scholarly journals Alignment of Hurricane-like Vortices on f and β Planes

2009 ◽  
Vol 66 (6) ◽  
pp. 1779-1792 ◽  
Author(s):  
Robert W. Jones ◽  
Hugh E. Willoughby ◽  
Michael T. Montgomery
Keyword(s):  
Rossby Waves ◽  
Critical Radius ◽  
Swirling Flow ◽  
Baroclinic Instability ◽  
Necessary Condition ◽  
Initial Condition ◽  
The Mean ◽  
Nonlinear Solutions ◽  
The Waves ◽  
Pv Gradient

Abstract A nonlinear, two-layer, vortex-tracking semispectral model (i.e., Fourier transformed in azimuth only) is used to study the evolution of dry, but otherwise hurricane-like, initially tilted vortices in quiescent surroundings on f and β planes. The tilt projects onto vorticity asymmetries that are dynamically vortex Rossby waves. Since the swirling wind in the principal mean vortex used here decays exponentially outside the eyewall, it has an initial potential vorticity (PV) minimum. The resulting reversal of PV gradient meets the necessary condition for inflectional (i.e., barotropic or baroclinic) instability. Thus, the vortex may be inflectionally stable or unstable. On an f plane, the tilt precesses relatively slowly because the critical radius, where the phase speeds of the waves match the mean swirling flow, is far from the center. An alternative Gaussian-like PV monopole that has a monotonic outward decrease of PV is stable to inflectional instability. It has a smaller critical radius and rapid tilt precession. Generally, vortices with fast tilt precession are more stable, as are stronger vortices in higher latitudes. On a β plane, the interaction between the symmetric vortex and the planetary PV gradient induces β gyres that push the vortex poleward and westward. The interaction between the β gyres and the planetary PV gradient may either create a PV minimum or intensify a minimum inherited from the initial condition. Thus, the nonlinear β effect reduces the ability of the vortex to recover from initial tilt, relative to the same vortex on an f plane. This result contrasts with previous studies of barotropic vortices on f planes, where the linear and nonlinear solutions were nearly identical.

Overtransmission of Rossby Waves at a Lower-Layer Critical Latitude in the Two-Layer Model

2020 ◽  
Vol 77 (3) ◽  
pp. 859-870 ◽  
Author(s):  
Matthew T. Gliatto ◽  
Isaac M. Held
Keyword(s):  
Rossby Waves ◽  
Lower Layer ◽  
Scattering Problem ◽  
Lower Troposphere ◽  
Vertical Shear ◽  
Mean Flow ◽  
External Mode ◽  
The Mean ◽  
Critical Latitude ◽  
Pv Gradient

Abstract Rossby waves, propagating from the midlatitudes toward the tropics, are typically absorbed by critical latitudes (CLs) in the upper troposphere. However, these waves typically encounter CLs in the lower troposphere first. We study a two-layer linear scattering problem to examine the effects of lower CLs on these waves. We begin with a review of the simpler barotropic case to orient the reader. We then progress to the baroclinic case using a two-layer quasigeostrophic model in which there is vertical shear in the mean flow on which the waves propagate, and in which the incident wave is assumed to be an external-mode Rossby wave. We use linearized equations and add small damping to remove the critical-latitude singularities. We consider cases in which either there is only one CL, in the lower layer, or there are CLs in both layers, with the lower-layer CL encountered first. If there is only a CL in the lower layer, the wave’s response depends on the sign of the mean potential vorticity gradient at this lower-layer CL: if the PV gradient is positive, then the CL partially absorbs the wave, as in the barotropic case, while for a negative PV gradient, the CL is a wave emitter, and can potentially produce overreflection and/or overtransmission. Our numerical results indicate that overtransmission is by far the dominant response in these cases. When an upper-layer absorbing CL is encountered, following the lower-layer encounter, one can still see the signature of overtransmission at the lower-layer CL.

scholarly journals Role of the Rossby Waves in the Broadening of an Eastward Jet

2012 ◽  
Vol 42 (3) ◽  
pp. 476-494 ◽  
Author(s):  
Genta Mizuta
Keyword(s):  
Potential Vorticity ◽  
Rossby Waves ◽  
Equation Model ◽  
Transient Region ◽  
Interior Flow ◽  
The Mean ◽  
The Difference ◽  
Vorticity Flux ◽  
The Waves

