Experimental Verification of Formulae for Natural Seiche Frequencies in a Two-layer Fluid with the Free Surface

A seiche is a standing wave in an enclosed or partially enclosed body of water (http://en.wikipedia.org/wiki/Seiche). Seiches generate significant horizontal and vertical velocities of water movements. It is unpleasant for ships and is essential for ecology. Both surface and internal seiches exist in water with stable density stratification. There are the explicit theoretical formulae for the wavelengths and frequencies of the different seiche modes in the case of homogeneous initially quiescent fluid filling a rectangular basin with the flat horizontal bottom (Kochin et al., 1963). The linear theory of the potential motion of fluid is used in the theory so the fluid viscosity is not taken into account. The results of an experimental verification of these formulae are contained in Bukreev (2011). The empirical formulae for surface seiches in basins of more complex forms may be found in Rabinovich, (2009).

The explicit formulae are available in Phillips (1967) and Dotsenko and Miklashevskaya (2010) or can also be derived (see below) in the case of a two-layer fluid. Only a two-layer fluid under a horizontal cover was considered in Phillips (1967). The so-cold long wave approximation in the framework of the cited theory was used in Dotsenko & Miklashevskaya, (2010). The theories give relative amplitudes of seiches only. Particular values of the amplitudes depend on the type of disturbance and its intensity. Verification of the theoretical formulae for the frequency oscillations due to surface and internal seiches in a two-layer fluid in controlled laboratory conditions was the main aim of the present work.

Natural seiches are generated by wind and atmospheric pressure variations, seismic activity, tsunamis, landslides, etc. The total property of these disturbances is their relative brevity. As the results, progressive waves are generated at first (Boegman et al., 2005). Seiches are born after the reflection of the progressive waves and are superimposed on the last. As a rule, the same properties of perturbations and waves are typical for laboratory experiments. This is also true for the present work, in which the waves were generated just as it has been done in the experiments of Thorpe (1971); Horn et al. (2001); Boegman (2004); Boegman et al. (2005). Only internal waves were studied in these experiments. Thorpe (1971) received the classical patterns of the shear instability in a two-layer fluid. Progressive internal surges in the form of the moving hydraulic jump were the main object of attenuation in the experiment of Horn et al. (2001); Boegman (2004).

Both surface and internal seiches are specially extracted in the present experiments and theoretical formulae for the wavelengths and frequencies of seiche oscillations are revised on this refined base. That is the main novelty of the present paper.

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(Author: Victor Ivanovich Bukreev, Victor Vasilievich Zykov, Alexey Vladimirovich Chebotnikov

 Published by Macrothink Institute)