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

CAPTIONS
Table 1. Compared structures of classical wave fields and Boussinesq gravity wave fields.
The characteristics of the latter are attributable to their wavelength
λg = 2π
Nt r
sin θ
Figure 1. Boussinesq internal waves radiated by a monochromatic point source oscillating
at frequency ω = N/2. Waves are confined on the characteristic cone of semi-
angle θ 0 = arc cos (ω/N), along which energy propagates with group velocity c g .
Surfaces of constant phase are parallel to the cone, and move perpendicular to it
with phase velocity c φ .
Figure 2. Boussinesq internal waves radiated by an impulsive point source. The conical
surfaces of constant phase Φ = Nt⏐cos θ⏐ = π/4 + nπ (n any integer), on which
the pressure and velocity fields are zero, are shown for Nt = 10π.
Figure 3. Wavenumber surface for non-Boussinesq internal waves of frequency ω = N/2.
The group velocity c g associated to a given wavevector k points along the
normal to this surface, out of the characteristic cone of semi-angle θ 0 = arc cos
(ω/N).
Internal wave generation. 1. Green’s function 57
Figure 4. Group velocity c g and phase velocity c φ of non-Boussinesq internal waves
generated by a monochromatic point source as a function of frequency ω, in a
direction making an angle θ = 60° with the vertical.
Figure 5. Coordinate system for internal wave radiation.
Figure 6. Branch cuts for the monochromatic Green’s function, and integration path for the
impulsive Green’s function.
Figure 7. Graphical determination of the frequencies ω s1 of gravity waves and ω s2 of
buoyancy oscillations, for propagation from a point source along a direction
inclined at θ = 60° to the vertical.
Figure 8. Regions for the validity of the Boussinesq approximation, for gravity (a torus of
radius 2Nt/β) and buoyancy (a cylinder with the same radius) waves.
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