Internal Wave Generation in Uniformly Stratified Fluids. 1 ... - LEGI

2. BIBLIOGRAPHICAL REVIEW
Investigations of the Green’s function of monochromatic internal waves generally
involve Fourier transform methods. In this way Sarma & Naidu (1972 a, b), omitting the use of
any radiation condition, then Ramachandra Rao (1973, 1975) and Tolstoy (1973 § 7.3),
restoring it, derived non-Boussinesq internal waves generated by point mass and force
sources. A similar calculation of the Boussinesq Green’s function has been achieved by Rehm
& Radt (1975), and partially performed by Miles (1971), Sturova (1980) and Gorodtsov &
Teodorovich (1980, 1983) during studies of internal wave radiation by moving point sources.
Unfortunately these results are often contradictory, like Ramachandra Rao’s (1973, 1975)
ones, which do not even coincide with each other.
A different angle of attack has more recently been adopted by some Soviet workers,
who directly considered the Green’s function of Boussinesq impulsive internal waves without
resorting to any monochromatic intermediate step. Teodorovich & Gorodtsov (1980) proved
Miropol’skii’s (1978) study by classical function theory to lead to erroneous conclusions, and
Sekerzh-Zen’kovich’s (1979) approach by generalized function theory to be the only valid
one. The latter writer proposed both exact and asymptotic results. Zavol’skii & Zaitsev (1984)
then investigated the physical meaning, and applicability, of the asymptotic one. In so doing
they but recovered an analysis by Dickinson (1969) who, as a particular case of acoustic-
gravity waves, i.e. internal waves coupled with acoustic waves by compressibility, had
performed a thorough asymptotic analysis of the Green’s function of Boussinesq impulsive
internal waves.
In a more general fashion a third series of studies have been devoted to the Green’s
function of acoustic-gravity waves and become, once the incompressible limit has been
applied to them, relevant to non-Boussinesq internal waves. Pierce (1963), by a shrewd
formulation of the radiation condition, Moore & Spiegel (1964), by Lighthill’s (1960)
asymptotic method, and Grigor’ev & Dokuchaev (1970), by the use of Fourier transforms,
independently obtained three coinciding expressions of the monochromatic Green’s function.
Kato (1966 a) made a more detailed examination of the equivalence of the first two
derivations. He later (Kato 1966 b) deduced from the group velocity theory, and Cole &
Greifinger (1969) from a stationary phase analysis, the wavefront structure of the impulsive
Green’s function. Then, Dickinson (1969) and Liu & Yeh (1971) derived the asymptotic
expansion of the associated waves while Row (1967) described a hydrostatic, that is low
frequency, approximation for them.
Internal wave generation. 1. Green’s function 5