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Nurijanyan, S.; Bokhove, O.; Maas, L. R. M.

A new semi-analytical solution for inertial waves in a rectangular parallelepiped. (English) Zbl 1320.76119

Phys. Fluids 25, No. 12, Paper No. 126601, 21 p. (2013).
Summary: A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane, the two dimensional solution is constructed via superposition of “inertial” analogs of surface Poincaré and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincaré waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by G. I. Taylor [“Tidal oscillations in gulfs and basins,” Proc. London Math. Soc., Ser. 2XX, 148–181 (1921)], D. B. Rao [“Free gravitational oscillations in rotating rectangular basins,” J. Fluid Mech. 25, 523–555 (1966)] and also, for inertial waves, by L. R. M. Maas [Fluid Dyn. Res. 33, No. 4, 373–401 (2003; Zbl 1032.76521)] upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas. In contrast to Maas’ approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.{
©2013 American Institute of Physics}

Cited in 4 Documents

MSC:

76U05 General theory of rotating fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction

Citations:

Zbl 1032.76521
PDFBibTeX XMLCite
\textit{S. Nurijanyan} et al., Phys. Fluids 25, No. 12, Paper No. 126601, 21 p. (2013; Zbl 1320.76119)
Full Text: DOI Link

References:

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