Trapped internal gravity waves in a geostrophic boundary current

1993 ◽  
Vol 247 ◽  
pp. 205-229
Author(s):  
Hong Ma
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Combined Effects ◽  
Kelvin Wave ◽  
Boundary Current ◽  
Trapping Mechanism ◽  
Rossby Radius Of Deformation ◽  
Wave Guides ◽  
Internal Kelvin Wave

The effect of a geostrophic boundary current on internal gravity waves is studied with a reduced-gravity model. We found that the boundary current not only modifies the coastal Kelvin wave, but also forms wave guides for short internal gravity waves. The combined effects of current shear, the boundary, and the slope of the interface create the trapping mechanism. These trapped internal gravity waves appear as groups of discrete zonal modes. They have wavelengths comparable to or shorter than the internal Rossby radius of deformation. Their phase speeds are close to that of the internal Kelvin wave. However, they can propagate both in, or opposite to, the direction of the Kelvin wave. The results of the present work suggest the possibility of finding an energetic internal gravity wave phenomenon with near-inertial frequency in a broad geostrophic boundary current.

scholarly journals Observations of Near-Inertial Internal Gravity Waves Radiating from a Frontal Jet

2013 ◽  
Vol 43 (6) ◽  
pp. 1225-1239 ◽  
Author(s):  
Matthew H. Alford ◽  
Andrey Y. Shcherbina ◽  
Michael C. Gregg
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Shear Layers ◽  
Adjustment Process ◽  
Vertical Wavelength ◽  
The North ◽  
Inertial Wave ◽  
The North Pacific

Abstract Shipboard ADCP and towed CTD measurements are presented of a near-inertial internal gravity wave radiating away from a zonal jet associated with the Subtropical Front in the North Pacific. Three-dimensional spatial surveys indicate persistent alternating shear layers sloping downward and equatorward from the front. As a result, depth-integrated ageostrophic shear increases sharply equatorward of the front. The layers have a vertical wavelength of about 250 m and a slope consistent with a wave of frequency 1.01f. They extend at least 100 km south of the front. Time series confirm that the shear is associated with a downward-propagating near-inertial wave with frequency within 20% of f. A slab mixed layer model forced with shipboard and NCEP reanalysis winds suggests that wind forcing was too weak to generate the wave. Likewise, trapping of the near-inertial motions at the low-vorticity edge of the front can be ruled out because of the extension of the features well south of it. Instead, the authors suggest that the wave arises from an adjustment process of the frontal flow, which has a Rossby number about 0.2–0.3.

Numerical Investigation of Mechanisms Underlying Oceanic Internal Gravity Wave Power-Law Spectra

2020 ◽  
Vol 50 (9) ◽  
pp. 2713-2733
Author(s):  
Yulin Pan ◽  
Brian K. Arbic ◽  
Arin D. Nelson ◽  
Dimitris Menemenlis ◽  
W. R. Peltier ◽  
...  
Keyword(s):  
Power Law ◽  
Gravity Waves ◽  
High Frequency ◽  
Internal Gravity Wave ◽  
Numerical Data ◽  
Field Measurements ◽  
Internal Gravity Waves ◽  
Collision Integral ◽  
Turbulence Theory ◽  
Nonlinear Interactions

AbstractWe consider the power-law spectra of internal gravity waves in a rotating and stratified ocean. Field measurements have shown considerable variability of spectral slopes compared to the high-wavenumber, high-frequency portion of the Garrett–Munk (GM) spectrum. Theoretical explanations have been developed through wave turbulence theory (WTT), where different power-law solutions of the kinetic equation can be found depending on the mechanisms underlying the nonlinear interactions. Mathematically, these are reflected by the convergence properties of the so-called collision integral (CL) at low- and high-frequency limits. In this work, we study the mechanisms in the formation of the power-law spectra of internal gravity waves, utilizing numerical data from the high-resolution modeling of internal waves (HRMIW) in a region northwest of Hawaii. The model captures the power-law spectra in broad ranges of space and time scales, with scalings ω−2.05±0.2 in frequency and m−2.58±0.4 in vertical wavenumber. The latter clearly deviates from the GM76 spectrum but is closer to a family of induced-diffusion-dominated solutions predicted by WTT. Our analysis of nonlinear interactions is performed directly on these model outputs, which is fundamentally different from previous work assuming a GM76 spectrum. By applying a bicoherence analysis and evaluations of modal energy transfer, we show that the CL is dominated by nonlocal interactions between modes in the power-law range and low-frequency inertial motions. We further identify induced diffusion and the near-resonances at its spectral vicinity as dominating the formation of power-law spectrum.

