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# lec3 - 3 NONLINEAR COEFFICIENTS IN DETAIL The method of...

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Unformatted text preview: 3 NONLINEAR COEFFICIENTS IN DETAIL The method of hydrodynamic coeﬃcients is a somewhat blind series expansion of the ﬂuid force in an attempt to provide a framework on which to base experiments and calculations to evaluate these terms. The basic dificulty, i.e. the intractability of the governing equations of motion of viscous ﬂuid prohibits, at least today and in the near future, a computation of these forces. Still, we are not totally ignorant about these forces, since a number of symmetries and basic laws can be applied to reduce the number of unknown coeﬃcients. This is the purpose of this section. The basic assumption in using the method of hydrodynamic coeﬃcients is that the forces have no memory effects, i.e. past motions have no impact on the ﬂuid forces at the present moment. This is not correct when the ﬂow separates, or when large vortices are shed, because then the vorticity in the ﬂuid affects the ﬂuid forces for a considerable time after they have been shed – i.e. until they move suﬃciently far away from the body. We will show later some methods which allow us to incorporate the effect of shed vorticity, because under certain conditions such effects can not be ignored. We employ the following basic facts and assumptions to derive the ﬂuid forces acting on a ship, submarine or vehicle: 1. We retain only first order acceleration terms. Based on Newton’s second law, we expect the inertia terms from the ﬂuid to be linearly dependent on acceleration. 2. We do not include terms coupling velocities and accelerations. Again, based on New- ton’s second law, we expect inertia forces to depend on acceleration alone....
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lec3 - 3 NONLINEAR COEFFICIENTS IN DETAIL The method of...

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