A new semianalytical solution for inertial waves in a rectangular parallelepiped
Nurijanyan, S.; Bokhove, O.; Maas, L.R.M. (2013). A new semianalytical solution for inertial waves in a rectangular parallelepiped. Phys. Fluids 25(2): 126601. dx.doi.org/10.1063/1.4837576
In: Physics of Fluids. American Institute of Physics: Woodbury, NY. ISSN 10706631; eISSN 10897666, more
 
Author keywords 
Eigenvalues; Boundary value problems; Inertial waves; Numerical solutions; Kelvin waves 
Authors   Top 
 Nurijanyan, S.
 Bokhove, O.
 Maas, L.R.M., more



Abstract 
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 semianalytical solution of a linear threedimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The threedimensional 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 Taylor [“Tidal oscillations in gulfs and basins,” Proc. London Math. Soc., Ser. 2XX, 148–181 (1921)], Rao [“Free gravitational oscillations in rotating rectangular basins,” J. Fluid Mech.25, 523–555 (1966)] and also, for inertial waves, by Maas [“On the amphidromic structure of inertial waves in a rectangular parallelepiped,” Fluid Dyn. Res.33, 373–401 (2003)] 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 semianalytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency. 
