Beyond ray tracing for internal waves. II. Finite-amplitude effects

Brown, Geoffrey L.; Bush, Andrew B. G.; Sutherland, Bruce

doi:10.1063/1.2993168

Cited by 9 publications

(10 citation statements)

References 22 publications

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“… Sutherland [1996, 1999, 2000] numerically investigated the reflection and transmission of internal waves under the wave propagation distance smaller than the density scale height by using a set of nonlinear 2‐D motion equations which showed that if the amplitude of wave packet was large, nonlinear effects could significantly enhanced the transmission of wave packet across the reflecting level as a result of the effective mean flow induced by the wave. For finite‐amplitude waves in a nonuniformly stratified fluid, the simulation showed that the transmission coefficient exhibits a monotonic increase as a function of the incident wave amplitude but little dependence on the wavepacket extent [ Brown et al , 2008]. However, the nonlinear physical process of atmospheric gravity wave reflection in the atmospheric jets is not quite clear.…”

Section: Introductionmentioning

confidence: 99%

Reflection and transmission of atmospheric gravity waves in a stably sheared horizontal wind field

2010

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[1] Applying a second-order fully nonlinear numerical scheme, we have investigated the characteristics of reflection and transmission of atmospheric gravity wave packets in a vertically sheared horizontal wind. When the leading edge of incident wave arrives at the reflecting level predicted by the linear theory, the wave reflection begins to occur. In the reflection process, the reflection and incident waves are superposed with obvious phase staggering, which is different from the wave reflection in a meridionally sheared horizontal wind. In the evanescent region, the wave phase has only weak variation; the wave amplitude decays with the sheared wind growth and vice versa, which is in good agreement with the evanescent wave configuration predicted by the linear theory. Some spectral components of the incident wave can penetrate through the evanescent region and produce a transmitted wave. Both the reflection and transmission coefficients slightly decrease with the moderate increase of the initial amplitude of the incident wave, which is because a large-amplitude wave can induce a strong mean flow; moreover, the waveinduced mean flow plays a more significant role in transferring the energy from the waves to the background flow than in enhancing the transmission of the waves. This is distinguished from the wave reflection in a sheared flow under the wave propagation distance smaller than the density scale height, in which the mean flow induced by a largeramplitude wave significantly strengthens the transmission of the wave. The simulation shows that the reflection loop predicted by the linear theory is not a common phenomenon in the wave reflection. Several groups of simulated cases indicate that the reflection and transmission coefficients depend on not only the amplitude, frequency, and wavenumbers of the incident wave but also the strength and thickness of the evanescent region. The reflection coefficient increases but the transmission coefficient decreases with the relative evanescent thickness growth, and once the strength and thickness of the evanescent region are large enough, the wave hardly penetrates through the sheared wind zone, and the reflection coefficient approaches a constant value, too. Except for the disappearance of the evanescent region, the total sum of the reflection and transmission coefficients of the wave pseudoenergy flux is slightly <1 because of the interaction between the wave and flow. These results suggest that the effects of wave reflection and transmission should be correctly included in the parameterization of gravity waves to attain more realistic middle atmospheric climatology from general circulation models.

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Section: Introductionmentioning

confidence: 99%

Reflection and transmission of atmospheric gravity waves in a stably sheared horizontal wind field

2010

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“…This analytic study was extended to examine the influence of shear [17]. Further numerical studies examined the transmission of waves through more complex stratification [18][19][20][21][22] and large-amplitude effects were also considered [23]. However, in all these studies except Ref.…”

Section: Introductionmentioning

confidence: 99%

Internal wave transmission through a thermohaline staircase

Sutherland

2016

Phys. Rev. Fluids

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With the aim to predict energy transport by internal waves incident upon observed density staircases in the ocean, the theory for internal wave tunneling through a single finite-size mixed region is extended to predict the transmission of internal waves through a piecewise-constant density profile with an arbitrary number of steps. An analytic solution is found if all steps have equal vertical extent. From this solution, bounds are established for the relative incident horizontal wave number and frequency of waves that have negligible transmission, a result that is independent of the number of steps. If the step sizes vary randomly about a mean vertical extent, the transmission can be computed numerically for several random realizations. Provided the horizontal wavelength is much longer than the total vertical extent of the staircase, the standard deviation of the computed transmission coefficients is small and the mean agrees well with the analytic prediction for equally spaced steps. The results are applied to thermohaline staircases observed in the ocean in order to put lower bounds on the wavelengths of long inertia gravity waves that significantly transmit to great depth.

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“…Finally, the parameters of the sponge layer are L sponge ¼ 5 m and s sponge ¼ 500 s for the layer length scale and decay time scale (26). We omit the upper and lower 25 m (192 grid points) of the domain from our analysis (Fig.…”

Section: A Model Setupmentioning

confidence: 99%

“…Therefore, we follow a similar procedure as in Ref. 26 and modify the initial velocity field so that the total horizontal momentum of the wave group times the vertical component of the group velocity is equal to the net momentum flux of the wave group. This is equivalent to adding an approximation of the pseudomomentum to the velocity at every point.…”

Section: B Initial Conditionsmentioning

confidence: 99%

Breaking internal wave groups: Mixing and momentum fluxes

Birch

Sundermeyer

2011

Physics of Fluids

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Breaking groups of large-amplitude internal gravity waves are simulated numerically and the resulting diapycnal mixing and residual momentum are quantified. The wave frequency strongly affects the mixing, with high-and low-frequency waves doing many times more mixing than intermediate-frequency waves with the same steepness. The total residual momentum remaining in the breaking region after the remnants of the wave group propagates away shows similar frequency dependence as the diapycnal mixing. Additionally, the propagation of the breaking events and the spatial distribution of the mixing are found to agree qualitatively with a kinematic description of breaking internal wave groups.

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Beyond ray tracing for internal waves. II. Finite-amplitude effects

Cited by 9 publications

References 22 publications

Reflection and transmission of atmospheric gravity waves in a stably sheared horizontal wind field

Reflection and transmission of atmospheric gravity waves in a stably sheared horizontal wind field

Internal wave transmission through a thermohaline staircase

Breaking internal wave groups: Mixing and momentum fluxes

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