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Introduction

In Arctic regions, drifting icebergs represent a very dangerous hazard for navigation, and indeed for offshore structures. To ensure safe operation, an iceberg management plan must be developped; covering iceberg detection to iceberg towing or platform evacuation. One important part of the plan is the iceberg drift forecast. Further to a review of existing drifting models, TOTAL have decided to develop and test a new numerical model that includes wave forces and a stochastic approach.

In previous models, wave effect was often taken into account via a slightly over-estimated wind effect, assuming that waves are only driven by local winds (see Smith [1993] for example). Masson [1991] proposed an hydrodynamic approach to the estimation of wave effect, assimilating the iceberg to a cylinder and computing the transfer function of the object. A similar approach will be generalized here. The new iceberg drift model has been written following the classic rules of drifting problems. The principle is to estimate as best as possible the forces that act on the iceberg, and to compute a trajectory during the course of a few hours using oceanic and meteorological forecasts. The uncertainties on the formulation of these forces are taken into account via a stochastic approach; the model computes areas of probability instead of a single trajectory. The model is validated using a series of drift measurements carried out during the months of June 1983 and 1984 in Canadian waters. This data is used to test the accuracy of the model and to estimate the impact of each parameter on the drift.

In the first section we describe briefly the equations solved by the model and the numerical scheme. Sections 2 is devoted to the validation of the model on the available test cases, and in section 3, we present the stochastic approach that is implemented in the code.

Model Formulation

Principle

The aim of the model is to predict the drift of an iceberg, knowing an estimation of its shape and mass and using environemental factors.

The drift is a result of:

• Current drag force (Fc)


• Wind drag force (Fw)


• Wave Force (Fwav)


• Inertia and Coriolis forces (Fm)

The model numerically solves the movement equation (eq. (1)) to compute the location of the iceberg.

(m+ma)

d2x

dt2 = Fc+ Fw + Fwav + Fm (1)

where m stands for the mass of the iceberg, ma for the added mass, and X for its position. ma is usually taken to be half of m. All the terms in this equation are two-dimensional vectors. We use a fourth-order RungeKutta scheme with adaptative time-step to integrate the equation in time.

Another equation could have been included in the system to compute the yaw of the object. Such a calculation requires having a good knowledge of the shape of the object to be accurate. Furthermore, the formulation of the problem can be very complex, because without using a damping term, we obtain a permanent rotation of the iceberg which is not realistic. And since the choice of the damping coefficient is often arbitrary, it incorporates another source of uncertainty in the model. So we consider that given the lack of details on the precise shape of the iceberg and the number of uncertainties that already exist, it is not significant to include the yaw motion of the iceberg in the calculation at this stage of development.

Drag forces

The classical formulation of drag forces is used: for the wind drag force, in projection on the x and y directions, the expression is simply:



where uw is the wind speed and _w is the wind incidence angle. For the current drag force, the code does not use a single value of current, but vertical profiles. So we have to sum the contribution of each layer to obtain the resulting effort:

where n is the number of layers and uc(k) the current speed at the kth layer. Given the fact that yaw motion is not taken into account in the calculation, the surfaces Sw and Sc must represent a "mean surface" exposed to wind and currents. The drag coeffi

Labels: iceberg Drift, oil gas russia, rogtec

posted by The Rogtec Team @ 15:55 

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