A Parameterization of DNV GL Storm Profile for Long-Term Analysis of Ocean Storms: Trapezoidal Storm Model

2019 ◽  
Author(s):  
Valentina Laface ◽  
Elzbieta M. Bitner-Gregersen ◽  
Felice Arena ◽  
Alessandra Romolo
Keyword(s):  
Wave Height ◽  
Return Period ◽  
Model Development ◽  
Closed Form Solution ◽  
Form Solution ◽  
Storm Intensity ◽  
Storm Duration ◽  
Storm Evolution ◽  
Fixed Constant

Abstract The paper introduces a parameterization of the DNV GL storm profile for developing an analytical model for calculations of the return period of a storm whose peak exceeds a given threshold. The DNV GL storm evolution is represented via an isosceles trapezoidal shape in which the minor base represents the storm peak duration, the major base the total storm duration and the height is half of the highest significant wave height in the actual storm. In this representation, the storm duration is not related to the storm intensity and it is fixed constant and equal to 42 hours, while the peak duration is assumed to be 6 hours. The parameterization proposed in the paper consists in expressing the peak duration as a fraction of the total storm duration allowing to investigate the effects of storm peak duration on long term estimates. The analytical solution for the return period is derived by following the classical approach of Equivalent Storm Models that is referring to the equivalent storm sequence, with the only difference that all the Trapezoidal Storm durations are identical whatever the storm intensity is. This assumption leads to significant simplification on the model development and potential employment as well. Further, a closed form solution is achieved for the return period which is also a generalization of the triangular shape. Finally, data analysis with NDBC buoys data is carried out for validating the model and elucidating analogies and differences with respect to classical Equivalent Storm approach. Results have shown that the Trapezoidal Model can be thought as a triangular one with a prudential factor on the storm peak duration which results in a reasonable overestimation of maximum expected wave height and return values.

On Sampling Between Data of Significant Wave Height for Long-Term Analysis With Equivalent Triangular Storm Model

2013 ◽  
Author(s):  
Felice Arena ◽  
Valentina Laface
Keyword(s):  
Wave Height ◽  
Return Period ◽  
Significant Wave Height ◽  
Significant Wave ◽  
Storm Duration ◽  
The Mean ◽  
Using Data ◽  
Two Parameters ◽  
Mean Time

This work proposes an analysis of storms in Pacific and Atlantic Ocean, which is carried out by applying the Boccotti’s Equivalent Triangular Storm (ETS) model. The ETS model represents any actual storm by means of two parameters. The former gives the storm intensity, which is equal to the maximum significant wave height during the actual storm; the latter represents the storm duration and it is such that the maximum expected wave height is the same in the actual storm and in the equivalent triangular storm. Data from buoys of the NOAA-NDBC (National Data Buoy Center, USA) are used in the applications, by considering different sampling Δt between two consecutive records, which varies between 1 and 6 hours. The sensitivity of the ETS model with the variation of Δt is investigated for the long-term modeling of severe storms. The results show that the structure of storms is strongly modified as Δt increases: both the intensity and the duration may change significantly. The effects of this results for long term statistics are investigated by means of the return period R(Hs > h) of a storm in which the maximum significant wave height exceeds the threshold h, which is evaluated by using data with different sampling Δt between two consecutive records. Finally for different values of the return period R, the return value of significant wave height and the mean persistence Dm(h), giving the mean time during which the significant wave height is greater than fixed threshold (in the storms where the threshold is exceeded), are calculated.

The Equivalent Power Storm Model for Long-Term Predictions of Extreme Wave Events

2009 ◽  
Author(s):  
Francesco Fedele ◽  
Felice Arena
Keyword(s):  
Wave Height ◽  
Return Period ◽  
Shape Parameter ◽  
Extreme Wave ◽  
Maximum Wave Height ◽  
Wave Measurements ◽  
Sea Storm ◽  
Storm Model ◽  
Good Agreement

We present the Equivalent Power Storm (EPS) model as a generalization of the Equivalent Triangular Storm (ETS) model of Boccotti for the long-term statistics of extreme wave events. In the EPS model, each actual storm is modeled in time t by a power law ∼|t−t0|λ, where λ is a shape parameter and t0 is the time when the storm peak occurs. We then derive the general expression of the return period R(Hs > h) of a sea storm in which the maximum significant wave height Hs exceeds a fixed threshold h as function of λ. Further, given the largest wave height Hmax, we identify the most probable storm in which the largest wave occurs and derive an explicit expression for the return period R(Hmax >H) of a storm in which the maximum wave height exceeds a given threshold H. Finally, we analyze wave measurements retrieved from two of the NOAA-NODC buoys in the Atlantic and Pacific oceans and find that the EPS predictions are in good agreement with those from the ETS model.

