On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics

Булатов, В. В.; Danilov, Vladimir G.; Данилов, В. Г.; Dobrokhotov, S.Ju.

doi:10.1007/bf02110777

Cited by 4 publications

(7 citation statements)

References 2 publications

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“…Probabilistic models are generally based on historical compilations of hurricane tracks for the site or region of interest; for instance, one can perform Markov chain simulations based on derived statistics from such hurricane track data. In recent studies, the trajectory of a cyclone has been modeled by solving shallow-water equations in which the typhoon eye is considered as a point singularity (weak singularity of square root type) (Bulatov and Vladimirov, 1994). Deterministic models may be alternatively employed by describing storms as physical phenomena and solving relevant differential equations of a cyclone's eye motion.…”

Section: Framework For Hurricane Risk Assessmentmentioning

confidence: 99%

“…Other approaches using a self-adapting model (Rostkova and Ordanovich, 1985) and a non-stationary axially symmetric model (Dobryshman, 1994) have also been proposed. In recent studies, the trajectory of a cyclone has been modeled by solving shallow-water equations in which the typhoon eye is considered as a point singularity (weak singularity of square root type) (Bulatov and Vladimirov, 1994). The propagation of this singularity (a model of the cyclone’s eye) is then represented as an infinite chain of ordinary differential equations.…”

Section: Framework For Hurricane Risk Assessmentmentioning

confidence: 99%

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Hurricane risk assessment for offshore wind plants

Kim

Manuel

2016

Wind Engineering

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This study describes a framework for estimation of structural damage to offshore wind plants during hurricanes. Related risk assessment is fundamentally dependent on the estimation of hurricane-generated wind speed exceedance probabilities at selected hub heights of wind turbines in the plant and on estimation of associated wind turbine loads. As part of a framework for risk assessment introduced here, synthetic storm tracks are first simulated over the ocean using available historical tropical storm data; then, a hurricane intensity evolution model based on thermodynamic and atmospheric environmental variables is developed for each simulated track as it approaches the chosen wind plant site. Based on this intensity model, a turbulent wind field can be simulated at any location of interest along the hurricane track. The simulated turbulent wind field can then be used to estimate wind speed exceedance probability distributions and, when combined with partially correlated waves, it can also be used in analyzing the response of individual turbines in a wind plant. A framework for the overall risk assessment is presented; individual components that are part of such a framework are described briefly in illustrative applications. Finally, a brief discussion is presented that addresses issues related to the concept of "robustness" checks that are often considered in the context of safe performance-based design. This concept employed in the oil and gas industries provides for a secondary margin for "beyond design-level" external conditions out to more extreme conditions as might accompany hurricanes.

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Section: Framework For Hurricane Risk Assessmentmentioning

confidence: 99%

Section: Framework For Hurricane Risk Assessmentmentioning

confidence: 99%

Hurricane risk assessment for offshore wind plants

Kim

Manuel

2016

Wind Engineering

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“…Let us consider a recent typhoon of the West Pacific region, Man Yi (4 category, July [8][9][10][11][12][13][14][15]2007). The historic trajectory and observational data are given on Figs.5 and 6 [18].…”

Section: Man Yimentioning

confidence: 99%

“…Following [10,11], we change the coordinate system so that the origin of the new system is located at the center of the typhoon eye. Now U = u+V, where…”

Section: System With Respect To the Velocity Pressure And Entropy Wit...mentioning

confidence: 99%

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Typhoon eye trajectory based on a mathematical model: Comparing with observational data

Rozanova

2010

Nonlinear Analysis: Real World Applications

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We propose a model based on the primitive system of the Navier-Stokes equations in a bidimensional framework as the l -plane approximation, which allows us to explain the variety of tracks of tropical cyclones (typhoons). Our idea is to construct special analytical solutions with a linear velocity profile for the Navier-Stokes systems. The evidence of the structure of linear velocity near the center of vortex can be proven by the observational data. We study solutions with the linear-velocity property for both barotropic and baroclinic cases and show that they follow the same equations in describing the trajectories of the typhoon eye at the equilibrium state (that relates to the conservative phase of the typhoon dynamics). Moreover, at the equilibrium state, the trajectories can be viewed as a superposition of two circular motions: one has period 2π/l, the other one has period 2π/b 0 , where l is the Coriolis parameter and b 0 is the height-averaged vorticity at the center of cyclone.Also, we compare our theoretical trajectories based on initial conditions from the flow with tracks obtained from the observational database. It is worth to mention that under certain conditions our results are still compatible with observational data although we did not truly consider the influence of steering effect. Finally, we propose the parameter-adopting method so that one could correct the weather prediction in real time. Examples of our analysis and the use of parameter-adopting method for the historic trajectories are provided.

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