We consider the internal gravity waves that are produced in an
inviscid Boussinesq
fluid, whose Brunt–Väisälä frequency N is
constant, by the small rectilinear vibrations
of a horizontal elliptic cylinder whose major axis is inclined at an
arbitrary angle to the
horizontal. When the angular frequency ω is greater than N,
no waves are produced
and the governing elliptic equation is solved using conformal transformations.
Analytic continuation in ω to values less than N, when
waves are produced, is then used
to determine the solution. It exhibits the surprising feature that,
apart from certain
phase differences, the form of the velocity distributions in each of
the beams of waves
that occur is the same for all values of the thickness ratio of the
ellipse, the inclination
of its major axis to the horizontal and the plane in which the vibrations
are occurring.
The Fourier decomposition of the velocity distribution is found and is
used
in a sequel, Part 2, to investigate the effects of viscous dissipation.In an important paper Makarov et al. (1990) have given
an approximate solution for
a vibrating circular cylinder in a viscous fluid. We show that the limit
of this solution as the viscosity tends to zero is not the exact inviscid
solution
discussed herein. Further
comparison of their work and ours will be made in Part 2.
Internal gravity waves generated by an impulsive plume