Acoustic scattering by a rigid elliptic cylinder in a slightly viscous medium

Abstract

A complete solution is obtained for the two-dimensional diffraction of a time-harmonic acoustic plane wave by an impenetrable elliptic cylinder in a viscous fluid. Arbitrary size, ellipticity, and angle of incidence are considered. The linearized equations of viscous flow are used to write down expressions for the dilatation and vorticity in terms of products of radially and angular dependent Mathieu functions. The no-slip condition on the rigid boundary then determines the coefficients. The resulting computations are facilitated by recently developed library routines for complex input parameters. The solution for the circular cylinder serves as a guide and a differently constructed solution for the strip is also given. Typical results in the "resonant" range of dimensionless wave number, displaying the surface vorticity and the far-field scattering pattern are included, with the latter allowing comparison with the inviscid case.

A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation

“…Furthermore, (local) visco–acoustic Newtonian fluids (e.g. [44]) can also be described by (3.6)–(3.8) by further letting μfalse→0 so that μfalse(ωfalse)=−iωημ which is a convenient way to model viscous fluids like water [45,46].…”

Field and earth‐return impedance for conductors inside an elliptic tunnel

“…Such a solution is formally permitted, and the radial Mathieu functions Mc m 4 ξ, q and Ms m 4 ξ, q (or similar functions with slightly different definition) are used more commonly in the literature [14][15][16][17][18][19][20][21][22][23][24]. However, if we proceeded with the analysis using ansatz (11), divergent sequences of the coefficients F n , G n or C m ′ , S m ′ would arise in the subsequent calculation procedure.…”

High-Frequency Diffraction by an Elliptic Cylinder With a Strongly Elongated Cross-Section

“…[1,2,3]. In classical high-frequency diffraction the body is characterized with as ingle scale, and it is assumed that the characteristic parameters describing the geometry of the problem do not form aquantity that can compete with the main asymptotic parameter proportional to the frequencyofthe incident wave.In [4,5] bodies with asymptotically large length to width ratio have been considered.…”