scholarly journals Wave–vortex decomposition of one-dimensional ship-track data

2014 ◽  
Vol 756 ◽  
pp. 1007-1026 ◽  
Author(s):  
Oliver Bühler ◽  
Jörn Callies ◽  
Raffaele Ferrari
Keyword(s):  
Energy Spectrum ◽  
Gravity Waves ◽  
Horizontal Velocity ◽  
Data Sets ◽  
Step Method ◽  
One Dimensional ◽  
Additional Information ◽  
Geostrophic Balance ◽  
The North ◽  
Inertia Gravity Waves

AbstractWe present a simple two-step method by which one-dimensional spectra of horizontal velocity and buoyancy measured along a ship track can be decomposed into a wave component consisting of inertia–gravity waves and a vortex component consisting of a horizontal flow in geostrophic balance. The method requires certain assumptions for the data regarding stationarity, homogeneity, and horizontal isotropy. In the first step an exact Helmholtz decomposition of the horizontal velocity spectra into rotational and divergent components is performed and in the second step an energy equipartition property of hydrostatic inertia–gravity waves is exploited that allows a diagnosis of the wave energy spectrum solely from the observed horizontal velocities. The observed buoyancy spectrum can then be used to compute the residual vortex energy spectrum. Further wave–vortex decompositions of the observed fields are possible if additional information about the frequency content of the waves is available. We illustrate the method on two recent oceanic data sets from the North Pacific and the Gulf Stream. Notably, both steps in our new method might be of broader use in the theoretical and observational study of atmosphere and ocean fluid dynamics.

On the appearance of inertia-gravity waves on the north-easterly side of an anticyclone

2003 ◽  
Vol 12 (1) ◽  
pp. 25-35 ◽  
Author(s):  
Dieter Peters ◽  
Peter Hoffmann ◽  
Matthias Alpers
Keyword(s):  
Gravity Waves ◽  
The North ◽  
Inertia Gravity Waves

scholarly journals The Mesoscale Kinetic Energy Spectrum of a Baroclinic Life Cycle

2009 ◽  
Vol 66 (4) ◽  
pp. 883-901 ◽  
Author(s):  
Michael L. Waite ◽  
Chris Snyder
Keyword(s):  
Life Cycle ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Linear Instability ◽  
Mature Stage ◽  
Flux Divergence ◽  
Full Spectrum ◽  
Kinetic Energy Spectrum ◽  
Inertia Gravity Waves

Abstract The atmospheric mesoscale kinetic energy spectrum is investigated through numerical simulations of an idealized baroclinic wave life cycle, from linear instability to mature nonlinear evolution and with high horizontal and vertical resolution (Δx ≈ 10 km and Δz ≈ 60 m). The spontaneous excitation of inertia–gravity waves yields a shallowing of the mesoscale spectrum with respect to the large scales, in qualitative agreement with observations. However, this shallowing is restricted to the lower stratosphere and does not occur in the upper troposphere. At both levels, the mesoscale divergent kinetic energy spectrum—a proxy for the inertia–gravity wave energy spectrum—resembles a −5/3 power law in the mature stage. Divergent kinetic energy dominates the lower stratospheric mesoscale spectrum, accounting for its shallowing. Rotational kinetic energy, by contrast, dominates the upper tropospheric spectrum and no shallowing of the full spectrum is observed. By analyzing the tendency equation for the kinetic energy spectrum, it is shown that the lower stratospheric spectrum is not governed solely by a downscale energy cascade; rather, it is influenced by the vertical pressure flux divergence associated with vertically propagating inertia–gravity waves.

The spontaneous generation of inertia–gravity waves during frontogenesis forced by large strain: theory

2014 ◽  
Vol 757 ◽  
pp. 817-853 ◽  
Author(s):  
Callum J. Shakespeare ◽  
J. R. Taylor
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Large Strain ◽  
Finite Amplitude ◽  
Spontaneous Generation ◽  
Time Varying ◽  
Geostrophic Balance ◽  
Wave Emission ◽  
Large Scale Flow ◽  
Inertia Gravity Waves

