The 14 th Asian Congress of Fluid Mechanics - 14ACFM October 15-19, 2013; Hanoi and Halong, Vietnam Simulation for Object Drift Forecast in the East Vietnam Sea by the Leeway Numerical Method Nguyen Quoc Trinh *, Nguyen Minh Huan *, Phung Dang Hieu, Du Van Toan * e-mail address of presenting authors: maitrinhvinh@gmail.com; nmhuan61@gmail.com. Abstract: Drift of objects in the ocean is potentially dangerous for human activities and marine ecosystems, The motion of a drifting object on the sea surface is the net result of a number of forces acting upon it (water currents due to tide wave, atmospheric wind, wave motion, wave induced currents, gravitational force and buoyancy force). It is possible to estimate the drift trajectory given information on the local wind, the surface current, and the shape and the buoyancy of the object. In this paper, we present the leeway numerical method and some forecast results the drift of objects in the Vietnam coastal and the Eats Vietnam Sea. The approach consists in estimating the probability of events linked to the drift using Monte Carlo simulations and in computing the object trajectories corresponding to a number of monthly marine meteorological and hydrological data series representative of the climatology on the search and rescue areas of Vietnam and the Eats Vietnam Sea. Key words: numerical method, drift motion, leeway trajectory, Monte Carlo simulation. 1. Introduction Exists a very large number of objects floating on the sea, the most important is the nutrients and phytoplankton are the foundation of life in the ocean. But in this study we will focus on a special group of floating objects: it is the things drift arising from human activities. Marine weather conditions increasingly harsh, appear storms, tropical cyclones, tornados, extreme on the scale level, intensity and unusual moving direction... Meanwhile, economic activities, environmental monitoring, maritime security and defense rapidly growing cause high density of marine traffic with means outdated status, force increasing of maritime incidents. Most of the accidents occur in bad weather conditions due to reasons such as loss of the ship driving, collision, puncture... In the case of this, rescue vessels to find ways to approache, anti-sinking and rescue of victims from the danger area so the prediction floating motion of drift things in the sea means to locate or collect narrow search area is a vital determinant of success and the cost of search and rescue work. In the case of floating objects, we focus on the object of great value as human beings, or fishing boats, the motion of these objects are all dependent on the physical conditions in the sea. In this study, we will present the scientific basis of the drift trajectory forecast model, the necessary background information and the application results predicted drift motion of objects on the waters of Vietnam and the East Vietnam Sea, to serve the search operation and recovery of missing objects (SAR) or tracking an object until the remedial action be taken. 2. The leeway numerical method Drift motion of an object floating on the sea surface is the net result of a number of forces acting on the surface (the flow of the water, the wind in the air, wave motion of the waves and currents), and the center of massof them (gravity, floating power). Being able to calculate the orbit drift motion of the object with the given information of the local wind, sea surface flow, shape and buoyancy of an object. The evolution of the position X ( t) = X ( t; x, v) and the velocity V ( t) = V ( t; x, v) of the considered object, having x and v as initial position and velocity, is given by: 1144 Page
dx = V, dv dt = d mtx (, ) +Λ w( t,x) V dt dt m = ( t, X ) + m ( t, X ) V +Λ w t,x V t where m m( t, x) w w ( tx, ) ( ) ( ) ( ( ) ) (1) is the ocean velocity field and the wind velocity field; m stands for the Jacobian matrix of m, constant Λ quantifies wind force. Life rafts are observed by Hodgins and Hodgins (1998) to reach terminal velocity in approximately 20 s under strong wind conditions (20 m/s). This implies that small objects (typically less than 30 m) accelerate very rapidly. This is confirmed by Fitzgerald et al. (1994) who found the highest cross-correlation between leeway speed and wind speed at zero lag for 10 min vector averaged samples. Infinite acceleration and constant velocity for the duration of a model timestep are thus acceptable simplifications. The length of the model timestep is then dictated by the temporal and spatial scale of the forces acting on the object (wind, waves and currents). These vary over much longer timescales (surface currents, including