show that the width of wave beams decreases as the shore is approached. Formally,
in the linear statement, the width of the reflected IGW beam can be arbitrarily small
for appropriate relations between the medium parameters (stratification, the ocean
floor slope angle); hence, a significant local intensification of waves occurs near the
ocean shore. It is clear that in the real ocean, the wave field energy remains finite in
such spatial domains due to the action of nonlinear mechanisms of dissipation and
turbulent mixing [1].
Conclusions
Thus, in the first section of the paper, a general method for calculating IGW fields in
the horizontally inhomogeneous ocean is outlined, namely,
• for an arbitrary distribution of the Brunt-Väisälä frequency, the basic vertical
spectral IGW problem is solved and the corresponding normalized eigenfunctions and eigenvalues are determined;
• the characteristic systems with appropriate initial conditions are solved
numerically;
• after the characteristics (rays) are calculated, the eikonal (phase value) of the
phase functions is determined by numerical integration along these rays;
• the geometric divergence of the ray tubes is determined, for example, by
numerical differentiation of closely located characteristics;
• the IGW amplitude is calculated from the equations of the corresponding conservation laws along the rays (characteristics), in which the right parts of the
relations are determined by using the locality principle, i.e., it is assumed that
the ocean parameters remain horizontally unchanged over specific spatial
intervals. Thus, it is assumed that the ocean is horizontally homogeneous on
these space-time scales, and its density arbitrarily depends on the vertical
coordinate.
The solutions obtained in the second section of the paper are exact and exhibit
typical ray pattern of the IGW fields in the stratified ocean of variable depth
obtained without using the mathematical methods of geometrical optics.
The universal character of the proposed asymptotic methods of modeling IGW
fields in the ocean allows us to efficiently calculate the wave fields and, in addition,
analyze qualitatively the solutions. This opens wide opportunities for investigating
the wave fields in general, which is also important for formulating correct statements of mathematical models of wave dynamics and for obtaining express evaluations in the field measurements of internal waves.
Internal Gravity Waves in Horizontally Inhomogeneous Ocean
125
in the linear statement, the width of the reflected IGW beam can be arbitrarily small
for appropriate relations between the medium parameters (stratification, the ocean
floor slope angle); hence, a significant local intensification of waves occurs near the
ocean shore. It is clear that in the real ocean, the wave field energy remains finite in
such spatial domains due to the action of nonlinear mechanisms of dissipation and
turbulent mixing [1].
Conclusions
Thus, in the first section of the paper, a general method for calculating IGW fields in
the horizontally inhomogeneous ocean is outlined, namely,
• for an arbitrary distribution of the Brunt-Väisälä frequency, the basic vertical
spectral IGW problem is solved and the corresponding normalized eigenfunctions and eigenvalues are determined;
• the characteristic systems with appropriate initial conditions are solved
numerically;
• after the characteristics (rays) are calculated, the eikonal (phase value) of the
phase functions is determined by numerical integration along these rays;
• the geometric divergence of the ray tubes is determined, for example, by
numerical differentiation of closely located characteristics;
• the IGW amplitude is calculated from the equations of the corresponding conservation laws along the rays (characteristics), in which the right parts of the
relations are determined by using the locality principle, i.e., it is assumed that
the ocean parameters remain horizontally unchanged over specific spatial
intervals. Thus, it is assumed that the ocean is horizontally homogeneous on
these space-time scales, and its density arbitrarily depends on the vertical
coordinate.
The solutions obtained in the second section of the paper are exact and exhibit
typical ray pattern of the IGW fields in the stratified ocean of variable depth
obtained without using the mathematical methods of geometrical optics.
The universal character of the proposed asymptotic methods of modeling IGW
fields in the ocean allows us to efficiently calculate the wave fields and, in addition,
analyze qualitatively the solutions. This opens wide opportunities for investigating
the wave fields in general, which is also important for formulating correct statements of mathematical models of wave dynamics and for obtaining express evaluations in the field measurements of internal waves.
Internal Gravity Waves in Horizontally Inhomogeneous Ocean
125