AbstractDensity fronts are common features of ocean and atmosphere boundary layers. Field observations and numerical simulations have shown that the sharpening of frontal gradients, or frontogenesis, can spontaneously generate inertia–gravity waves (IGWs). Although significant progress has been made in describing frontogenesis using approximations such as quasi-geostrophy (Stone, J. Atmos. Sci., vol. 23, 1966, pp. 455–565, Williams & Plotkin J. Atmos. Sci., vol. 25, 1968, pp. 201–206) semi-geostrophy (Hoskins, Annu. Rev. Fluid Mech., vol. 14, 1982, pp. 131–151), these models omit waves. Here, we further develop the analytical model of Shakespeare & Taylor (J. Fluid Mech., vol. 736, 2013, pp. 366–413) to describe the spontaneous emission of IGWs from an initially geostrophically balanced front subjected to a time-varying horizontal strain. The model uses the idealised configuration of an infinitely long, straight front and uniform potential vorticity (PV) fluid, with a uniform imposed convergent strain across the front, similar to Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp. 11–37). Inertia–gravity waves are generated via two distinct mechanisms: acceleration of the large-scale flow and frontal collapse. Wave emission via frontal collapse is predicted to be exponentially small for small values of strain but significant for larger strains. Time-varying strain can also generate finite-amplitude waves by accelerating the cross-front flow and disrupting geostrophic balance. In both cases waves are trapped by the oncoming strain flow and can only propagate away from the frontal zone when the strain field weakens sufficiently, leading to wave emission that is strongly localised in both time and space.

scholarly journals Diffusion of inertia-gravity waves by geostrophic turbulence

2019 ◽  
Vol 869 ◽  
Author(s):  
Hossein A. Kafiabad ◽  
Miles A. C. Savva ◽  
Jacques Vanneste
Keyword(s):  
Energy Spectrum ◽  
Gravity Waves ◽  
Wave Energy ◽  
Large Scale ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Constant Frequency ◽  
Geostrophic Turbulence ◽  
Wave Energy Spectrum ◽  
Inertia Gravity Waves

The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumber diffusion results in a $k^{-2}$ wave energy spectrum consistent with as-yet-unexplained features of observed atmospheric and oceanic spectra.

scholarly journals Investigation of inertia-gravity waves in the upper troposphere/lower stratosphere over northern Germany observed with collocated VHF/UHF radars

2004 ◽  
Vol 4 (4) ◽  
pp. 4339-4381 ◽  
Author(s):  
A. Serafimovich ◽  
P. Hoffmann ◽  
D. Peters ◽  
V. Lehmann
Keyword(s):  
Gravity Waves ◽  
Lower Stratosphere ◽  
Wave Parameter ◽  
Data Sets ◽  
Northern Germany ◽  
Vhf Radar ◽  
Upper Troposphere ◽  
Rossby Wave Breaking ◽  
Uhf Wind Profiler ◽  
Inertia Gravity Waves

Abstract. A case study to investigate the properties of inertia-gravity waves in the upper troposphere/lower stratosphere has been carried out over Northern Germany during the occurrence of an upper tropospheric jet in connection with a poleward Rossby wave breaking event from 17-19 December 1999. The investigations are based on continuous radar measurements with the OSWIN VHF radar at Kühlungsborn (54.1° N, 11.8° E) and the 482 MHz UHF wind profiler at Lindenberg (52.2° N, 14.1° E). Both radars are separated by about 265 km. Based on wavelet transformations of both data sets, the dominant vertical wavelengths of about 2–4 km for fixed times as well as the dominant observed periods of about 11 h for the altitude range between 5 and 8 km are comparable. Gravity wave parameter have been estimated at both locations separately and by a complex cross-spectral analysis of the data of both radars. The results show the appearance of dominating inertia-gravity waves with characteristic horizontal wavelengths between 600 and 300 km moving in the opposite direction than the mean background wind and a secondary less pronounced wave with a horizontal wavelength in the order of about 200 km moving with the wind. Temporal and spatial differences of the observed waves are discussed.

scholarly journals Investigation of inertia-gravity waves in the upper troposphere/lower stratosphere over Northern Germany observed with collocated VHF/UHF radars

2005 ◽  
Vol 5 (2) ◽  
pp. 295-310 ◽  
Author(s):  
A. Serafimovich ◽  
P. Hoffmann ◽  
D. Peters ◽  
V. Lehmann
Keyword(s):  
Gravity Waves ◽  
Lower Stratosphere ◽  
Data Sets ◽  
Northern Germany ◽  
Vhf Radar ◽  
Upper Troposphere ◽  
Rossby Wave Breaking ◽  
Spatial Differences ◽  
Uhf Wind Profiler ◽  
Inertia Gravity Waves

Abstract. A case study to investigate the properties of inertia-gravity waves in the upper troposphere/lower stratosphere has been carried out over Northern Germany during the occurrence of an upper tropospheric jet in connection with a poleward Rossby wave breaking event from 17-19 December 1999. The investigations are based on the evaluation of continuous radar measurements with the OSWIN VHF radar at Kühlungsborn (54.1 N, 11.8 E) and the 482 MHz UHF wind profiler at Lindenberg (52.2 N, 14.1 E). Both radars are separated by about 265 km. Based on wavelet transformations of both data sets, the dominant vertical wavelengths of about 2-4 km for fixed times as well as the dominant observed periods of about 11 h and weaker oscillations with periods of  6 h for the altitude range between 5 and 8 km are comparable. Gravity wave parameters have been estimated at both locations separately and by a complex cross-spectral analysis of the data of both radars. The results show the appearance of dominating inertia-gravity waves with characteristic horizontal wavelengths of  300 km moving in the opposite direction than the mean background wind and a secondary less pronounced wave with a horizontal wavelength in the order of about 200 km moving with the wind. Temporal and spatial differences of the observed waves are discussed.