scholarly journals Pricing and Allotment in a Sea-Cargo Supply Chain with Reference Effect: A Dynamic Game Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Lei Xu ◽  
Govindan Kannan ◽  
Xiaoli Yang ◽  
Jian Li ◽  
Xiukun Zhao
Keyword(s):  
Supply Chain ◽  
Wholesale Price ◽  
Closed Form Solution ◽  
Dynamic Game ◽  
Spot Market ◽  
Form Solution ◽  
Purchasing Decisions ◽  
Purchasing Decision ◽  
Pricing Decisions

The contract between the carrier and forwarder is a long-term issue, and the repeated contract business makes the forwarder develop a reference point based on the contract prices, and this reference effect, to a large extent, affects the forwarder’s contract purchasing decisions. Based on that, this paper introduces the reference effect in the sea-cargo supply chain and studies a multiple-period contract problem between the carrier and the forwarder. It is found that when the capacity price in the spot market is less than the forwarder’s willingness-to-pay, the forwarder’s contract purchasing decision is not affected by the reference effect, only by the capacity price in the spot market, and the multiple-period contract problem can be simplified into a single-period game. In addition, the carrier’s optimal contract wholesale price approaches the capacity price in the spot market. Although, the forwarder’s contract purchasing decision depends upon the reference effect, it is difficult to derive the closed-form solution. Moreover, because of the risk in the spot market, the carrier tends to sell his/her capacity in the contract market. Finally, we employ the numerical simulation to study the carrier’s contract pricing decisions and the forwarder’s capacity purchasing decisions in two cases.

On Long Term Statistics of Ocean Storms Starting From Partitioned Sea States

2017 ◽  
Author(s):  
Valentina Laface ◽  
Felice Arena ◽  
Christophe Maisondieu ◽  
Alessandra Romolo
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Wind Waves ◽  
Storm Events ◽  
Significant Wave ◽  
Open Sea ◽  
Storm Duration ◽  
Two Parameters ◽  
Actual Seas

The paper proposes an analysis of ocean storms carried out starting from significant wave height time series of HOMERE sea-states hindcast database based on WAVEWATCH III model. Considering that wave spectra often exhibit multiple peaks due to the coexistence of wind waves and swells, here sea states are described by partitioned sea states that can be interpreted physically as representing independent wave systems. The analysis presented here in the paper deals with the contribution of swells to the storm peaks and on how they influence the long term statistics. The sensitivity of return values of significant wave height to swell contribution is investigated via an application of the Equivalent Triangular Storm Model (ETS). The ETS model provides analytical solution for the calculation of the return period R(Hs>h) of a sea storm whose maximum significant wave height exceeds a given threshold h. The approach of ETS consists in substituting each actual storm with an ETS described by two parameters: the storm intensity, that is the triangle height and it is equal to the maximum significant wave height during the actual storm; the storm duration, that is achieved imposing the equality between the maximum expected wave height of actual and equivalent storms. It has been experimentally proved that the actual storm and associated ETS are statistically equivalent because they have the same maximum significant wave height and the same probability P(Hmax>H) that the maximum wave height exceeds a given threshold H. The sequence of ETSs obtained in this way represents the equivalent sea, while the sequence of actual storms is the actual sea. The equivalent and actual seas present the same wave risk because they are characterized by the same number of storm events, each of them with the same intensity and the same P(Hmax>H). For the proposed analysis a set of four points from open sea to the coast is considered in area of the Gulf of Biscay (France). The results show that the contribution of swells is more significant for the storms of small and medium intensity and decreases for increasing storm intensities. Further return values variability neglecting swell is less than 7% at any point for return periods up to 100 years.