tidal motion, and the synoptic weather situation change appreciably in hours, not minutes). Position of the floating object is determined by integrating the total drift velocity of the object ( V drift ) identified by wind and wave effects which are calculated relative to the current: Vdrift Vcurr Vrel Vcurr = + (2) which is the velocity of the flow relative to the Earth and Vrel is the drift velocity of the object relative to the ambient water. Model based on the equation (2) can be separated into two groups based on the power to determine the drift velocity of the object relative to the water V rel around. Hodgins and Hodgins (1998) the impact of the waves will be smaller when the length scale of the object is smaller than the wavelength and significantly increased the length equivalent. Depending on the size, drift objects can be divided into two groups: (1) The first group of small-sized objects may ignore the effects of the waves, impact of wind is important and it depends on the structure of the floating objects, objects of this type including: person in water, the small ship... (2) The second group is the large objects (the length scale of the object is equal to the wavelength. 2.1 Drift caused by wind movement of objects We define the leeway (windage) of an object to be the drift associated with the wind force on the overwater structure of the object as measured relative to the 10 min averaged wind measured at 10 m height (or reduced to this height). This coincides with the meteorological convention for measuring surface wind and is consistent with earlier work in this field (Hodgins and Mak, 1995). It is observed that an object moving under the influence of the wind will diverge to some extent from the downwind direction due to balance between the hydrodynamic lift and drag of the subsurface area and the aerodynamic lift and drag of the wind. In the maritime, we can see that due to the asymmetric nature of most of the floating objects, there will exist a net force from the side make objects floating under a certain angle with respect to the wind direction. Therefore, we can separate the drift velocity of an object into two components: the wind component and the component perpendicular to the wind, these components are shown in the figure 1. Figure. 1. The leeway L of a drifting object consists of a downwind component (DWL), Ld, and a crosswind component (CWL), Lc. The angle between the downwind direction and the leeway drift direction is termed the leeway divergence angle, Lα [adapted from Allen and Plourde, 1999]. 1145 Page
The experimental data shown in Figure. 2 suggest an almost linear relationship between wind speed W10 and the downwind component of the leeway. This linear relationship is also observed by other workers (see Hodgins and Hodgins, 1998). The downwind and crosswind leeway measurements described in Figures. 2 are corrected for windinduced drift by measuring the slippage. Figure. 2. Measured downwind component of leeway, US Coast Guard has compiled data for 63 classes of S&R objects through extensive field campaigns [from Allen and Plourde, 1999]. Allen, A A (2005) found that it is better to decompose the leeway into downwind (DWL) and crosswind components of leeway (CWL) because the downwind component tends to follow an almost linear relationship with the wind speed and this allows an analysis of the crosswind component relationship with the wind separately from the downwind component. The use of downwind and crosswind components of leeway is also better suited for implementation into Monte Carlo SAR planning tools. Some drift objects (usually nearly radial symmetrical) have very little crosswind drift and it may not be possible to discern a clear relationship between the wind speed and the crosswind drift while other objects (e.g. sailboats) have significant right (positive) and left (negative) crosswind components of leeway leading to rapid expansion of two separate search areas (one for right-drifting and another for the left-drifting scenario). Thus, at low wind speeds where the wind direction starts to fluctuate, the variance of the leeway angle increases with decreasing wind speed, making it a non-stationary statistic which is difficult to work with. An almost linear relationship between the 10 m wind speed W 10 (ms 1) and the leeway of the object is invariably found in field studies by Allen, A A (2005), albeit with non-uniform (heteroscedastic) spread increasing with wind speed. This allows us to perform a linear regression between the wind speed and downwind and crosswind leeway components. Using this approach, leeway measurements can be condensed down to nine coefficients (see Breivik Ø, Allen AA. (2008)) For calculating the motion passed in the forecasting business, the DWL and CWL component is determined directly from the linear regression formula volume as a function of wind speed in determining the shape of the object. The standard deviation is used in the determination of the uncertainty in determining the direction and speed of drift due to wind. Initial orientation of the object drift usually is not clear so the forecast is made for both possibilities. 