Abstract To investigate the effect of the Rossby waves on an eastward jet such as the Kuroshio or Gulf Stream Extensions, a series of numerical experiments is conducted using a primitive equation model. In these experiments, an inflow and an outflow imposed on the western and eastern boundaries drive an unstable narrow jet and a broad interior flow in the western and eastern regions of the model domain, respectively. The barotropic Rossby waves are radiated from the transient region between the two regions. The eddy potential vorticity flux by the waves tends to compensate for the difference in the mean potential vorticity along mean streamlines between both sides of the transient region. Instability of the jet is insufficient for this compensation and weakens the mean potential vorticity gradient too much. Moreover, as the potential vorticity of the outflow is increased, the Rossby waves are intensified in order to compensate for the increase in the difference in the mean potential vorticity. These features strongly suggest that the Rossby waves are substantial in matching a jet with an interior flow. The speed of the waves and properties of eddies in recirculations of the jet are consistent with a two-layer analytic model, which indicates that the Rossby waves are radiated from eddies in recirculations. These eddies as well as the Rossby waves increase in amplitude with the transport of the recirculation near the surface presumably because of mean advection. Therefore, the mean potential vorticity of the interior flow, the intensity of the Rossby waves, and the transport of the recirculation change consistently with one another.

Modification of Long Equatorial Rossby Wave Phase Speeds by Zonal Currents

2011 ◽  
Vol 41 (6) ◽  
pp. 1077-1101 ◽  
Author(s):  
Theodore S. Durland ◽  
Roger M. Samelson ◽  
Dudley B. Chelton ◽  
Roland A. de Szoeke
Keyword(s):  
Rossby Wave ◽  
Rossby Waves ◽  
Current System ◽  
Phase Speed ◽  
Meridional Velocity ◽  
Zonal Velocity ◽  
The Mean ◽  
Meridional Mode ◽  
Mean Current ◽  
Pv Gradient

Abstract Previously unaddressed aspects of how equatorial currents affect long Rossby wave phase speeds are investigated using solutions of the shallow-water equations linearized about quasi-realistic currents. Modification of the background potential vorticity (PV) gradient by curvature in the narrow equatorial currents is shown to play a role comparable to the Doppler shift emphasized by previous authors. The important variables are the meridional projections of mean-current features onto relevant aspects of the wave field. As previously shown, Doppler shifting of long Rossby waves is determined by the projection of the mean currents onto the wave’s squared zonal-velocity and pressure fields. PV-gradient modification matters only to the extent that it projects onto the wave field’s squared meridional velocity. Because the zeros of an equatorial wave’s meridional velocity are staggered relative to those of the zonal velocity and pressure, and because the meridional scales of the equatorial currents are similar to those of the low-mode Rossby waves, different parts of the current system dominate the advective and PV-gradient modification effects on a single mode. Since the equatorial symmetry of classical equatorial waves alternates between symmetric and antisymmetric with increasing meridional mode number, the currents produce opposite effects on adjacent modes. Meridional mode 1 is slowed primarily by a combination of eastward advection by the Equatorial Undercurrent (EUC) and the PV-gradient decrease at the peaks of the South Equatorial Current (SEC). The mode-2 phase speed, in contrast, is increased primarily by a combination of westward advection by the SEC and the PV-gradient increase at the core of the EUC. Perturbation solutions are carried to second order in ε, the Rossby number of the mean current, and it is shown that this is necessary to capture the full effect of quasi-realistic current systems, which are asymmetric about the equator. Equatorially symmetric components of the current system affect the phase speed at O(ε), but antisymmetric components of the currents and distortions of the wave structures by the currents do not influence the phase speed until O(ε2).

scholarly journals Balancing the Potential Vorticity Seesaw: The Bare Essentials of Baroclinic Instability

2019 ◽  
Vol 3 (3) ◽  
pp. 341-351
Author(s):  
Enda O’Brien
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Phase Locking ◽  
Baroclinic Instability ◽  
Mechanistic Explanation ◽  
Atmospheric Model ◽  
Key Characteristics ◽  
Background Temperature ◽  
Pv Gradient