An experimental study of the free evolution of rotating, nonlinear internal gravity waves in a two-layer stratified fluid

2014 ◽  
Vol 742 ◽  
pp. 308-339 ◽  
Author(s):  
Hugo N. Ulloa ◽  
Alberto de la Fuente ◽  
Yarko Niño
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Internal Gravity Waves ◽  
Kelvin Wave ◽  
Nonlinear Processes ◽  
Transfer Energy ◽  
Type Wave ◽  
Basin Scale ◽  
Layer Flow

AbstractThe temporal evolution of nonlinear large-scale internal gravity waves, in a two-layer flow affected by background rotation, is studied via laboratory experiments conducted in a cylindrical tank, mounted on a rotating turntable. The internal wave field is excited by the relaxation of an initial forced tilt of the density interface ($\eta _{i}$), which generates internal waves, such as Kelvin and Poincaré waves, in response to rotation effects. The behaviour of $\eta _{i}$, in the shore region, is analysed in terms of the background rotation and the nonlinear steepening of the basin-scale waves. The results show that the degeneration of the fundamental Kelvin wave into a solitary-type wave packet is caused by nonlinear steepening and it is influenced by the background rotation. In addition, the physical scales of the leading solitary-type wave are closer to Korteweg–de Vries theory as the rotation increases. Moreover, the nonlinear interaction between the Kelvin wave and the Poincaré wave can transfer energy to higher or lower frequencies than the frequency of the fundamental Kelvin wave, as a function of the background rotation. In particular, a specific normal mode in the off-shore region could be energized by this interaction. Finally, the bulk decay rate of the fundamental Kelvin wave, $\tau _{dk}$, was investigated. The results exhibit that $\tau _{dk}$ is concordant with the Ekman damping time scale when there is no evidence of steepening in the basin-scale waves. However, as nonlinear processes increase, $\tau _{dk}$ shows a strong decrease. In this context, the nonlinear processes play an important role in the decay of the fundamental Kelvin wave, via the energy radiation to other modes. The results reported demonstrate that the background rotation and nonlinear processes are essential aspects in understanding the degeneration and the decay of large-scale internal gravity waves on enclosed basins.

scholarly journals Analysis of internal gravity waves with GPS RO density profiles

2014 ◽  
Vol 7 (12) ◽  
pp. 4123-4132 ◽  
Author(s):  
P. Šácha ◽  
U. Foelsche ◽  
P. Pišoft
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Atmospheric Density ◽  
Retrieval Process ◽  
Density Profiles ◽  
Height Range ◽  
Upper Troposphere ◽  
The Past

Abstract. GPS radio occultation (RO) data have proved to be a great tool for atmospheric monitoring and studies. In the past decade, they were frequently used for analyses of the internal gravity waves in the upper troposphere and lower stratosphere region. Atmospheric density is the first quantity of state gained in the retrieval process and is not burdened by additional assumptions. However, there are no studies elaborating in detail the utilization of GPS RO density profiles for gravity wave analyses. In this paper, we introduce a method for density background separation and a methodology for internal gravity wave analysis using the density profiles. Various background choices are discussed and the correspondence between analytical forms of the density and temperature background profiles is examined. In the stratosphere, a comparison between the power spectrum of normalized density and normalized dry temperature fluctuations confirms the suitability of the density profiles' utilization. In the height range of 8–40 km, results of the continuous wavelet transform are presented and discussed. Finally, the limits of our approach are discussed and the advantages of the density usage are listed.

