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The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with Sommerfeld radiation condition at infinity. The domain where propagation takes place is characterised by density and sound speed values ρ 0 and c 0 , respectively, while ρ 1 and c 1 are the corresponding density and sound speed values of an immersed object that is responsible of the scattered field. Since Helmholtz equation is separable in prolate/oblate spheroidal coordinates, its exact solution for the scattered field can be expressed as an expansion on prolate/oblate spheroidal functions multiplied by coefficients whose values depend upon the boundary conditions verified at the medium-immersed fluid obstacle interface. The general case (c 0 = c 1 ) is cumbersome because it requires to solve successive matrix systems that are ill-conditioned when c 1 /c 0 is far from unity. In this paper, a numerical implementation of the general exact solution that is valid for any range of eccentricity values and for c 0 = c 1 , is provided. The high level solver code has been written in the Julia programming language while a software package recently released in the literature has been used to compute the spheroidal functions. Several limit cases (Dirichlet and Neumann boundary conditions, spheroid tending to sphere) have been satisfactorily verified using the implemented code. The corresponding example scripts can be downloaded from the authors' web (GitHub) site. The numerical implementation of the exact solution leads to results that are in agreement with reported results obtained through approximate solutions for far-field and nearfield regimes. Additionally, the new code has been used to extend results reported in the literature.

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Engraulis anchoita is a physostomous fish with a dual chambered swimbladder (sb). In situ target strength (TS) measurements on this species are only possible at night, when anchovies disperse forming a scattering layer near the sea surface. A survey data series comprising more than 50000 single target detections, recorded from 1995 to 2008, was analyzed in order to study the species specific TS at 38 kHz. A TS vs. fish total length (L) equation was obtained from the in situ measurements (TS = 31.9 log L – 82.4 dB; r2= 0.78). When the slope of the regression line was forced to 20 into the TS equation, the resulting value for the constant term (b20) was −68.6 dB. In any case, these results indicate an average difference of +3 dB (higher TS values) when compared with the general model suggested for clupeoid fish. The TS measurements obtained inside the nighttime sound scattering layer exhibited a negative trend with depth. An empirical depth dependence term for the anchovy TS equation was obtained through a three parameter least square fitting of the data [TS = 31.3 log L – 79.6 dB – 4.74 log (1 + z/10); r2 = 0.74]. Anatomical data obtained through high resolution X-Ray Computed Tomography was employed as input for a Prolate Spheroidal Model (PSM). Theoretical TS vs. tilt angle functions were obtained considering the compression of the sb at different depths and under the assumption of different contraction rates. The TS functions were then averaged over different fish tilt angle distributions and used to derive theoretical depth dependence curves of average fish TS. The implications of the adopted sb contraction rate and tilt angle distribution are discussed by comparing the modelled TS(z) curves against the empirical data.