Balance in non-hydrostatic rotating stratified turbulence

2008 ◽  
Vol 596 ◽  
pp. 201-219 ◽  
Author(s):  
WILLIAM J. McKIVER ◽  
DAVID G. DRITSCHEL
Keyword(s):  
Gravity Waves ◽  
Potential Vorticity ◽  
Acoustic Waves ◽  
Buoyancy Frequency ◽  
Scaling Analysis ◽  
Stratified Turbulence ◽  
Dynamical Equations ◽  
Geostrophic Balance ◽  
Vorticity Balance ◽  
Inertia Gravity Waves

It is now well established that two distinct types of motion occur in geophysical turbulence: slow motions associated with potential vorticity advection and fast oscillations due to inertia–gravity waves (or acoustic waves). Many studies have theorized the existence of a flow for which the entire motion is controlled by the potential vorticity (or one ‘master variable’) – this is known as balance. In real geophysical flows, deviations from balance in the form of inertia–gravity waves or ‘imbalance’ have often been found to be small. Here we examine the extent to which balance holds in rotating stratified turbulence which is nearly balanced initially.Using the non-hydrostatic fluid dynamical equations under the Boussinesq approximation, we analyse properties of rotating stratified turbulence spanning a range of Rossby numbers (Ro≡|ζ|max/f) and the frequency ratios (c≡N/f) where ζ is the relative vertical vorticity, f is the Coriolis frequency and N is the buoyancy frequency. Using a recently introduced diagnostic procedure, called ‘optimal potential vorticity balance’, we extract the balanced part of the flow in the simulations and assess how the degree of imbalance varies with the above parameters.We also introduce a new and more efficient procedure, building upon a quasi-geostrophic scaling analysis of the complete non-hydrostatic equations. This ‘nonlinear quasi-geostrophic balance’ procedure expands the equations of motion to second order in Rossby number but retains the exact (unexpanded) definition of potential vorticity. This proves crucial for obtaining an accurate estimate of balanced motions. In the analysis of rotating stratified turbulence at Ro≲1 and N/f≫1, this procedure captures a significantly greater fraction of the underlying balance than standard (linear) quasi-geostrophic balance (which is based on the linearized equations about a state of rest). Nonlinear quasi-geostrophic balance also compares well with optimal potential vorticity balance, which captures the greatest fraction of the underlying balance overall.More fundamentally, the results of these analyses indicate that balance dominates in carefully initialized simulations of freely decaying rotating stratified turbulence up to O(1) Rossby numbers when N/f≫1. The fluid motion exhibits important quasi-geostrophic features with, in particular, typical height-to-width scale ratios remaining comparable to f/N.

scholarly journals Normal Mode Spectra of Idealized Baroclinic Waves

2020 ◽  
Vol 77 (3) ◽  
pp. 813-833
Author(s):  
Matthew R. Ambacher ◽  
Michael L. Waite
Keyword(s):  
Energy Spectrum ◽  
Potential Energy ◽  
Gravity Waves ◽  
Normal Modes ◽  
Helmholtz Decomposition ◽  
Wave Spectra ◽  
Baroclinic Wave ◽  
Vertical Mode ◽  
Baroclinic Waves ◽  
Inertia Gravity Waves

Abstract Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal spectra (GE and AE, respectively) are compared to the rotational and divergent kinetic energy (RKE and DKE, respectively), which are often employed as proxies for vortex and wave energy. In our idealized f-plane framework, the horizontal modes are Fourier, and the vertical modes are found by solving an appropriate eigenvalue problem. For low vertical mode number n, both the GE and AE spectra are steep; however, for higher n, while both spectra are shallow, the AE is shallower than the GE and the spectra cross. The AE spectra are peaked at the Rossby deformation wavenumber knR, which increases with n. Analysis of the horizontal mode equations suggests that, for large wavenumbers k≫knR, the GE is approximated by the RKE, while the AE is approximated by the sum of the DKE and potential energy. These approximations are supported by the simulations. The vertically averaged RKE and DKE spectra are compared to the sum of the GE and AE spectra over all vertical modes; the spectral slopes of the GE and AE are close to those of the RKE and DKE, supporting the use of the Helmholtz decomposition to estimate vortices and waves in the midlatitudes. However, the AE is consistently larger than the DKE because of the contribution from the potential energy. Care must be taken when diagnosing the mesoscale transition from the intersection of the vortex and wave spectra; GE and AE will intersect at a different scale than RKE and DKE, despite their similar slopes.

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