For realistic numerical modelling of ocean currents with the zone of wave influence, the effect of the waves on the current should be accounted for in a dynamically consistent manner. The following phenomena are relevant:

  1. The wave-induced Stokes drift, which is a result of the water particle orbits due to the wave motion not being closed.

  2. The transfer of momentum from the wind into the waves, instead of Into the current.

  3. The transfer of wave momentum to the current as a result of wave dissipation.

  4. The vertical transfer of momentum due to turbulent motions.

  5. The effect of the Earth's rotation. This includes a Coriolis force due to the wave-induced Stokes drift.

A theoretical model has been developed which takes account of the above effects. It uses a perturbation expansion technique in a Lagrangian coordinate system (a coordinate system m which a water particle's coordinates remain constant throughout a wave cycle). Vertically varying eddy viscosities are used to parameterise both the wave dissipation and the turbulent transfer of momentum between the current at different depths. Using a theoretical wind-wave directional spectrum, results are presented which are in reasonable agreement with observations.

The model WIU be suitable for incorporation into three-dimensional numerical hydrodynarmic models for ocean current simulation.

Engineering requirements

The current near the sea surface has an influence on offshore oil-related activities m the following ways: it gives rise to an extra force on offshore structures and other objects in the water m addition to the wave forcing, and it causes oil slicks and other forms of pollution near the sea surface to move around.

Eulerian and Lagrangian mean currents

There are basically two ways of defining the current with the wave zone. The first way is to take a vector average (over many wave cycles) of the fluid velocity at fixed points m space, to obtain the Eulerian mean current The second way is to follow water particles for a tune corresponding to many wave cycles: the average velocity over such a tune period 1s the Lagrangian mean current. The vector difference between the two types of current is the Stokes drift, which is dependent just on the wave field and can be calculated directly from the directional wave spectrum.

Forces on structures due to near-surface currents

The current causes of its own accord forces on objects m the water, but its most important forcing effect is a result of the combination of wave and current forces, since the orbital velocities in large waves are generally considerably larger than the maximum current velocities, and the drag force on an object m the water has a non-hear dependence on the fluid velocity, being in general proportional to the square of the velocity The current which is relevant for calculating forces on structures is the Eulerian mean current, since the Stokes drift part of the current does not given rise to any extra forces over and above those due to the wave motions themselves.

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