Physical Fields of Ship and Ocean   
DOI: http://www.dx.doi.org/10.24866/2227-6858/2020-1-10

Lobova T.

TATIANA LOBOVA, Assistant of the Department Physics 
Postgraduate, Far Eastern Federal University, e-mail: daydream_2012@mail.ru
MSU named after admiral G.I. Nevelskoy
50a Verkhny Portovaya St., Vladivostok, Russia, 690003

Improvement of the mathematical model of a point radiator 
for detecting aqueous biological resources

Abstract: This article covers the possibilities for and results of usage of hydroacoustic devices and methods for detecting aquatic biological resources. The principle of operation of these methods is based on the solution of wave equations (Helmholtz equations), which can be reduced to stable algorithms under appropriate boundary conditions. Such approach to calculation of characteristics of antennas radiation means the complexity of perception of a single algorithm in the development of antenna theory. In this case, specialists have to apply different calculation methods for one practical task – development of the optimal design for adirectional system.
This article discusses the mathematical algorithm based on the theory of directed Green's functions and of an angular dependence, which can significantly reduce the calculation time using a common computer. This angular dependence makes it possible to identify areas at the boundaries which are of a uniform structure. This model allows to detect aquatic biological resources by the pressure value of the reflected signal, which characterizes the acoustic resistance of objects, including density and phase velocity. Capabilities of this algorithm are demonstrated with analysis of the field of a point source.
The proposed algorithm enables solving the equation by engineering approximate methods 10 times faster than traditional ones. The time for calculating of the field using a common computer with Mathcad software package was approximately 1–2 min. Calculation models were obtained in a curvilinear coordinate system. Numerical experiments were carried out, which showed the applicability of the derived mathematical model for practical calculations. The error of the calculation model does not exceed 20%. The considered approximate calculation methods allow engineering calculations for antennas located in a shallow sea with ice cover.
Keywords: echolocation, hydroacoustic method, assessment of bioresources, theory of Green functions, field of hydroacoustic radiator, mathematical algorithm.

See the reference in English at the end of the article