The article is devoted to the analysis of the spatial structure of acoustic pressure and particle velocity fields in hydroacoustic waveguides of the sea shelf. Waveguides with two types of sound velocity profile are considered: constant and having an underwater sound channel. The bottom is assumed to be a transitional layer with a sound velocity gradient and a half-space. The acoustic properties of the layer are assumed to be those of silt or sand. The interference structure of the pressure field and the field of the vertical component of the particle velocity is analyzed. The spatial laws of attenuation pressure and particle velocity fields are analyzed. It is shown that the interference structure and the laws of decrease of the pressure field and the vertical component of the particle velocity do not coincide. The article is devoted to the analysis of the spatial structure of acoustic pressure and particle velocity fields in hydroacoustic waveguides of the sea shelf. Waveguides with two types of sound velocity profile are considered: constant and having an underwater sound channel. The bottom is assumed to be a transitional layer with a sound velocity gradient and a half-space. The acoustic properties of the layer are assumed to be those of silt or sand. The interference structure of the pressure field and the field of the vertical component of the particle velocity is analyzed. The spatial laws of attenuation pressure and particle velocity fields are analyzed. It is shown that the interference structure and the laws of decrease of the pressure field and the vertical component of the particle velocity do not coincide.

Keywords: normal modes, particle velocity, seabed, interference structure, incoherent addition

Vector fields in ocean acoustics are the fields of particle velocity and power flow density. Vector analysis methods are used for theoretical analysis and classification of singular points in a hydroacoustic waveguide. Modeling of the power flow field is carried out as a product of the pressure fields and the components of the velocity particle field. The fields of pressure and velocity particles are calculated by the method of normal modes. The simulation of the power flow field in hydroacoustic waveguides with different sound velocity profiles and different acoustic properties of the bottom is carried out. Some regularities in the location of singular points are revealed.

Keywords: hydroacoustic waveguide, pressure field, particle velocity field, power flow field, singular points

The article is devoted to the analysis of the vertical structure of the acoustic pressure field and the first-mode particle velocity in a hydroacoustic waveguide in shallow water. A waveguide consisting of a water layer with a constant sound velocity profile, a transition layer, and a half-space is considered. The acoustic properties of the transition layer are assumed to be frequency dependent. Formulas are derived that describe the vertical profile of the normal mode of a particle velocity. The transformation of the vertical profile of the first mode with increasing frequency is analyzed. The phase difference relations between the normal mode of acoustic pressure and particle velocity are analyzed. A relationship is established between the change in the vertical structure of the normal modes of pressure and particle velocity and the acoustic properties of the transition layer.

Keywords: normal modes, particle velocity, seabed, attenuation coefficient

The article considered the propagation of a long impulse signal in a hydroacoustic waveguide. A solution is given for a replica of a impulse signal in the second approximation of the dispersion theory. The propagation of a single-mode and multimode impulse in a Pekeris waveguide with a bottom in the form of an absorbing half-space is simulated. The acoustic properties of the half-space correspond to medium sand with an average grain size 0,3 mm. The result of the solution in the second approximation of the dispersion theory is compared with the result of the simulation of the impulse replica obtained as a convolution of the input signal with the impulse response of the waveguide. The disadvantages of the solution in the second approximation of the dispersion theory are shown and analyzed. It is shown that the theory of dispersion incorrectly reproduces the transients when the signal is switched on and off in cases where the signal frequency lies near the critical frequency of the first or second mode. It is shown that the theory of dispersion correctly reproduces the envelope of a multimode impulse signal.

Keywords: impulse signal, normal modes, group velocity, dispersion theory, intramode dispersion, intermode dispersion

A hydroacoustic waveguide is considered as a linear system with parameters distributed over dis-tance. A method is proposed for modeling the impulse response of a waveguide. The fields of indi-vidual normal modes at fixed frequencies are calculated so that discretization theorems are satisfied. By performing the inverse Fourier transform of the fields of all modes separately, the time realiza-tions are restored. Then, summing the mode fields, the impulse response of the waveguide is calcu-lated. This approach allows you to "turn off" the fields of individual modes, add, if necessary, the fields of higher modes, or to study all fields separately, simulating the operation of mode selection. The impulse response is considered as a tool for solving the problems of inverting the acoustic characteristics of the seabed and modeling the propagation of signals in waveguides. The impulse response of the first mode of the Pekeris waveguide with the bottom in the form of an intermediate layer and half-space is restored, its wave attributes are revealed: ground wave, water wave, Airy wave. The frequency dependences of the group velocity of normal modes and the multimode im-pulse response are restored. Low-pass filtering of the impulse response makes it possible to reveal the Airy phase of the first mode.

Keywords: normal modes, seabed, attenuation coefficient, group velocity, impulse response, intramode dispersion, intermode dispersion

The article is devoted to the study of the adequacy of the model of a waveguide with a bottom in the form of half-space in broadband calculations of sound fields. Two bottom models are considered: liquid and porous. Two depths of the water layer are considered - units of meters and tens of meters. In the case of a liquid bottom, the speed of sound and the loss tangent in the bottom are considered to be frequency independent (model with a bottom with constant quality factor). In the case of a porous bottom, the frequency dependence of the speed of sound and the loss tangent is extracted from experimental data published in open sourses. The frequency dependences of the group velocities of the modes and modal attenuation coefficients are calculated. The frequency dependences of the group velocity of the first mode for the two waveguide models coincide, and the critical frequency of the normal modes changes in proportion to the depth of the water layer. The frequency dependences of the attenuation coefficient of normal modes turn out to be significantly different. The impulse response of shallow and deep-water waveguides are simulated. It is shown that in the case of a waveguide with a water layer depth of a few meters, the temporal structure of the impulsive field is indistinguishable - the bottom model without dispersion is adequate. In the case of a water layer depth of tens of meters, the temporal structure of the pulsed field for two bottom models is different - the waveguide model with a bottom without dispersion is inadequate.

Keywords: liquid bottom, porous bottom, marine sediments, dispersion of phase velocity, group velocity, intramode dispersion, intermode dispersion

An analytical representation of the velocity potential of a point source of sound is constructed for a model of a marine acoustic waveguide with a rigid stepped bottom, where a sound velocity profile varies with depth. Inhomogeneity of the bottom in the form of a cylindrical protrusion is modeled on the basis of the method of partial regions. The sound field is represented in the form of the sum of normal modes to construct the sound velocity potential in each partial region. The continuity of solutions at the boundary of partial regions leads to an infinite system of linear equations with respect to the coefficients under normal modes. In this work, formulas are obtained that describe the energy characteristics of the propagation of each of the normal modes along the waveguide. Examples of numerical modeling are given. An analysis of the excitation coefficients of normal modes is carried out for waveguide parameters are true to type of the Black Sea region.

Keywords: waveguide, normal modes, bottom inhomogeneity, excitation coefficient, partial regions, infinite system of linear equations, asymptotics