Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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The Influence of a Bottom Mud Layer on the Steady-State Hydrodynamics of Marine Vehicles
The Influence of a Bottom Mud Layer on the Steady-State Hydrodynamics of Marine Vehicles
Pages 727-742
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From page 727... ...
Indeed, the whole curve of wave resistance as a function of the speed is, in some general sense, an average between those two limiting extreme cases; however, one can only properly determine the precise influence of the mud layer by means of the detailed calculations required by the new theory, as described here. In the current work, the theory has been extended to permit the computation of the hydro
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From page 728... ...
Once again, it is observed from the numerical results that the influence of the mud layer on these force components is such as to suggest that the equivalent overall water depth lies somewhere between that of the water layer alone and that of the total mud-water domain, depending on the physical properties of the mud. ~ Introduction I.1 Previous Work During the last few years, there has been a renewed effort to develop a better hydrodynamic understanding of marine vehicles in water of finite depth.
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From page 729... ...
As in the previous work discussed above, it is assumed that the sea-water mud behaves like a viscoelastic substance. To keep the analysis tractable, we will use here only a linear viscoelastic model, in which the shear stress is related to the rate of strain by a convolution-type integral, with the relaxation function serving as a kernel.
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From page 730... ...
(8) It may also be noted that the three velocity components must vanish on the bottom of the mud layer.
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From page 731... ...
, and this is equivalent to evaluating the shear stress according to the formula: T = G'e + it' do , where e is the shear strain, the mud viscosity is it' = p'u', J = G'/p', and G' is the mud shear modulus. 2.4 Hydrodynamic Forces The forces generated by the disturbance are defined as the relevant integrals of the normal stress over the surface area that characterizes the vehicle.
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From page 732... ...
, the result can be simplified using the Poisson summation formula and this procedure has been followed by a number of researchers in similar circumstances. The final result for the formula for the induced generalized forces on a vessel moving in a channel is R*
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From page 733... ...
and Lunde t25~. In a similar vein, if either the mud complex kinematic viscoelasticity I,' or the mud density p' approaches infinity, then the classic inviscid case corresponding to a water depth d is obtained, as expected.
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From page 734... ...
It should be added that the ~error" related to using different step sizes in the transverse wave number corresponds to the difference in generalized forces when running in channels of the relevant different widths; it can be used to estimate the restrictive influence of finite channel width. Previous experience with oscillatory integrals with an infinite range of this nature has shown that it is difficult to improve on the procedure outlined here.
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From page 735... ...
for the case of a dimensionless channel width of 0.25. The most striking feature of these results is the well-known jump in the resistance at the critical value of unity of the depth Froude number Fc~ = U/~, which is seen for the two limiting cases, namely Mud 1 and Mud 5.
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From page 736... ...
The next intermediate case, that of Mud 4, utilizes the same values of mud viscosity and shear modulus, but also includes now a higher dimensionless density p'/p, with a value of 2. This fourth case produces results approaching those of the previously noted instance of an almost solid mud layer, that of Mud 5.
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From page 737... ...
The four parts of Figure 3 show the sinkage force for the same four dimensionless tank widths. The general behavior is one in which the more solid mud yields results with more extreme behavior, particularly near the critical depth Froude number, as already discussed in the case of wave resistance.
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From page 738... ...
l l6CsF2, t/l = 22.32CMF2. Figure 5 show the sinkage of the vessel in question for the four dimensionless tank widths under consideration.
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From page 739... ...
4 Concluding Remarks The analysis using the Kelvin-Voigt model implemented in this paper shows that the generalized forces due to a disturbance moving in the water layer above a dense mud layer depend strongly on the parameters of such a two-layer system. The most important feature of the curves for the forces is that the maximal values are not always a monotonic function of the mud density, mud viscosity, or elasticity.
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From page 740... ...
, suggesting that the mud has less chance to respond to the hydrodynamic pressures at these higher speeds. Certainly, for intermediate values of the mud properties, the general effects of the mud layer are to moderate any distinct features of the traditional linearized wave-resistance theory.
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From page 741... ...
L17] L71 ZILMAN, G., DOCTORS, L.J., AND Minor, T.: "The Influence of a Bottom Mud Layer on the Resistance of Marine Vehicles", Ship Technology Research: Schiffstechnik, Vol.
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From page 742... ...
Wateru~ay, Port, Coastal, arid Ocean Enginee7iT`g, DISCUSSION W.W. Schultz University of Michigan, USA Your potential flow upper layer ensures zero shear stress on the mud interface.
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