central America and Africa. However, MERRA-2 showed substantially lower wind errors in the poles when compared with the other reanalyses.

scholarly journals The Probability Distribution of Sea Surface Wind Speeds: Effects of Variable Surface Stratification and Boundary Layer Thickness

2010 ◽  
Vol 23 (19) ◽  
pp. 5151-5162 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Surface Wind ◽  
Sea Surface ◽  
Surface Winds ◽  
Free Atmosphere ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
Variable Surface

Abstract Air–sea exchanges of momentum, energy, and material substances of fundamental importance to the variability of the climate system are mediated by the character of the turbulence in the atmospheric and oceanic boundary layers. Sea surface winds influence, and are influenced by, these fluxes. The probability density function (pdf) of sea surface wind speeds p(w) is a mathematical object describing the variability of surface winds that arises from the physics of the turbulent atmospheric planetary boundary layer. Previous mechanistic models of the pdf of sea surface wind speeds have considered the momentum budget of an atmospheric layer of fixed thickness and neutral stratification. The present study extends this analysis, using an idealized model to consider the influence of boundary layer thickness variations and nonneutral surface stratification on p(w). It is found that surface stratification has little direct influence on p(w), while variations in boundary layer thickness bring the predictions of the model into closer agreement with the observations. Boundary layer thickness variability influences the shape of p(w) in two ways: through episodic downward mixing of momentum into the boundary layer from the free atmosphere and through modulation of the importance (relative to other tendencies) of turbulent momentum fluxes at the surface and the boundary layer top. It is shown that the second of these influences dominates over the first.

scholarly journals Derivation of Global Parametric Performance of Mixed Flow Hydraulic Turbine Using CFD

1970 ◽  
Vol 7 ◽  
pp. 60-64 ◽  
Author(s):  
Ruchi Khare ◽  
Vishnu Prasad Prasad ◽  
Sushil Kumar
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Numerical Solutions ◽  
Guide Vane ◽  
Hydraulic Turbine ◽  
Francis Turbine ◽  
Mixed Flow ◽  
Flow Equations ◽  
Laboratory Setup ◽  
Wide Range

The testing of physical turbine models is costly, time consuming and subject to limitations of laboratory setup to meet International Electro technical Commission (IEC) standards. Computational fluid dynamics (CFD) has emerged as a powerful tool for funding numerical solutions of wide range of flow equations whose analytical solutions are not feasible. CFD also minimizes the requirement of model testing. The present work deals with simulation of 3D flow in mixed flow (Francis) turbine passage; i.e., stay vane, guide vane, runner and draft tube using ANSYS CFX 10 software for study of flow pattern within turbine space and computation of various losses and efficiency at different operating regimes. The computed values and variation of performance parameters are found to bear close comparison with experimental results.Key words: Hydraulic turbine; Performance; Computational fluid dynamics; Efficiency; LossesDOI: 10.3126/hn.v7i0.4239Hydro Nepal Journal of Water, Energy and EnvironmentVol. 7, July, 2010Page: 60-64Uploaded date: 31 January, 2011

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

An Approximate Method for Transient Radial Flow

1962 ◽  
Vol 2 (03) ◽  
pp. 225-256 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Infinite Series ◽  
Analytical Solutions ◽  
Radial Flow ◽  
Numerical Solutions ◽  
Basic Theory ◽  
Variable Pressure ◽  
Flow Problems ◽  
Disturbed Zone ◽  
Approximate Analytical Solutions ◽  
Wide Range

Abstract The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including; gravity drainage of depletion-type reservoirs; multiple well systems; well interference. Introduction A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages - the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov, whopostulated a disturbed zone in the reservoir, the radius of which increases with time, andreplaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following:That the flow is irrotational.That the formation is of constant thickness.Darcy's Law is valid.The formation is saturated with a single homogeneous fluid. SPEJ P. 225^

scholarly journals A Two-Season Impact Study of the WindSat Surface Wind Retrievals in the NCEP Global Data Assimilation System

2010 ◽  
Vol 25 (3) ◽  
pp. 931-949 ◽  
Author(s):  
Li Bi ◽  
James A. Jung ◽  
Michael C. Morgan ◽  
John F. Le Marshall
Keyword(s):  
Data Assimilation ◽  
Surface Wind ◽  
Temperature Fields ◽  
Experimental Simulation ◽  
Naval Research ◽  
Surface Winds ◽  
Control Simulation ◽  
Wind Retrievals ◽  
Global Data ◽  
Assimilation System

Abstract A two-season observing system experiment (OSE) was used to quantify the impacts of assimilating the WindSat surface winds product developed by the Naval Research Laboratory (NRL). The impacts of assimilating these surface winds were assessed by comparing the forecast results through 168 h for the months of October 2006 and March 2007. The National Centers for Environmental Prediction’s (NCEP) Global Data Assimilation/Global Forecast System (GDAS/GFS) was used, at a resolution of T382-64 layers, as the assimilation system and forecast model for these experiments. A control simulation utilizing all the data types assimilated in the operational GDAS was compared to an experimental simulation that added the WindSat surface winds. Quality control procedures required to assimilate the surface winds are discussed. Anomaly correlations (ACs) of geopotential heights at 1000 and 500 hPa were evaluated for the control and experiment during both seasons. The geographical distribution of the forecast impacts (FIs) on the wind field and temperature fields at 10-m height and 500 hPa is also discussed. The results of this study show that assimilating the surface wind retrievals from the WindSat satellite improve the NCEP GFS wind and temperature forecasts. A positive FI, which suggests that the error growth of the experiment is slower than the control, has been realized in the NCEP GDAS/GFS wind and temperature forecasts through 24 h. The WindSat experiment AC scores are similar to the control simulation AC scores until the day 6 forecasts, when the improvements in the WindSat experiment become greater for both seasons and in most of the cases.