2.2 Drift motion of the ship Drift motion of the train approached by the method of analysis, based on the hydrodynamic structure. The drift motion of the ship model is now based on the results at Det Norske Veritas (DNV) is Sorgard, and Vada published 1998 which defines the force of wind and wave action on the vessel rather than the regression formula, the force is used to determine the relative velocity (V rel ). The progress of this method is that the object can be represented by a number of basic parameters. The research results of Sorgard and Vada (1998) shows that the relative drift velocity of the ship will increase rapidly (in about 2-10 minutes) to a stable solution. Therefore, it s not necessary to integrate the acceleration over time as the relative drift velocity is calculated in the simulation for a few hours, the stability test can be used as a good approximation. Balanced force acting on the object can be written as: Fwind + Fwave + fform + fwave = 0 (3) which F is the drag of the wind on board, F wind wave effects of wave impact on chronic ship; f is form friction or drag blocks of water impact on the ship's side by the shift relative; f is wave wave resistance is a type of reaction occurs when the ship moves to create a wave of themselves. 1146 Page
The Stokes drift is a downwave drift induced by the orbital motion that water particles undergo under the influence of a wave field. These particle orbits are not closed and a Lagrangian drift is set up. This drift is confined to a narrow layer next to the sea surface (Kundu, 1990, pp. 223 225). It is well known that the Stokes drift can be a dominant factor in the advection of suspended material and objects on the sea surface. Many studies have been done to determine the floating vessel and wave drag. The simulation of each hull transport and idealized objects Sorgard and Vada (1998) shows that the hull can represent approximately the same as the simple rectangular box of the same size, such a ship can be parameterized by quantities such as length, draft and high chronic dry. The wave forces acting on the hull is defined as the function of the wave spectrum. Sorgard and Vada has set the table conversion function for ship drift motion due to waves and wave drag for the entire spectrum space. The forces acting on a ship can be determined by interpolation from the values in the database. 2.3 Approaches random forecast position drifting ship While performing calculations predict the location ship floating on the sea surface, we faced the challenge is the existence of uncertainty due to the modeling of objects and vessels in experimental parameters (or the empirical formula) combined with imperfect approximation of the laws of hydrodynamics, but also due to the lack of accurate information about the objects and their location (possibly in sometime). Even if we have all the information above, there is still a lot of uncertainty in the data on wind, waves and currents are used to control the ship drift forecast models. Therefore, the probability method is the most appropriate approach. By assigning probabilities to the corresponding parameters and the set of allowed numerical analysis can determine where the random effects parameters. The fluctuations are controlled by the appropriate probability distribution, we will have a "cloud" of the object's position can drift, the cloud will ship position measurements with high probability post (Berloff and McWilliams, 2002). This technique is called the Monte Carlo method. Figure.3 Diagram describes the random movement of objects The ship's last known position (LKP), is an important information, so the accuracy of this information to decide the outcome of the search. In the random approach, the uncertainty is attached to the ship's last known position LKP in both space and time. If LKP considered very accurate (eg emergency signal is received from a ship with GPS), a small search radius can be set as a standard and all the objects (the set of section) can exit at the same point and at the same time. In an emergency when there is little information about the time and location of occurrence of accidents - need to use