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31.
Efim Pelinovsky Andrey V. Razin Elena V. Sasorova 《Waves in Random and Complex Media》1998,8(2):255-268
The problem of the propagation of small-amplitude surface gravity waves in a basin of constant mean depth with one- and two-dimensional bottom roughness is solved in the framework of the Berkhoff model by a mean-field method. In both cases the solutions obtained are compared with the solutions of sets of exact linearized equations of the hydrodynamics of an incompressible fluid. The comparison of the exact and approximate mean-field attenuation coefficients has shown that the Berkhoff approximation is appropriate for the solution of this problem in the case of shallow water for an arbitrary correlation length of bottom irregularities and in the case of arbitrary depth and large-scale irregularities. An explanation is given for the limits of applicability of the Berkhoff approximation which are connected with the weak variability of the vertical structure of the wave field in shallow water and in a basin with large-scale depth fluctuations. The mean-field attenuation coefficients reach their maximum values in the region koho≥1 (where ko is the wavenumber of the surface gravity wave in a basin of constant depth ho). The location of these maxima is practically independent of the correlation length of the bottom irregularities. For the case of one-dimensional irregularities the effect of bottom roughness on the surface gravity wave velocity is investigated. It is shown that the surface wave in a basin with an uneven bottom may propagate more slowly, as well as faster than the wave in a basin with an even bottom, depending on the relations between the wavelength, depth and correlation length of the bottom imperfections. 相似文献
32.
The Cauchy problem for the Navier–Stokes system for vorticity on plane is considered. If the Fourier transform of the initial data decays as a power at infinity, then at any positive time the Fourier transform of the solution decays exponentially, i.e. the solution is analytic. 相似文献
33.
We consider the two-dimensional Navier-Stokes system on the unit square with no-slip boundary condition. The nonlinear evolution
equation for the stream function is studied. Under some hypothesis, we show that the decay of Fourier modes of solutions is
power-like. 相似文献
34.
Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied. 相似文献
35.
We formulate a new boundary value problem for the 2D Navier-Stokes system on the unit square. Under some suitable assumptions
on the initial velocity, we obtain quantitative decay estimates of the Fourier modes of both the vorticity and the velocity.
It is found that in one direction the Fourier modes decay exponentially and along the other direction their decay is only
power like. 相似文献
36.
We study the extended Korteweg-de Vries equation, that is, the usual Korteweg-de Vries equation but with the inclusion of an extra cubic nonlinear term, for the case when the coefficient of the cubic nonlinear term has an opposite polarity to that of the coefficient of the linear dispersive term. As this equation is integrable, the number and type of solitons formed can be determined from an appropriate spectral problem. For initial disturbances of small amplitude, the number and type of solitons generated is similar to the well-known situation for the Korteweg-de Vries equation. However, our interest here is in initial disturbances of larger amplitude, for which there is the possibility of the generation of large-amplitude "table-top" solitons as well as small-amplitude solitons similar to the solitons of the Korteweg-de Vries equation. For this case, and in contrast to some earlier results which assumed that an initial disturbance in the shape of a rectangular box would be typical, we show that the number and type of solitons formed depend crucially on the disturbance shape, and change drastically when the initial disturbance is changed from a rectangular box to a "sech"-profile. (c) 2002 American Institute of Physics. 相似文献
37.
Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector
0 H(
0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0)
0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them. 相似文献
38.
39.
The paper provides the set of all stabilizing causal controllers in a parameterized form for the forward model of any strictly causal discrete-time MIMO LTI model. As an example the causal stabilization of the double integrator is considered. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
40.
Efim Bronshtein 《PAMM》2007,7(1):2060067-2060068
The class of investment projects (named correct projects) and its efficiency characteristic (named limited profitability) is defined. Some properties of limited profitability showing its practical advantage are established. It is proved that limited profitability coincides with Arrow-Levhari characteristic. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献