NUMERICAL SOLUTIONS OF SMOLUCHOWSKI'S EQUATIONS FOR THE COAGULATION OF UNCHARGED AEROSOLS

1965 ◽  
Vol 43 (8) ◽  
pp. 2312-2318 ◽  
Author(s):  
J. M. Beeckmans
Keyword(s):  
Particle Size ◽  
Numerical Solutions ◽  
Coagulation Factor ◽  
Dispersion Parameter ◽  
Particle Size Range ◽  
Mean Particle Size ◽  
A Value ◽  
Wide Range ◽  
Differential Sedimentation ◽  
Smoluchowski’S Equation

Smoluchowski's equations for the coagulation of uncharged aerosol particles were programmed for solution by electronic computer. Terms representing differential sedimentation, turbulence, and mean aggregate density in solid aerosols were included. The effect of heterogeneity in the particle-size distribution of the aerosols on their rate of coagulation was illustrated by means of a slip-corrected coagulation factor Fc, which assumes a value of unity in all non-turbulent homogeneous aerosols. Curves of Fc vs. σg, the geometrical standard deviation, were calculated for aerosols of various mean particle-size. The effects due to turbulence, and to differential sedimentation, were illustrated in a similar manner. It was also found that the process of coagulation gives rise to a degree of dispersion which is independent of the original dispersion parameter, and depends only slightly on the mean particle-size of the aerosol over a wide range of particle-sizes. In the particle-size range in which differential sedimentation is inappreciable, the relatively constant value of the dispersion parameter implies that heterogeneous aerosols must obey the simplified integrated form of Smoluchowski's equation, which is applicable to homogeneous aerosols. The coagulation constant exceeds that predicted by the simple theory by about 10% for liquid aerosols of 0.1 μ or less.

Application of minimal mathematical models for the dynamics of the signaling pathway of the p53 - miRNA to the analysis of laboratory data

2021 ◽  
pp. 4-49
Author(s):  
Софья Дмитриевна Сенотрусова ◽  
Ольга Фалалеевна Воропаева ◽  
Юрий Иванович Шокин
Keyword(s):  
Mathematical Models ◽  
Signaling Pathway ◽  
Numerical Solutions ◽  
Laboratory Data ◽  
Minimal Models ◽  
Basic Model ◽  
P53 Signaling ◽  
Wide Range ◽  
P53 Signaling Pathway

Работа посвящена практическому использованию минимальных математических моделей динамики сигнального пути p53 для описания достаточно широкого круга лабораторных экспериментов, в которых взаимодействие p53 и белковингибиторов p53 опосредуется микроРНК, образующими с p53 петлю положительной обратной связи. Представлены базовая модель, разработанные на ее основе новые минимальные модели, алгоритм численного решения прямых и обратных коэффициентных задач и результаты сопоставления полученных численных решений с экспериментальными данными о динамике уровней белков p53, p21, Bax, белков-ингибиторов Mdm2, Wip1, Sirt1 и различных микроРНК (miR-16, miR-34a, miR-192, miR-194, miR-215) в условиях стрессовых воздействий. С привлечением полученных математических моделей исследованы базовые механизмы функционирования сигнального пути p53 в условиях, приближенных к условиям конкретных лабораторных экспериментов in vitro и in vivo. Продемонстрированы синергический эффект гиперактивации сигнального пути p53, в котором задействованы микроРНК, и механизмы бимодального переключения. Показана ключевая роль p53-зависимых микроРНК в реализации некоторых гипотетических терапевтических стратегий, связанных с управлением механизмом активации апоптоза клеток. В рамках принятой базовой модели даны оценки вероятности рассогласования в диагностике дегенеративных заболеваний, основанной на анализе уровня p53зависимых микроРНК и p53, при слабой и умеренной дерегуляции микроРНК. This study addresses the practical use of minimal mathematical models of the dynamics of a hypothetical system of the p53 signaling pathway to describe a fairly wide range of laboratory experiments. In such system, the interaction of p53 and p53 inhibitor proteins is mediated by microRNAs that form a positive feedback loop with p53. A basic model, new minimal models developed on its basis, an algorithm for the numerical solution of direct and inverse coefficient problems, and the results of comparing the obtained numerical solutions with experimental data on the dynamics of the levels of p53, p21, Bax proteins, inhibitor proteins Mdm2, Wip1, Sirt1, and various microRNAs (miR-16, miR-34a, miR-192, miR-194, miR-215) under stress conditions are presented. In numerical experiments, the main mechanisms of the p53 signaling pathway were investigated. A synergistic effect of hyperactivation of the p53 signaling pathway and bimodal switching mechanisms has been demonstrated. We show the key role of p53-dependent microRNAs in the implementation of some hypothetical therapeutic strategies associated with the control mechanism for activation of cells apoptosis. Within the framework of the accepted basic model, we estimated the probability of mismatch in the diagnosis of the patient’s status. The status is based on the analysis of the level of p53-dependent microRNAs and p53, with weak and moderate deregulation of microRNAs.

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