On the interaction between internal gravity waves and a shear flow

1968 ◽  
Vol 34 (4) ◽  
pp. 711-720 ◽  
Author(s):  
C. J. R. Garrett
Keyword(s):  
Wave Propagation ◽  
Stress Tensor ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Basic Flow ◽  
Radiation Stress ◽  
Interaction Stress ◽  
The Waves ◽  
Uniform Plane

The theory of wave action conservation is summarized, and its interpretation in terms of the working, against the rate of strain of the basic flow, of an interaction stress associated with the waves is discussed. Usually this interaction stress is identical with the radiation stress of a uniform plane wave. The problem of internal gravity wave propagation in an incompressible, stratified Boussinesq liquid is considered in detail for a more general basic flow than has hitherto been treated, and the interaction stress is derived. One component of the interaction stress tensor is only equal to the corresponding component of the radiation stress tensor if we include in the latter, in addition to the Reynolds stress, a term associated with the redistribution of matter, on the average, by the wave. Two other components of the radiation stress tensor are modified in a similar manner, but the corresponding components of the interaction stress tensor are undefined, and so no comparison is possible.

An explicit potential-vorticity-conserving approach to modelling nonlinear internal gravity waves

2002 ◽  
Vol 458 ◽  
pp. 75-101 ◽  
Author(s):  
ÁLVARO VIÚDEZ ◽  
DAVID G. DRITSCHEL
Keyword(s):  
Gravity Waves ◽  
Potential Vorticity ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Numerical Approach ◽  
Internal Gravity Waves ◽  
Static Stability ◽  
Three Dimensions ◽  
Fluid Particles ◽  
Monge Ampere

This paper discusses a potential-vorticity-conserving approach to modelling nonlinear internal gravity waves in a rotating Boussinesq fluid. The focus of the work is on the pseudo-plane motion (motion in the x, z-plane), for which we present a broad range of numerical results. In this case there are two material coordinates, the density and the y-component of the velocity in the inertial frame of reference, which are related to the x and z displacements of fluid particles relative to a reference configuration. The amount of potential vorticity within a fluid region bounded by isosurfaces of these material coordinates is proportional to the area within this region, and is therefore conserved as well. Two new potentials, defined in terms of the displacements and combining the vorticity and density fields, are introduced as new dependent variables. These potentials entirely govern the dynamics of internal gravity waves for the linearized system when the basic state has uniform potential vorticity. The final system of equations consists of three prognostic equations (for the potential vorticity and the Laplacians of the two potentials) and one diagnostic equation, of Monge–Ampère type, for a third potential. This diagnostic equation arises from the nonlinear definition of potential vorticity. The ellipticity of the Monge–Ampère equation implies both inertial and static stability. In three dimensions, the three potentials form a vector, whose (three-dimensional) Laplacian is equal to the vorticity plus the gradient of the perturbation density.Numerical simulations are carried out using a novel algorithm which directly evolves the potential vorticity, in a Lagrangian manner (following fluid particles), without diffusion. We present results which emphasize the way in which potential vorticity anomalies modify the characteristics of internal gravity waves, e.g. the propagation of internal wave packets, including reflection, refraction, and amplification. We also show how potential vorticity anomalies may generate internal gravity waves, along with the subsequent ‘geostrophic adjustment’ of the flow to a ‘balanced’ wave-less state. These examples, and the straightforward extension of the theoretical and numerical approach to three dimensions, point to a direct and accurate means to elucidate the role of potential vorticity in internal gravity wave interactions. As such, this approach may help a better understanding of the observed characteristics of internal gravity waves in the oceans.

