Application of a Numerical Wind-Driven Model in Hindcasting Storm-Generated Current Velocity Profiles

Abstract In order to adequately account for hydrodynamic forces on an offshore structure under storm conditions, it is necessary to determine the vertical profile of maximum current velocity to which the structure will be subjected. Additionally, the, time history of the current velocity profile is required to obtain the currents associated with the largest waves. The time-dependent, one-dimensional wind driven model of Mellor and Durbin1 represents a significant improvement in hind casting physically realistic velocity profiles in the upper layer of the ocean where horizontal boundary conditions are not important. It employs a non-constant, stability dependent eddy viscosity coefficient that is a function of the vertical profile of the Richardson number, i.e., depends on the vertical velocity shear and density profile. Three test cases of the model are presented; one involving a storm over a deep continental slope region; the second, a storm over a continental shelf region; and a third, a hurricane in deep water. Introduction One-dimensional numerical models of the surface-wind-mixed layer of the ocean can provide an alternative to the more cumbersome and costly two or three dimensional models when attempting to hind cast site-specific, wind-driven currents. Their applicability stems from the fact that water properties such as temperature and salinity varies more, by several orders of magnitude, along the vertical then along the horizontal. As a result, vertical mixing and momentum exchange from the surface downward has a much more rapid and profound effect on local conditions than do horizontal advection and horizontal mixing. If a site is sufficiently far from the coast so that horizontal boundary effects are negligible, then a one-dimensional model has a definite application. Wind-mixed layer current velocity models are generally of two types: those that consider only the bulk properties of the surface layer and those that consider the mechanism of vertical transfer of those properties. An example of the former is the Pollard and Millard2 model in which a mixed layer depth is prescribed and the properties of that layer such as current speed and direction, density, etc. are assumed to be uniform from the surface to the bottom of the mixed layer. The wind stress is modeled as a body force so that it is assumed to be instantaneously and uniformly distributed throughout the surface mixed layer. Models of this type are attractive because of their computational simplicity and they can yield reasonably accurate results (see, e.g., Pollard &Millard2). They are particularly appropriate in the case when a shallow well-mixed surface layer overlies a strong density interface. However, a criticism that may leveled at this type of model is that they tend to be disconnected from the underlying physics. That is especially true when a wind-mixed surface layer is not well-defined prior to a storm and consequently the density structure determines the rate of vertical exchange of momentum and, therefore, the time-dependent velocity profile. A more physically realistic approach to modeling the wind-mixed surface layer is taken by so called "eddy-viscosity" type models.