Modal Interpretation for the Ekman Destabilization of Inviscidly Stable Baroclinic Flow in the Phillips Model

2010 ◽  
Vol 40 (4) ◽  
pp. 830-839 ◽  
Author(s):  
Gordon E. Swaters
Keyword(s):  
Phase Velocity ◽  
Boundary Layers ◽  
Rossby Wave ◽  
Classical Theory ◽  
Baroclinic Instability ◽  
Ekman Layer ◽  
Modal Interpretation ◽  
Phase Velocities ◽  
Phillips Model ◽  
Baroclinic Flow

Abstract Ekman boundary layers can lead to the destabilization of baroclinic flow in the Phillips model that, in the absence of dissipation, is nonlinearly stable in the sense of Liapunov. It is shown that the Ekman-induced instability of inviscidly stable baroclinic flow in the Phillips model occurs if and only if the kinematic phase velocity associated with the dissipation lies outside the interval bounded by the greatest and least neutrally stable Rossby wave phase velocities. Thus, Ekman-induced destabilization does not correspond to a coalescence of the barotropic and baroclinic Rossby modes as in classical inviscid baroclinic instability. The differing modal mechanisms between the two instability processes is the reason why subcritical baroclinic shears in the classical theory can be destabilized by an Ekman layer, even in the zero dissipation limit of the theory.

scholarly journals Stability Analysis of the Labrador Current

2014 ◽  
Vol 44 (2) ◽  
pp. 445-463 ◽  
Author(s):  
Sören Thomsen ◽  
Carsten Eden ◽  
Lars Czeschel
Keyword(s):  
Stability Analysis ◽  
Growth Rates ◽  
Baroclinic Instability ◽  
Cross Flow ◽  
Vertical Shear ◽  
Maximal Growth ◽  
Phase Velocities ◽  
Labrador Current ◽  
Lateral Mixing ◽  
Weak Stratification

Abstract Mooring observations and model simulations point to an instability of the Labrador Current (LC) during winter, with enhanced eddy kinetic energy (EKE) at periods between 2 and 5 days and much less EKE during other seasons. Linear stability analysis using vertical shear and stratification from the model reveals three dominant modes of instability in the LC: 1) a balanced interior mode with along-flow wavelengths of about 30–45 km, phase velocities of 0.3 m s−1, maximal growth rates of 1 day−1, and surface-intensified but deep-reaching amplitudes; 2) a balanced shallow mode with along-flow wavelengths of about 0.3–1.5 km, phase velocities of 0.55 m s−1, about 3 times larger growth rates, but amplitudes confined to the mixed layer (ML); and 3) an unbalanced symmetric mode with the largest growth rates, vanishing phase speeds, and along-flow structure, and very small cross-flow wavelengths, also confined to the ML. Both balanced modes are akin to baroclinic instability but operate at moderate-to-small Richardson numbers Ri with much larger growth rates as for the quasigeostrophic limit of Ri ≫ 1. The interior mode is found to be responsible for the instability of the LC during winter. Weak stratification and enhanced vertical shear due to local buoyancy loss and the advection of convective water masses from the interior result in small Ri within the LC and up to 3 times larger growth rates of the interior mode in March compared to summer and fall conditions. Both the shallow and the symmetric modes are not resolved by the model, but it is suggested that they might also play an important role for the instability in the LC and for lateral mixing.

Finite-Difference Modeling and Characteristics Analysis of Love Waves in Anisotropic-Viscoelastic Media

2021 ◽  
Author(s):  
Shichuan Yuan ◽  
Zhenguo Zhang ◽  
Hengxin Ren ◽  
Wei Zhang ◽  
Xianhai Song ◽  
...  
Keyword(s):  
Finite Difference ◽  
Phase Velocity ◽  
Velocity Dispersion ◽  
Love Waves ◽  
Velocity Anisotropy ◽  
Viscoelastic Media ◽  
Phase Velocities ◽  
Phase Velocity Dispersion ◽  
Anisotropic Elastic ◽  
Attenuation Anisotropy