Comparison of Design Wave Approach and Short Term Approach With Increased Wave Height in the Evaluation of Whipping Induced Bending Moment

2012 ◽  
Author(s):  
Quentin Derbanne ◽  
Fabien Bigot ◽  
Guillaume de Hauteclocque
Keyword(s):  
Wave Height ◽  
Return Period ◽  
Significant Wave Height ◽  
Bending Moment ◽  
Short Term ◽  
Sea State ◽  
Significant Wave ◽  
Non Linear ◽  
Term Analysis

The evaluation of extreme bending moment corresponding to a 25 years return period requires very long simulations on a large number of sea states. This long term analysis is easy to do with a linear model of the ship response, but is impractical when using a time consuming model including non linear and slamming loads. In that case some simplified methods need to be applied. These methods are often based on Equivalent Design Waves (EDW) which are calibrated on the extreme linear value. The general practice is to define the EDW as a regular wave. A very simple method is to compute the non linear bending moment applying the pressure correction on the hull without recomputing the ship motions. A better method is to recompute in time domain the non linear ship response on this Design Wave. It is even possible to define a more realistic Design Wave, taking into account the frequency and directional content of the sea states used in the long term analysis: those waves are called Response Conditioned Wave and Directional Response Conditioned Waves. The different methods are applied to an Ultra Large Container Ship (ULCS). Hydro-structure calculations are carried out on a severe design sea state, taking into account Froude-Krylov pressure correction, slamming forces and whipping response. Results of a very long computation are compared to the results of the Design Wave approaches. Another method is proposed to compute very rare events. It is based on an artificial increase of the significant wave height of the sea state, and the assumption of the independence of the non linear effects to the significant wave height. Using this method it is possible, with a simulation of only a few hours, to predict a very rare short term event, corresponding to a very long return period. The results are compared to the Design Wave results and appear to be much more precise.

Long-Term Reliability Analysis of a Spar Buoy-Supported Floating Offshore Wind Turbine

2011 ◽  
Author(s):  
A. Sultania ◽  
L. Manuel
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Reliability Analysis ◽  
Wave Height ◽  
Wind Turbines ◽  
Return Period ◽  
Random Variables ◽  
Offshore Wind ◽  
Floating Platform

Most offshore wind turbines constructed to date have support structures for the turbine towers that extend to the seabed. Such bottom-supported turbines are confined to shallow waters closer to the shore. Sites farther offshore provide a better wind resource (i.e., stronger wind and less turbulence) while also reducing concerns related to visual impact and noise. However, in deeper waters, bottom-supported turbines are less economical. Wind turbines mounted atop floating platforms are, thus, being considered for deepwater sites. Several floating platform concepts are being considered; they differ mainly in how they provide stability to counter the large mass of the rotor-nacelle assembly located high above the water. One of these alternative concepts is a spar buoy floating platform with a deep draft structure and a low center of gravity, below the center of buoyancy. The reliability analysis of a spar-supported 5MW wind turbine based on stochastic simulation is the subject of this study. Environmental data from a selected deepwater reference site are employed in the numerical studies. Using time-domain simulations, the dynamic behavior of the coupled platform-turbine system is studied; statistics of tower and rotor loads as well as platform motions are estimated and critical combinations of wind speed and wave height identified. Long-term loads associated with a 50-year return period are estimated using statistical extrapolation based on loads derived from the simulations. Inverse reliability procedures that seek appropriate load fractiles for the underlying random variables consistent with the target return period are employed; these include use of: (i) the 2D Inverse First-Order Reliability Method (FORM) where an extreme load is selected at its median level (conditional on a derived critical wind speed and wave height combination); and (ii) the 3D Inverse FORM where variability in the environmental and load random variables is fully represented to derive the 50-year load.

A New Solution for the Return Period of a Sea Storm in Which the Largest Wave Height Exceeds a Fixed Threshold

2005 ◽  
Author(s):  
Felice Arena ◽  
Diego Pavone
Keyword(s):  
Analytical Solution ◽  
Wave Height ◽  
Return Period ◽  
Significant Wave Height ◽  
Extreme Waves ◽  
Significant Wave ◽  
Storm Intensity ◽  
Large Probability ◽  
Fixed Threshold ◽  
Sea Storm

A new analytical solution for the return period of a sea storm in which the largest wave height exceeds a fixed threshold is obtained, by applying the Boccotti’s Equivalent Triangular Storm (ETS) model. An expression is then given for the probability that a wave, which is both higher than a fixed threshold and the highest of its own storm, will occur during a sea storm with a given intensity (the storm intensity being the maximum significant wave height during the storm). In the applications it is shown that the new solution has a simpler form than the Boccotti’s original one (two integrals to solve numerically, compared with the four integrals of the Boccotti’s solution), and that they give identical results. Finally it is achieved that the extreme waves of given height H, with large probability will occur in a sea storm with maximum significant wave height Hs max close to 0.5H.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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