Field In Horizontal Plane Research Articles

Whispering gallery waves in horizontal plane in vicinity of curved isobaths in shallow water

Interference structure of the sound field in horizontal plane in shallow water with parameters variable in horizontal plane is studied within the framework of the so-called 3D problem. Formally, this problem can be solved using separation of the vertical coordinate (depth) in the wave equation in supposition that depth dependence of the sound field is described by adiabatic waveguide modes. Remaining part is two-dimensional dispersive wave equation which can be solved by different methods (PE, ray approximation, and modal decomposition). It is shown in the paper that in a shallow water waveguide with variable bathymetry with curvilinear isobaths (Laguna, lake) there exist specific solutions of this equation, concentrated in horizontal plane approximately along isobath lines (whispering gallery waves), up to formation of the waveguide modes in the horizontal plane. Number of modes and their shape depend on position of the source, frequency and radius of curvature. Remark that this whispering gallery modes can exist in real conditions, for example, for frequency about a few hundreds Hz and radius of curvature about 5–10 km. Analytical expression and results of modeling using ray approximation and PE are presented for real shallow water conditions. [Work was supported by ISF, grant 565/15.]Interference structure of the sound field in horizontal plane in shallow water with parameters variable in horizontal plane is studied within the framework of the so-called 3D problem. Formally, this problem can be solved using separation of the vertical coordinate (depth) in the wave equation in supposition that depth dependence of the sound field is described by adiabatic waveguide modes. Remaining part is two-dimensional dispersive wave equation which can be solved by different methods (PE, ray approximation, and modal decomposition). It is shown in the paper that in a shallow water waveguide with variable bathymetry with curvilinear isobaths (Laguna, lake) there exist specific solutions of this equation, concentrated in horizontal plane approximately along isobath lines (whispering gallery waves), up to formation of the waveguide modes in the horizontal plane. Number of modes and their shape depend on position of the source, frequency and radius of curvature. Remark that this whispering gallery modes ...

Three-dimensional adiabatic mode parabolic equation method and its applications

Complex zone of the ocean is often characterized by horizontal variations of environmental parameters(bathymetry, sound speed profile, bottom properties etc.), initiating redistribution of the sound field in horizontal plane, which is the so-called three-dimensional (3D) effect. Based on the adiabatic mode parabolic equation method, modeling of 3D effects is carried out, in which the eigenvalues and eigenfunctions are calculated by the standard normal mode model KRAKEN, and the amplitude corresponding to each mode is computed by the wide-angle parabolic equation model RAM. The present 3D model is very efficient and can give clear physical meaning, but it can be only applied to a waveguide whose properties vary gradually with horizontal range due to the adiabatic assumption between different modes. This model is then used to analyze the horizontal refraction caused by internal waves and by a coastal wedge. The numerical results show that there are several areas in the horizontal plane, corresponding to different structures of intensity distributions. Moreover, the redistribution of the sound field in horizontal plane depends on source frequency and mode number. Frequency and modal dependences lead to variations of spectrum, distortion of signal with some spectrum, and spatiotemporal fluctuations of the sound field.

Horizontal refraction and whispering gallery sound waves in area of curvilinear coastal wedge in shallow water

Horizontal refraction of sound signals in area of coastal wedge determines specific structure of the sound field in horizontal plane, including multipath areas and caustics (in the framework of approximation of horizontal rays and vertical modes). This structure depends on mode number and frequency. In the paper sound field of signal, radiated by the point source is studied in the shallow water area which can be considered as a wedge with curvilinear coastal line (lake, gulf, cape, etc.). It is shown that for some distances from the source to the beach whispering gallery waves (whispering gallery horizontal rays) exist, propagating along the coast, where energy is concentrated in narrow area in horizontal plane. Structure and characteristic of these rays depend on mode number, frequency and waveguide parameters (in particular, steepness of sea floor and radius of curvature). Intensity fluctuations as well as variation of pulse shape and frequency spectrum are studied; analytical estimations are presented as well as discussion of possible experimental observations. [Work was supported by RFBR and BSF.]

Numerical Simulation of Atmospheric Flow Field around Bridge

This paper carries out a numerical simulation of the atmospheric flow field around bridge. The variation law of airflow field around bridge is studied. Velocity and pressure distribution laws of flow field in horizontal plane and the cross-section are discussed, and influence range of flow field around bridge area is identified.

Variability of horizontal interference structure of the sound field in the presence of moving nonlinear internal waves

Variations of the low-frequency sound field when a train of nonlinear internal wave (NIW) crosses the acoustic track are considered. Three positions of moving NIW train, during 10:30 to 11:37 GMT on 19 August 2006 are examined. During this time, three periods of sound transmission took place, each lasting about 7.5 min. These periods referred to as starting time (10:30–10:37.5 GMT), mid-time (11:00–11:07.5 GMT), and the end-time (11:30–11:37.5 GMT). Low frequency modulated signals centered at 300 Hz, and bandwidth of 60 Hz with duration of about 2 s were transmitted. During this time, NIW consisting of 6-7 separate solitons was shifted in horizontal position by 2.5 to 2.8 km, moving toward the coast at the velocity of about 0.75 m/s. Fluctuations of the sound field in horizontal plane are described in detail for three periods of the sound pulses radiation: near the forward front, in the middle of the train, and near the back front using the fluctuations of an angle of horizontal refraction. Estimation of this angle using experimental data and those of the corresponding theory show the same value. [Work supported by ONR.]