Shoaling of an Internal Wave Packet in an almost Three-Layer Sea over a Steep Shelf

We derive a higher order nonlinear evolution equation for a broader bandwidth three-dimensional capillary–gravity wave packet, in the presence of a surface current produced by an internal wave. Instead of a set of coupled equations, a single nonlinear evolution equation is obtained by eliminating the velocity potential for the wave-induced slow motion. Finally, the equation is expressed in an integro-differential equation form, similar to Zakharov’s integral equation. Using the evolution equation derived here, we show that the two sidebands of a surface capillary–gravity wave get excited as a result of resonance with an internal wave, all propagating in the same direction. It is also shown that surface waves can grow exponentially with time at the expense of the energy of the internal wave.

Download Full-text

Observation and interpretation of a high-frequency internal wave packet and surface slick pattern

Journal of Geophysical Research Atmospheres ◽

10.1029/jc080i006p00882 ◽

1975 ◽

Vol 80 (6) ◽

pp. 882-894 ◽

Cited By ~ 18

Author(s):

Thomas B. Curtin ◽

Christopher N. K. Mooers

Keyword(s):

Wave Packet ◽

Internal Wave ◽

High Frequency

Download Full-text

Mean flow generated by an internal wave packet impinging on the interface between two layers of fluid with continuous density

Theoretical and Computational Fluid Dynamics ◽

10.1007/s00162-008-0078-1 ◽

2008 ◽

Vol 22 (2) ◽

pp. 107-123 ◽

Cited By ~ 7

Author(s):

John P. McHugh

Keyword(s):

Wave Packet ◽

Internal Wave ◽

Mean Flow ◽

Continuous Density

Download Full-text

Internal waves detected with a continental shelf current-meter array

Marine and Freshwater Research ◽

10.1071/mf9810001 ◽

1981 ◽

Vol 32 (1) ◽

pp. 1 ◽

Cited By ~ 6

Author(s):

GR Cresswell

Keyword(s):

Shear Flow ◽

Wave Packet ◽

Continental Shelf ◽

Internal Wave ◽

Internal Waves ◽

Temperature Structure ◽

M Current

A 1-km square current-meter array at 130 m depth on the Sydney continental shelf revealed an internal wave packet at 100 m depth propagating coastward at 0.5 m s-1 with a period of c. 15 min and a wavelength of c. 400 m. Current meters at 35 and 70 m depth on one mooring showed what was possibly an independent packet that was detected 20 min before the deeper one and that showed depressions of the temperature structure (of 20 m) and shear flow between the two meters.

Download Full-text

Anelastic Internal Wave Packet Evolution and Stability

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-11-097.1 ◽

2011 ◽

Vol 68 (12) ◽

pp. 2844-2859 ◽

Cited By ~ 19

Author(s):

Hayley V. Dosser ◽

Bruce R. Sutherland

Keyword(s):

Nonlinear Dynamics ◽

Growth Rate ◽

Wave Packet ◽

Internal Wave ◽

Internal Gravity Wave ◽

Nonlinear Effects ◽

Mean Flow ◽

Weakly Nonlinear ◽

Stability And Instability ◽

Anelastic Equations

Abstract As upward-propagating anelastic internal gravity wave packets grow in amplitude, nonlinear effects develop as a result of interactions with the horizontal mean flow that they induce. This qualitatively alters the structure of the wave packet. The weakly nonlinear dynamics are well captured by the nonlinear Schrödinger equation, which is derived here for anelastic waves. In particular, this predicts that strongly nonhydrostatic waves are modulationally unstable and so the wave packet narrows and grows more rapidly in amplitude than the exponential anelastic growth rate. More hydrostatic waves are modulationally stable and so their amplitude grows less rapidly. The marginal case between stability and instability occurs for waves propagating at the fastest vertical group velocity. Extrapolating these results to waves propagating to higher altitudes (hence attaining larger amplitudes), it is anticipated that modulationally unstable waves should break at lower altitudes and modulationally stable waves should break at higher altitudes than predicted by linear theory. This prediction is borne out by fully nonlinear numerical simulations of the anelastic equations. A range of simulations is performed to quantify where overturning actually occurs.

Download Full-text