Inviscid waves on a Lamb–Oseen vortex in a rotating stratified fluid: consequences for the elliptic instability

The inviscid waves propagating on a Lamb–Oseen vortex in a rotating medium for an unstratified fluid and for a strongly stratified fluid are analysed using numerical and asymptotic approaches. By a local Lagrangian description, we first provide the characteristics of the local plane waves (inertia–gravity waves) as well as the local growth rate associated with the centrifugal instability when the vortex is unstable. A global WKBJ approach is then used to determine the frequencies of neutral core modes and neutral ring modes. We show that these global Kelvin modes only exist in restricted domains of the parameters. The consequences of these domain limitations for the occurrence of the elliptic instability are discussed. We argue that in an unstratified fluid the elliptic instability should be active in a small range of the Coriolis parameter which could not have been predicted from a local approach. The wavenumbers of the sinuous modes of the elliptic instability are provided as a function of the Coriolis parameter for both an unstratified fluid and a strongly stratified fluid.

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The Okubo-Weiss criterion in hydrodynamic flows:Geometric aspects and further extension

Fluid Dynamics Research ◽

10.1088/1873-7005/ac495d ◽

2022 ◽

Author(s):

Bhimsen Shivamoggi ◽

G Heijst ◽

Leon Kamp

Keyword(s):

Flow Field ◽

Polar Coordinates ◽

Coriolis Parameter ◽

Laminar Jet ◽

Type Criterion ◽

Burgers Vortex ◽

2D Flow ◽

Flow Configurations ◽

Elliptic Regions ◽

Oseen Vortex

Abstract The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

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Diffraction of plane waves at a horizontal half-plane in a compressible stratified fluid

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(84)90174-5 ◽

1984 ◽

Vol 24 (5) ◽

pp. 165-170

Author(s):

A.K. Shatov

Keyword(s):

Half Plane ◽

Plane Waves ◽

Stratified Fluid

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Elliptic instability of a stratified fluid in a rotating cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112010002636 ◽

2010 ◽

Vol 660 ◽

pp. 240-257 ◽

Cited By ~ 15

Author(s):

D. GUIMBARD ◽

S. LE DIZÈS ◽

M. LE BARS ◽

P. LE GAL ◽

S. LEBLANC

Keyword(s):

Stratified Fluid ◽

Angular Frequency ◽

Nonlinear Regime ◽

Finite Cylinder ◽

Linear Growth Rate ◽

Small Eccentricity ◽

Weakly Nonlinear ◽

Instability Modes ◽

Centrifugal Instability ◽

New Type

In this paper, we analyse the characteristics of the elliptic instability in a finite cylinder in the presence of both background rotation and axial stratification. A general formula for the linear growth rate of the stationary sinuous modes is derived including viscous and detuning effects in the limit of small eccentricity. This formula is discussed and compared to experimental results which are obtained in a cylinder filled with salted water for two different eccentricities by varying the stratification, the background rotation and the cylinder rotation. A good agreement with the theory concerning the domain of instability of the sinuous modes is demonstrated. Other elliptic instability modes, oscillating at the cylinder angular frequency are also evidenced together with a new type of instability mode, which could be connected to a centrifugal instability occurring during the experimental phase of spin-up. The nonlinear regime of the elliptic instability is also documented. In contrast with the homogeneous case, no cycle involving growth, breakdown and re-laminarization is observed in the presence of strong stratification. The elliptic instability in a stratified fluid seems to yield either a persistent turbulent state or a weakly nonlinear regime.

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Multiarrival Kirchhoff beam migration

Geophysics ◽

10.1190/geo2010-0403.1 ◽

2011 ◽

Vol 76 (5) ◽

pp. WB109-WB118 ◽

Cited By ~ 24

Author(s):

Jonathan Liu ◽

Gopal Palacharla

Keyword(s):

Model Updating ◽

Plane Waves ◽

Beam Width ◽

Velocity Model ◽

Model Complexity ◽

Depth Migration ◽

Kirchhoff Migration ◽

Optimal Beam ◽

Local Plane ◽

Gaussian Beam Migration

Kirchhoff-type prestack depth migration is the method most popular for outputting offset gathers for velocity-model updating because of its flexibility and efficiency. However, conventional implementations of Kirchhoff migration use only single arrivals. This limits its ability to image complex structures such as subsalt areas. We use the beam methodology to develop a multiarrival Kirchhoff beam migration. The theory and algorithm of our beam migration are analogs to Gaussian beam migration, but we focus on attaining kinematic accuracy and implementation efficiency. The input wavefield of every common offset panel is decomposed into local plane waves at beam centers on the acquisition surface by local slant stacking. Each plane wave contributes a potential single-arrival in Kirchhoff migration. In this way, our method is able to handle multiarrivals caused by model complexity and, therefore, to overcome the limitation of conventional single-arrival Kirchhoff migration. The choice of the width of the beam is critical to the implementation of beam migration. We provide a formula for optimal beam width that achieves both accuracy and efficiency when the velocity model is reasonably smooth. The resulting structural imaging in subsalt and other structurally complex areas is of better quality than that from single-arrival Kirchhoff migration.