A general method for solving steady-state internal gravity wave problems

1972 ◽  
Vol 56 (4) ◽  
pp. 721-740 ◽  
Author(s):  
D. G. Hurley
Keyword(s):  
Steady State ◽  
Circular Cylinder ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Two Dimensional ◽  
Wave Problem ◽  
Wave Problems ◽  
General Method ◽  
Stratified Liquid

The paper describes a simple but general method for solving 'steady-state’ problems involving internal gravity waves in a stably stratified liquid. Under the assumption that the motion is two-dimensional and that the Brunt-Väisälä frequency is constant, the method is used to re-derive in a very simple way the solutions to problems where the boundary of the liquid is either a wedge or a circular cylinder. The method is then used to investigate the effect that a model of the continental shelf has on an incident train of internal gravity waves. The method involves analytic continuation in the frequency of the disturbance, and may well prove to be effective for other types of wave problem.

Spatial and temporal analysis of high-frequency internal gravity wave signatures in brightness temperature satellite images

2021 ◽  
Author(s):  
Robert Vicari
Keyword(s):  
Water Vapor ◽  
Brightness Temperature ◽  
Gravity Wave ◽  
Gravity Waves ◽  
High Frequency ◽  
Satellite Images ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Small Scale ◽  
Wave Patterns

<p>Highly idealized model studies suggest that convectively generated internal gravity waves in the troposphere with horizontal wavelengths on the order of a few kilometers may affect the lifetime, spacing, and depth of clouds and convection. To answer whether such a convection-wave coupling occurs in the real atmosphere, one needs to find corresponding events in observations. In general, the study of high-frequency internal gravity wave-related phenomena in the troposphere is a challenging task because they are usually small-scale and intermittent. To overcome case-by-case studies, it is desirable to have an automatic method to analyze as much data as possible and provide enough independent and diverse evidence.<br>Here, we focus on brightness temperature satellite images, in particular so-called satellite water vapor channels. These channels measure the radiation at wavelengths corresponding to the energy emitted by water vapor and provide cloud-independent observations of internal gravity waves, in contrast to visible and other infrared satellite channels where one relies on the wave impacts on clouds. In addition, since these water vapor channels are sensitive to certain vertical layers in the troposphere, combining the images also reveals some vertical structure of the observed waves.<br>We propose an algorithm based on local Fourier analyses to extract information about high-frequency wave patterns in given brightness temperature images. This method allows automatic detection and analysis of many wave patterns in a given domain at once, resulting in a climatology that provides an initial observational basis for further research. Using data from the instrument ABI on board the satellite GOES-16 during the field campaign EUREC<sup>4</sup>A, we demonstrate the capabilities and limitations of the method. Furthermore, we present the respective climatology of the detected waves and discuss approaches based on this to address the initial question.</p>

On strongly nonlinear gravity waves in a vertically sheared atmosphere

2021 ◽  
Author(s):  
Georg Sebastian Voelker ◽  
Mark Schlutow
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Mean Flow ◽  
Flow Strength ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
The Mean

<p>Internal gravity waves are a well-known mechanism of energy redistribution in stratified fluids such as the atmosphere. They may propagate from their generation region, typically in the Troposphere, up to high altitudes. During their lifetime internal waves couple to the atmospheric background through various processes. Among the most important interactions are the exertion of wave drag on the horizontal mean-flow, the heat generation upon wave breaking, or the mixing of atmospheric tracers such as aerosols or greenhouse gases.</p><p>Many of the known internal gravity wave properties and interactions are covered by linear or weakly nonlinear theories. However, for the consideration of some of the crucial effects, like a reciprocal wave-mean-flow interaction including the exertion of wave drag on the mean-flow, strongly nonlinear systems are required. That is, there is no assumption on the wave amplitude relative to the mean-flow strength such that they may be of the same order.</p><p>Here, we exploit a strongly nonlinear Boussinesq theory to analyze the stability of a stationary internal gravity wave which is refracted at the vertical edge of a horizontal jet. Thereby we assume that the incident wave is horizontally periodic, non-hydrostatic, and vertically modulated. Performing a linear stability analysis in the vicinity of the jet edge we find necessary and sufficient criteria for instabilities to grow. In particular, the refracted wave becomes unstable if its incident amplitude is large enough and both mean-flow horizontal winds, below and above the edge of the jet, do not exceed particular upper bounds.</p>

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