Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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The Forces Exerted by Internal Waves on a Restrained Body Submerged in a Stratified Fluid
The Forces Exerted by Internal Waves on a Restrained Body Submerged in a Stratified Fluid
Pages 827-838
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From page 827... ...
The linear 2-D problem of internal wave scattering on a restricted cylinder is considered theoretically. The fluid is assumed to be nonviscous, incompressible and composed of three layers (the upper and lower layers are homogeneous and the middle layer is linearly stratified)
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From page 828... ...
However, a realistic smooth density variation gives rise to new physical effects that are beyond the domain of two-layer model. The present paper deals with theoretical and experimental study of forces exerted by internal waves on horizontal elliptic cylinder in the case of stratification characterized by the presence of a finite region of high density gradient.
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From page 829... ...
In the fluid system described, the forces exerted on the elliptic cylinder by internal waves of the first mode depend on the following nondimensional parameters: hub, H/b, h = h/b, ~ = ~/b, k = fib, ~ = bit, where b is the minor axis of elliptic cylinder, ~ is the amplitude of internal waves, h is the distance from the cylinder centre to the free surface, ~ is the kinematic viscosity. The value H/b = 15 was kept constant.
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From page 830... ...
, the coefficient Cal fairly well agrees with the above-mentioned theoretical estimate in a wide range of k. It seems likely that the increase of Cal with ~ is associated with the effect kindred to flow contraction as the increase of pycnocline thickness decreases the upper layer of constant density.
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From page 831... ...
Buoyancy force is major at c' < 1 while inertial loads dominate at c' > 1. The case of the cylinder located in the lower layer close to the pycuocline at h = 5.4 is illume bated in Fig.
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From page 832... ...
To each wave mode there corresponds a dispersion dependence of the wave frequency on the wave number. We investigate the scattering of an internal wave of the first mode, incident on a solid horizontal elliptic cylinder.
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From page 833... ...
This ap proximation allows to 'filter off' the surface waves without distorting significantly the internal ones. The disturbed oscillating motion of the fluid is assumed to be steady and the flow inside upper and lower layers is potential.
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From page 834... ...
For a body located in the upper layer one should derive the Green function describing the field of a point source of pulsating strength which is placed at the fixed point ((,() of the upper layer.
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From page 835... ...
Number of finite elements accounted by CFEM is equal 18. In numerical realization, the main difference between two-layer fluid and smooth pycnocline is that, in the latter case, the Green function has infinite number of simple poles in integral term and infinite number of items in a sum, what corresponds to the existence of countable number of free internal wave modes for pycuocline stratification.
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From page 836... ...
The reported comparisons of measured and calculated loads exerted by surface waves on a cylinder submerged in homogeneous fluid are restricted to the case of circular cylinder. In this case, the estimates of both components of wave-induced forces obtained within the framework of linear theory are in good agreement with the experimental values measured at low Keulegan-Carpenter numbers for the waves of small steepness (see, for example, Chaplin t63~.
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From page 837... ...
4. CONCLUSIONS This study is among the first attempts to determine the diffraction loads induced by internal waves on restricted horizontal elliptic cylinder in the case of continuous pycnocline stratification.
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