ABSTRACT In this study, the characteristics of Love waves in viscoelastic vertical transversely isotropic layered media are investigated by finite-difference numerical modeling. The accuracy of the modeling scheme is tested against the theoretical seismograms of isotropic-elastic and isotropic-viscoelastic media. The correctness of the modeling results is verified by the theoretical phase-velocity dispersion curves of Love waves in isotropic or anisotropic elastic or viscoelastic media. In two-layer half-space models, the effects of velocity anisotropy, viscoelasticity, and attenuation anisotropy of media on Love waves are studied in detail by comparing the modeling results obtained for anisotropic-elastic, isotropic-viscoelastic, and anisotropic-viscoelastic media with those obtained for isotropic-elastic media. Then, Love waves in three typical four-layer half-space models are simulated to further analyze the characteristics of Love waves in anisotropic-viscoelastic layered media. The results show that Love waves propagating in anisotropic-viscoelastic media are affected by both the anisotropy and viscoelasticity of media. The velocity anisotropy of media causes substantial changes in the values and distribution range of phase velocities of Love waves. The viscoelasticity of media leads to the amplitude attenuation and phase velocity dispersion of Love waves, and these effects increase with decreasing quality factors. The attenuation anisotropy of media indicates that the viscoelasticity degree of media is direction dependent. Comparisons of phase velocity ratios suggest that the change degree of Love-wave phase velocities due to viscoelasticity is much less than that caused by velocity anisotropy.

scholarly journals The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

2004 ◽  
Vol 130 (596) ◽  
pp. 233-258 ◽  
Author(s):  
E. Heifetz ◽  
J. Methven ◽  
B. J. Hoskins ◽  
C. H. Bishop
Keyword(s):  
Rossby Wave ◽  
Baroclinic Instability

Do traveltimes in pulse‐transmission experiments yield anisotropic group or phase velocities?

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1774-1779 ◽  
Author(s):  
Joe Dellinger ◽  
Lev Vernik
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Elastic Constants ◽  
Near Field ◽  
Frequency Dispersion ◽  
Transversely Isotropic ◽  
Sh Waves ◽  
Phase Velocities ◽  
Pulse Transmission ◽  
Transmission Technique

The elastic properties of layered rocks are often measured using the pulse through‐transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal (e.g., Vernik and Nur, 1992; Lo et al., 1986; Jones and Wang, 1981). In this method transducers are attached to the flat ends of the three cores (see Figure 1), the first‐break traveltimes of P, SV, and SH‐waves down the axes are measured, and a set of transversely isotropic elastic constants are fit to the results. The usual assumption is that frequency dispersion, boundary reflections, and near‐field effects can all be safely ignored, and that the traveltimes measure either vertical anisotropic group velocity (if the transducers are very small compared to their separation) or phase velocity (if the transducers are relatively wide compared to their separation) (Auld, 1973).

Coriolis-force attenuation of blocking in a stratified flow

1979 ◽  
Vol 94 (4) ◽  
pp. 711-727 ◽  
Author(s):  
M. R. Foster
Keyword(s):  
Boundary Layers ◽  
Detailed Examination ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Number ◽  
Coriolis Forces ◽  
Ekman Layers ◽  
The Face ◽  
Vorticity Generation ◽  
Upstream Flow

Even very small Coriolis forces are shown to alter significantly the nature of the upstream wake of an object in slow (small Froude number) translation through a non-diffusive stratified fluid. If the Ekman number is of order one, the far upstream extent of the wake is reduced. If the fluid rotation is sufficient to make the Ekman number small, the contraction of the wake is much greater. We study a particular case in detail; the Ekman number is small enough to make horizontal boundary layers Ekman layers. In this case, the wake is confined to the vicinity of the object, the upstream flow arising from a combination of Ekman pumping and baroclinic vorticity generation. The upstream flow is described by an eigenfunction whose amplitude is dependent on object geometry. If the object is a semi-infinite rectangular parallelepiped, that amplitude is determined by detailed examination of the shear layer at the face of the parallelepiped and its interaction with the Ekman layer on the top surface of the object

Wall Pressure Phase Velocity Measurements in a Turbulent Boundary Layer

2012 ◽  
Author(s):  
Teresa S. Miller ◽  
Mark J. Moeller
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Phase Velocity ◽  
Group Velocity ◽  
Noise Source ◽  
Wall Pressure ◽  
Interior Noise ◽  
Convection Velocity ◽  
Phase Velocities ◽  
Wall Pressure Fluctuation

The turbulent boundary layer that forms on the outer surfaces of vehicles can be a significant source of interior noise. In automobiles this is known as wind noise, and at high speeds it dominates the interior noise. For airplanes the turbulent boundary is also a dominant noise source. Because of its importance as a noise source, it is desirable to have a model of the turbulent wall pressure fluctuations for interior noise prediction. One important parameter in building the wall pressure fluctuation model is the convection velocity. In this paper, the phase velocity was determined from the streamwise pressure measurements. The phase velocity was calculated for three separation distances ranging from 0.25 to 1.30 boundary layer thicknesses. These measurements were made for a Mach number range of 0.1 < M < 0.6. The phase velocity was shown to vary with sensor spacing and frequency. The data collapsed well on outer variable normalization. The phase velocities were fit and the group velocity was calculated from the curve fit. The group velocity was consistent with the array measured convection velocities. The group velocity was also estimated by a band limited cross correlation technique that used the Hilbert transform to find the energy delay. This result was consistent with the group velocity inferred from the phase velocities and the array measured convection velocity. From this research, it is suggested that the group velocity found in this study should be used to estimate the convection velocity in wall pressure fluctuation models.

