The paper examined the spectral characteristics of shallow water waves, which was based on the wave data collected along the south coast of Jiangsu. It proposes a tentative spectra model which can work better than Joint North Sea Wave Project (JONSWAP)spectra. Both of the value of tentative spectral parameters (α and γ) increase with significant wave height and spectral peak frequency. According to a regression analysis, empirical equations are achieved, which is related to the parameters with significant wave height and spectral peak frequency. The study shows that the measured wave spectra can be represented by tentative spectra, and the fitting results in high-frequency tail of tentative spectra are better than that of JONSWAP spectrum with modified parameters.
IQ the matrix elements in Eq. (28) of MG, bare masses are to be used 5A counterterm was included in the quantum-statistical theory of C. Bloch and C. DeDominicis, Nucl. Phys. 10, 181 (1959). In nuclear physics, Hartree-Fock calculations make use of countertermssee G. E. Brown, Unified Theory of Nuclear Models (North-Holland, Amsterdam, 1964). A counterterm has been used in a quantum-statistical theory of the normal Fermi liquid by E.R. Tuttle, Phys. Rev. A 1, 1243 (1970). The formulation of MRS-I has been extended to include the counterterm technique and generalized to apply to a system of charged and neutral particles by F. Mohling and C. (North-Holland, Amsterdam, 1965), Vol. III.We exclude systems which could exhibit Bose condensation, although it is straightforward to include such a possibibty.OSimilar equations were used in the application of Green's function techniques to the ground state of a degenerate Bose gas by S. T. Beliaev, Zh. Eksperim. i Teor. Fiz. 34, 417 (1958) [Soviet Phys. JETP 7, 289 (1958)j. See also Hef. 2.The expression for the grand potential in terms of the (0, 0) master graphs of this paper can be obtained by a careful translation of Eq. (4.25) of MRS-II to the present formalism.These are finite temperature analogs of the anomalous Green's functions used by Beliaev (Ref. 10).More properly, one should refer to these as free quasiparticle Green's functions, since they involve the quasiparticle energy given in Eq. (3.14).40n the basis of Eqs. {5. 7)-(5.9) the rules in Appendix A could be amended so that the diagrammatic expansions for the G»(t» t&, k ) apply to the Green's functions s~"(t,, t"&)
SUMMARYThis paper focuses on the fluid boundary separation problem of the conventional dynamic solid boundary treatment (DSBT) and proposes a modified DSBT (MDSBT). Classic 2D free dam break flows and 3D dam break flows against a rectangular box are used to assess the performance of this MDSBT in free surface flow and violent fluid-structure interaction, respectively. Another test, water column oscillations in a U-tube, is specially designed to reveal the applicability of dealing with two types of particular boundaries: the wet-dry solid boundary and the large-curvature solid boundary. A comparison between the numerical results and the experimental data shows that the MDSBT is capable of eliminating the fluid boundary separation, improving the accuracy of the solid boundary pressure calculations and preventing the unphysical penetration of fluid particles. Using a 2D SPH numerical wave tank with MDSBT, the interactions between regular waves and a simplified vertical wave barrier are simulated. The numerical results reveal that the maximum horizontal force occurs at the endpoint of the vertical board, and with the enlargement of the relative submerged board length, the maximum moment grows linearly; furthermore, the relative average mass transportation under the breakwater initially increases to 11.14 per wave strike but is later reduced. The numerical simulation of a full-scale 3D wave barrier with two vertical boards shows that the wave and structure interactions in the practical project are far more complicated than in the simplified 2D models. The SPH model using the MDSBT is capable of providing a reference for engineering designs.
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