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Scattering of surface waves on restricted submerged bodies has been much studied theoretically and experimentally. In contrast, the investigation of internal wave scattering is not yet sufficiently advanced though the loads induced by internal waves on marine structures and submerged vehicles are quite essential as demonstrated by field and laboratory experiments (see, for example, Ermanyuk & Sturova [3], Razumeenko [4]).

In most cases, natural pycnocline structure is approximated as a two-layer fluid with a step change of density at the interface. 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.


The experiments were carried out in a test tank (4.5×0.2×0.6m) filled with stratified two-layer fluid. The density of the upper layer (distilled water) was ρ1=0.999g/cm3, the density of the lower layer (glycerine—water solution) was ρ2=1.011g/cm3. The experimental installation is shown in Fig.1. The waves were generated by heaving motion of a semi-cylinder 1. The test-tank was equipped with a wave-breaker 2. The elliptic cylinder 3 of 3cm minor axis and axis ratio 2:1 was mounted on the 2-component hydrodynamic scales 4 so that the gaps between the ends of the cylinder and the walls of the test tank did not exceed 0.1cm. The minimum natural frequency of scales was 2.4Hz. The maximum wave frequency throughout the experiments was 0.21Hz. The loads acting on the cylinder were transmitted to flexible elements 5 by the system of strings 6 and streamlined arms 7. The deformations of elements were measured by induction displacement sensors. As the maximum amplitude of wave loading in experiments did not exceed 1.1·10–3N, the corresponding displacement

Fig. 1.

of the cylinder under the action of waves was less than 5 · 10–3mm. A series of experiments was undertaken to study the influence of streamlined arms on the accuracy of force measurements. The corresponding error was found to be less than 0.5%.

In the reference frame with the origin taken at free surface (the y-axis points upwards), the measured density distribution closely matched the following relation:


where ρ0=(ρ1+ρ2)/2, ε=(ρ2ρ1)/ρ1,h1 is the depth of the upper layer, δ is the parameter characterizing the thickness of the region of large density gradient (pycnocline). The total depth of fluid was H=45cm.

The parameters of wave motion were measured by resistive wave gauges 8 of length greater than the overall pycnocline thickness which is equal 3δ for the density distribution (1). The time-dependent output w(t) of the wave gauges may be written as the integral of local conductivity variations over the length of probes. As the local conductivity is directly proportional to local density, the integral looks as follows:


where w0 is dimensional constant, η(y) is the distribution of local vertical displacements of fluid particles, y1,y2 are the ordinates of the ends of the probe, f(t) is the harmonic function of time. The function η(y) reaches its maximum ηm at

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