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Imaging diffractors using wave-equation migration

Geophysics ◽

10.1190/geo2016-0029.1 ◽

2016 ◽

Vol 81 (6) ◽

pp. S459-S468 ◽

Cited By ~ 12

Author(s):

Lu Liu ◽

Etienne Vincent ◽

Xu Ji ◽

Fuhao Qin ◽

Yi Luo

Keyword(s):

Wave Equation ◽

Field Data ◽

Recursive Algorithm ◽

Median Filter ◽

Random Noise ◽

Plane Waves ◽

Computationally Efficient ◽

Imaging Point ◽

Local Plane ◽

Dip Angle

We have developed a fast and practical wave-equation-based migration method to image subsurface diffractors. The method is composed of three steps in our implementation. First, it decomposes extrapolated receiver wavefields at every imaging point into local plane waves by a linear Radon transform; the transform is realized by a novel computationally efficient recursive algorithm. Second, the decomposed plane waves are zero lag-correlated with the incident source wavefields, where the incident angles are computed via the structure tensor approach. The resulting prestack images are binned into dip-angle gathers according to the directions of the decomposed plane waves and the calculated incident angles. Third, a windowed median filter is applied to the dip-angle gathers to suppress the focused reflection energy, and it produces the desired diffraction images. This method is tested on synthetic and field data. The results demonstrate that it is resistant to random noise, computationally efficient, and applicable to field data in practice. The results also indicate that the diffraction images are able to provide important discontinuous geologic features, such as scattering and faulting zones, and thus are helpful for seismic interpretation.

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Some aspects of time-dependent motion of a stratified rotating fluid

Journal of Fluid Mechanics ◽

10.1017/s0022112069001662 ◽

1969 ◽

Vol 36 (2) ◽

pp. 289-307 ◽

Cited By ~ 81

Author(s):

GÖUsta Walin

Keyword(s):

Stratified Fluid ◽

Decay Process ◽

Time Dependent ◽

Characteristic Scale ◽

Rotating Fluid ◽

Horizontal Scale ◽

Coriolis Parameter ◽

The Stability ◽

Stability Frequency ◽

Rotating Stratified Fluid

Time-dependent motion of a rotating stratified fluid is analyzed within the quasigeostrophic approximation. A few examples of mechanically driven flow are analyzed. It is found that the motion is characterized by the ratio B of the stability frequency and the Coriolis parameter. Thus the ratio of the horizontal and vertical characteristic scale is in general O(B). In particular the decay process caused by a horizontal boundary will penetrate a distance B−1L into the fluid, L denoting the horizontal scale of the motion.

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Generation and Propagation of Inertia–Gravity Waves from Vortex Dipoles and Jets

Journal of the Atmospheric Sciences ◽

10.1175/2008jas2830.1 ◽

2009 ◽

Vol 66 (5) ◽

pp. 1294-1314 ◽

Cited By ~ 39

Author(s):

Shuguang Wang ◽

Fuqing Zhang ◽

Chris Snyder

Keyword(s):

Ray Tracing ◽

Gravity Waves ◽

Mesoscale Model ◽

Rossby Number ◽

Small Range ◽

Grid Spacing ◽

Coriolis Parameter ◽

Vortex Dipoles ◽

Horizontal Variations ◽

Inertia Gravity Waves

Abstract This study investigates gravity wave generation and propagation from jets within idealized vortex dipoles using a nonhydrostatic mesoscale model. Two types of initially balanced and localized jets induced by vortex dipoles are examined here. These jets have their maximum strength either at the surface or in the middle levels of a uniformly stratified atmosphere. Within these dipoles, inertia–gravity waves with intrinsic frequencies 1–2 times the Coriolis parameter are simulated in the jet exit region. These gravity waves are nearly phase locked with the jets as shown in previous studies, suggesting spontaneous emission of the waves by the localized jets. A ray tracing technique is further employed to investigate the propagation effects of gravity waves. The ray tracing analysis reveals strong variation of wave characteristics along ray paths due to variations (particularly horizontal variations) in the propagating environment. The dependence of wave amplitude on the jet strength (and thus on the Rossby number of the flow) is examined through experiments in which the two vortices are initially separated by a large distance but subsequently approach each other and form a vortex dipole with an associated amplifying localized jet. The amplitude of the stationary gravity waves in the simulations with 90-km grid spacing increases as the square of the Rossby number (Ro), when Ro falls in a small range of 0.05–0.15, but does so significantly more rapidly when a smaller grid spacing is used.

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