a larger search radius and longer. The result is to create a "cloud" of the original position can be dispersed over a wide area of the sea surface over a long period of time. Therefore, many components of the collection will have different types of motion under the action of the flow conditions, the wind and the waves. Obviously, the initial distribution of choice sets will strongly influence the search area. The Monte Carlo method to assign probabilities to the corresponding parameters and the set of allowed numerical analysis can determine where the random effects parameters, theresult will be a "cloud" of the object's position can drift, the cloud will be the measurement of vessel positions have the highest probability. Monte Carlo ensemble approach: + Object represented by particles, each with the characteristics of the object; + Uncertainties in the model, initial conditions and forcing are accounted for by seeding strategy and perturbations to the forcing; + Stokes drift is assumed included in the empirical leeway data og USCG; + The changing cloud of particles represents a probability density for the object location. 1147 Page
Orientation of floating objects, a final factor is the orientation of the object relative to the direction of the local wind, moving away by the wind of most objects contain components perpendicular to the wind direction thiswould be a big difference between the drift direction of the object to the downwind direction. When the user passes the object to the right or left of the wind direction is not defined and even more information about floating objects we must assign the same probability for all computing schemes, results that will exist in two separate search areas with high probability. Moreover, a phenomenon that can affect the class of objects without any information about an object, in fact this can be done as perform some analysis from the same class of initial conditions such as the lifeboat drifting in the water or or water overflow vessel. Overlay layers will have different orbital total search area. 3. Application result Monter Carlo method that we use to determine the orbit drift motion of the fishing vessel lost control, similar to the determination of the probability will exist at a given location at a given timeor the probability of moving in the given region. Results include the trajectory of the object corresponding to the sequence of dynamic data elements (wind at 10m high and flows on the surface of the sea) average over time to represent the climate regime at 03 the rescue of Vietnamese waters in the East Vietnam Sea. 3.1 System to calculate and input information Linux cluster system consists of parallel computing and information storage to ensure professional computing by Nguyen Minh Huan et al (2010). + The computer system includes 04 host computer server with 02 Duo processor Pentium Xeon Quad core speed of 2.44Ghz, 8Gb of RAM operating system Linux 2.6.18-8.el5PAE (x86), which is connected viahigh-speed network; + 01 PC Pentium core i7 and Microsoft Windows XP SP3; + System data store 40TB NAS; + Large capacity UPS System APC - 6KVA. The data on the wind at the sea surface and the average flow on the surface of the month 2 and month 7 represent two season climate of Vietnam Sea and the East Vietnam Sea is a product of KC.09.16/06-10 project (see Nguyen Minh Huan et al (2010)) is used as input to control the orbital model predicts the movement of fishing vessels assumed lost control drift during 07 days with the distress position and startlkp drift in three regions Vietnamese maritime search and rescue. Figure. 4 Principle diagram of parallel computer systems Linux cluster The figure 5 shows the main characteristics of laminar flow systems in the season, the surface flow in winter is dominated mainly by the prevailing northeast wind field in the East Vietnam Sea and the affected part oflocal flow transfer system created by the temperature and salinity of seawater; summer flow surface formed mainly by Southwest wind field with characteristics strongly split by the impact of the tropical convergence zonemiddle position on the diagonal across the sea in the direction from northwest to southeast. On the whole axis of the flow over the sea from the southwest to the northeast accompanied by medium-scale vortex system. The figure 6 shows the average sea surface wind field in February (above) and July (below) in the East Vietnam Sea area, the map shows that the rule changes the fact that the winds in the month winter and summer wind direction exists in two main directions (northeast and southwest) is characterized by typical tropical monsoon. 1148 Page
