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Open Access Publications from the University of California

Modeling Steep Two-Dimensional Random Seas Using Green-Naghdi Theory


In analyzing problems of fluid motion, one develops a model of the fluid that describes the necessary characteristics of the fluid and its motion. In studying the macroscopic properties of the flow, the continuum definition of the fluid, which disregards the microscopic processes, is found appropriate. A continuous distribution of the material of the fluid is considered throughout the volume of the fluid. For devel­oping a purely mechanical theory (ignoring the thermal effects), one then postulates the balance of mass and momentum to derive a pointwise relationship describing the motion of the fluid. These conservation equations, or governing equations, do not form a closed system due to the presence of force terms (stresses) which are related to the forces acting on an element of the fluid. Further progress can be made in the development of the theory only by postulating the relationship of these forces with the kinematic quantities that describe the basic flow characteristics [21]. Experimental observations prove to be the key to this part of the development. The relationship thus postulated, called the constitutive relation, links the stresses in the fluid to the kinematic flow quantities.

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