On the precession of a resonant cylinder

1970 ◽  
Vol 41 (4) ◽  
pp. 865-872 ◽  
Author(s):  
Roger F. Gans
Keyword(s):  
Boundary Layers ◽  
Solvability Condition ◽  
Rotating Cylinder ◽  
Resonant Mode ◽  
Ekman Layer ◽  
Resonant Response ◽  
Order Problem ◽  
Precession Rate ◽  
Resonance Phenomena ◽  
Strong Amplitude

A fluid contained in a rotating cylinder has an inertial mode which is excited by forced precession of the container. Wood's (1965, 1966) early work specifically excluded resonance phenomena. Recently McEwan (1970) has discussed resonance phenomena for strong amplitude of excitation, corresponding to rapid precession in this work.In this paper the magnitude of the resonant response for small precession rate is precisely calculated by matching the Ekman layer suction to the precessional forces. The procedure is to find the resonant mode v1, compute its boundary layers, $\tilde{{\bf v}}_1$, and the associated Ekman layer suction. The second-order problem has a solvability condition which is satisfied by matching the Ekman layer suction to the precession.

scholarly journals Characteristics of very large aspect angle E-region coherent echoes at 933 MHz

1997 ◽  
Vol 15 (1) ◽  
pp. 54-62 ◽  
Author(s):  
B. J. Jackel ◽  
D. R. Moorcroft ◽  
K. Schlegel
Keyword(s):  
Phase Velocity ◽  
Scattering Layer ◽  
Aspect Angle ◽  
Ion Drift ◽  
Phase Velocities ◽  
F Region ◽  
E Region ◽  
Inversion Techniques ◽  
Coherent Backscatter ◽  
Uhf Radar

Abstract. The EISCAT UHF radar system was used to study the characteristics of E-region coherent backscatter at very large magnetic aspect angles (5–11°). Data taken using 60 μs pulses during elevation scans through horizontally uniform backscatter permitted the use of inversion techniques to determine height profiles of the scattering layer. The layer was always singly peaked, with a mean height of 104 km, and mean thickness (full width at half maximum) of 10 km, both independent of aspect angle. Aspect sensitivities were also estimated, with the Sodankylä-Tromsø link observing 5 dB/degree at aspect angles near 5°, decreasing to 3 dB/degree at 10° aspect angle. Observed coherent phase velocities from all three stations were found to be roughly consistent with LOS measurements of a common E-region phase velocity vector. The E-region phase velocity had the same orientation as the F-region ion drift velocity, but was approximately 50% smaller in magnitude. Spectra were narrow with skewness of about +1 (for negative velocities), increasing slightly with aspect angle.

scholarly journals Surface-wave images of western Canada: lithospheric variations across the Cordillera–craton boundary

2018 ◽  
Vol 55 (8) ◽  
pp. 887-896 ◽  
Author(s):  
Taras Zaporozan ◽  
Andrew W. Frederiksen ◽  
Alexey Bryksin ◽  
Fiona Darbyshire
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Upper Mantle ◽  
High Velocity ◽  
Western Canada ◽  
Low Velocity ◽  
Phase Velocities ◽  
Slave Province ◽  
Upper Mantle Structure ◽  
Tectonically Active

Two-station surface-wave analysis was used to measure Rayleigh-wave phase velocities between 105 station pairs in western Canada, straddling the boundary between the tectonically active Cordillera and the adjacent stable craton. Major variations in phase velocity are seen across the boundary at periods from 15 to 200 s, periods primarily sensitive to upper mantle structure. Tomographic inversion of these phase velocities was used to generate phase velocity maps at these periods, indicating a sharp contrast between low-velocity Cordilleran upper mantle and high-velocity cratonic lithosphere. Depth inversion along selected transects indicates that the Cordillera–craton upper mantle contact varies in dip along the deformation front, with cratonic lithosphere of the Taltson province overthrusting Cordilleran asthenosphere in the northern Cordillera, and Cordilleran asthenosphere overthrusting Wopmay lithosphere further south. Localized high-velocity features at sub-lithospheric depths beneath the Cordillera are interpreted as Farallon slab fragments, with the gap between these features indicating a slab window. A high-velocity feature in the lower lithosphere of the Slave province may be related to Proterozic or Archean subduction.

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