Figure. 5 The average flow on the surface of the sea in February (above) and July (below) in the East Vietnam Sea. (Source: KC.09.16/06-10 Project (see Nguyen Minh Huan et al (2010))). Figure. 6 The average wind on the surface of the sea in February (above) and July (below) in the East Vietnam Sea. (Source: KC.09.16/06-10 Project (see Nguyen Minh Huan et al (2010))). 1149 Page
3.2 Discussion of Results The results calculated orbit drift motion of fishing vessels assumption takes control drift during 07 days for 03 positions occur in the coordinates TN01 (107 o 24'E; 19 o 30 'N); TN02 (111 o 00'E; 13 o 00'N) and TN03 (108 o 00 '; 8 o 00'N) under the Vietnam rescue at sea in the area may 02 and may 07 are shown in figure 7 shows the average drift motion of the ship in 02 east-west from off the shore, the total search area location probability boat drifting with the wind to the left orbit higher than the average facefor all three cases in three areas of rescue, the average orbit drift motion of the ship in may 07 in the West-East from separate offshore bank for TN01 case in the rescue 1, the orbit drift motion ofship has tended in the direction of East and West as in 02. Successfully developed and tested methods of calculation predict the drift motion of objects in coastal waters with information about local wind, surface runoff, the object's shape and buoyancy. Methods used include the determination of the probability of events related to the drift motion using Monte Carlo simulation and calculating the orbits of objects corresponding to the chain average data over time in May 02 and 07 represent the climate regime, the customs office at the search and rescue area on the waters of Vietnam and the East Vietnam Sea, these results will be used as the initial indication of the direction of travel general drift when the accident happened, more specific orbit for search and rescue work will be determined with the detailed calculations using wind forecasts and data flow. Conclusions In this paper, we have explored and applied a method to make probabilistic forecasts of floating objects submitted to wind and current in ocean. Operational drift forecasting must be continuously updated and expanded with operational current, wind, and wave prognoses. Need good interface to the users, speed and reliability of delivery are essential. Particle-based drift models are also applicable to other objects. Figure. 7 The trajectory of moving away the calculation of fishing vessels assumed to take control in the 02 months (above) and 07 (below) References [1] Allen, A A, 2005: Leeway divergence, Technical Report CG-D-05-05, US Coast Guard Research and Development Center, 1082 Shennecossett Road, Groton, CT, USA. [2] Allen, A A and JV Plourde, 1999: Review of Leeway: Field Experiments and Implementation, Technical Report CG-D-08-99, US Coast Guard Research and Development Center, 1082 Shennecossett Road, Groton, CT, USA. 1150 Page
[3] Fitzgerald, R.B., Finlayson, D.J., Allen, A., 1994. Drift of Common Search and Rescue Objects Phase III. Report, Canadian Coast Guard. Canadian Coast Guard, Research and Development, Ottawa. [4] Hodgins DO, Hodgins SLM., 1998 Phase II leeway dynamics program: development and verification of a mathematical drift model for liferafts and small boats. Technical report. 5741. Canada (Nova Scotia): Canadian Coast Guard. [5] Hodgins, D.O., Mak, R.Y., 1995. Leeway Dynamic Study Phase I Development and Verification of a Mathematical Drift Model for Four-person Liferafts. Report TP 12309E, Transport Canada. Transport Canada, Transport Development Centre. [6] Kundu, P.J., 1990. Fluid Mechanics. Academic Press, London. [7] Nguyễn Minh Huấn và nnk. 2010. Nghiên cứu phát triển và ứng dụng công nghệ dự báo hạn ngắn trường các yếu tố thủy văn biển khu vực Biển Đông. Báo cáo tổng hợp kết quả khoa học công nghệ đề tài KC.09.16/06-10. Hà Nội. (Vietnam) [8] Sorgard, E and T Vada, 1998. Observations and modelling of drifting ships. Report DnV 96-2011, Det norske Veritas (DnV), Norway, Oslo. [9] Berloff, P. S and J. C McWilliams, 2002. Material Transport in Oceanic Gyres. Part II: Hierarchy of Stochastic Models. Journal Phys Oceanogr 32(March), 797 830. [10] Breivik Ø, Allen AA., 2008. An operational search and rescue model for the Norwegian Sea and the North Sea. Journal of Marine Systems.;69(1 2):99 113. Author Information National Centre for Hydro-Meteorological Forecasting, E-mail: maitrinhvinh@gmail.com; Faculty of Hydrology Meteorology and Oceanography, VNU University of Science,Email: nmhuan61@gmail.com; Institute for Marine and Island Research and Management, Institute for Marine and Island Research and Management, 1151 Page