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Beyond ray tracing for internal waves. II. Finite-amplitude effects
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10.1063/1.2993168
/content/aip/journal/pof2/20/10/10.1063/1.2993168
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.2993168
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The time evolution of the wave-induced mean flow, given by Eq. (8), for fully nonlinear numerical simulations of a horizontally compact wavepacket in uniform background stratification. The vertical coordinate is set to translate at the vertical group speed: . Wavepackets are initialized with , and , , and in the left, center, and right panels, respectively. The initial amplitudes are prescribed by (a) and (b) .

Image of FIG. 2.
FIG. 2.

Results of fully nonlinear numerical simulations of a wavepacket given initially by Eq. (10) impinging on an -barrier of width , as depicted by the gray center at . Wavepackets are initialized with , , and (a) and (b) . Grayscale contours are of the normalized vertical displacement field, , at , , and in the left, center, and right panels, respectively. The background wind moves with speed so that small-amplitude wavepackets should remain approximately centered in the horizontal.

Image of FIG. 3.
FIG. 3.

Horizontal slices of the normalized vertical displacement field, , at , for several simulations of a wavepacket impinging on an -barrier of width . Wavepackets are prescribed by Eq. (10) with . Profile (a) is taken at height for a wavepacket initialized with , , and . Profile (b) is the same as (a) except . Profile (c) is from a downward-propagating wavepacket at height with , , and .

Image of FIG. 4.
FIG. 4.

The wave-induced mean flow given by Eq. (8) at various times for fully nonlinear numerical simulations. The small- and large-amplitude simulations used in (a) and (b), respectively, are the same as those used in Fig. 2. The dashed lines in the right panels represent an idealized if the transmitted and reflected wavepackets retained Gaussian shapes.

Image of FIG. 5.
FIG. 5.

The wave-induced mean flow given by Eq. (8) at late times for three simulations with varying vertical wavenumbers. Wavepackets are initialized with (a) and , (b) and , and (c) and . In all simulations and . Profiles are taken at , , and in (a), (b), and (c), respectively. The dashed lines represent an idealized where the transmitted and reflected wavepackets are Gaussian.

Image of FIG. 6.
FIG. 6.

Wavepacket transmission values plotted against initial amplitude for horizontally localized wavepackets prescribed initially by Eq. (10) impinging on an -barrier of width . The computed transmission values are normalized by the linearly predicted transmission values for horizontal plane waves, , given by Eq. (2). Wavepackets are initialized with and (solid line), (dotted line), (dashed-dotted line), and (dashed line).

Image of FIG. 7.
FIG. 7.

As in Fig. 6 but plotting relative transmission against the relative vertical wavenumber for horizontally localized wavepackets with four different initial vertical displacement amplitudes, as indicated.

Image of FIG. 8.
FIG. 8.

Wavepacket transmission values through an -barrier of width plotted against (a) the horizontal and (b) the vertical extent of the wavepackets for values of the vertical wavenumber as indicated. Computed transmission values are normalized by the linearly predicted transmission values for horizontal plane waves, , given by Eq. (2). Wavepackets are initially prescribed by Eq. (10) with (or ) and in (a) while in (b) .

Image of FIG. 9.
FIG. 9.

Localized wavepacket transmission values plotted against -barrier depths for various initial amplitudes. Wavepackets are initially prescribed by Eq. (10) with and . The dashed line represents the linearly predicted transmission values for horizontal plane waves, , given by Eq. (2).

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/content/aip/journal/pof2/20/10/10.1063/1.2993168
2008-10-16
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Beyond ray tracing for internal waves. II. Finite-amplitude effects
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.2993168
10.1063/1.2993168
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