Abstract This paper bypasses the mathematical technicalities of baroclinic instability and tries to provide a more conceptual, mechanistic explanation for a phenomenon that is fundamentally important to the dynamics of the earth’s atmosphere and oceans. The standard conceptual picture of baroclinic instability is reviewed and stripped down to identify the most essential features. These are: (a) Regions with both positive and negative potential vorticity (PV) gradients, (b) separate Rossby wave perturbations in each region where PV gradients are of different signs, and (c) cooperative phase locking between Rossby waves in regions of opposite PV gradient, which renders them stationary, and allows them to amplify to reduce the background temperature gradient (or baroclinicity) while still conserving total PV. These three factors constitute the “counterpropagating Rossby wave” perspective, and suggest the heuristic picture of a “PV seesaw”, which remains balanced as the instabilities (i.e., the phase-locked PV wave perturbations) grow out along opposite limbs. After reviewing the key characteristics of PV and Rossby waves, the process is illustrated by the spontaneous onset of baroclinic instability during spin-up of the Held–Suarez dynamical core atmospheric model.

Getting Rid of Fast Waves: Slow Dynamics

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Rossby Waves ◽  
Baroclinic Instability ◽  
Nonlinear Effects ◽  
Kelvin Wave ◽  
Beta Plane ◽  
Equatorial Wave ◽  
Flow Over Topography ◽  
Wave Guides ◽  
Rotating Shallow Water ◽  
Fast Waves

After analysis of general properties of horizontal motion in primitive equations and introduction of principal parameters, the key notion of geostrophic equilibrium is introduced. Quasi-geostrophic reductions of one- and two-layer rotating shallow-water models are obtained by a direct filtering of fast inertia–gravity waves through a choice of the time scale of motions of interest, and by asymptotic expansions in Rossby number. Properties of quasi-geostrophic models are established. It is shown that in the beta-plane approximations the models describe Rossby waves. The first idea of the classical baroclinic instability is given, and its relation to Rossby waves is explained. Modifications of quasi-geostrophic dynamics in the presence of coastal, topographic, and equatorial wave-guides are analysed. Emission of mountain Rossby waves by a flow over topography is demonstrated. The phenomena of Kelvin wave breaking, and of soliton formation by long equatorial and topographic Rossby waves due to nonlinear effects are explained.

scholarly journals Properties of Steady Geostrophic Turbulence with Isopycnal Outcropping

2012 ◽  
Vol 42 (1) ◽  
pp. 18-38 ◽  
Author(s):  
G. Roullet ◽  
J. C. McWilliams ◽  
X. Capet ◽  
M. J. Molemaker
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Mechanical Energy ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Primary Source ◽  
Eddy Diffusivity ◽  
Energy Cycle ◽  
Geostrophic Turbulence ◽  
Pv Gradient

Abstract High-resolution simulations of β-channel, zonal-jet, baroclinic turbulence with a three-dimensional quasigeostrophic (QG) model including surface potential vorticity (PV) are analyzed with emphasis on the competing role of interior and surface PV (associated with isopycnal outcropping). Two distinct regimes are considered: a Phillips case, where the PV gradient changes sign twice in the interior, and a Charney case, where the PV gradient changes sign in the interior and at the surface. The Phillips case is typical of the simplified turbulence test beds that have been widely used to investigate the effect of ocean eddies on ocean tracer distribution and fluxes. The Charney case shares many similarities with recent high-resolution primitive equation simulations. The main difference between the two regimes is indeed an energization of submesoscale turbulence near the surface. The energy cycle is analyzed in the (k, z) plane, where k is the horizontal wavenumber. In the two regimes, the large-scale buoyancy forcing is the primary source of mechanical energy. It sustains an energy cycle in which baroclinic instability converts more available potential energy (APE) to kinetic energy (KE) than the APE directly injected by the forcing. This is due to a conversion of KE to APE at the scale of arrest. All the KE is dissipated at the bottom at large scales, in the limit of infinite resolution and despite the submesoscales energizing in the Charney case. The eddy PV flux is largest at the scale of arrest in both cases. The eddy diffusivity is very smooth but highly nonuniform. The eddy-induced circulation acts to flatten the mean isopycnals in both cases.

The Coordination of Visual Observation and Instrumental Behavior in Early Infancy

Perception ◽  
1973 ◽  
Vol 2 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Iize V Kalnins ◽  
J S Bruner
Keyword(s):  
Baseline Level ◽  
Visual Observation ◽  
Voluntary Control ◽  
Early Infancy ◽  
Initial Condition ◽  
Instrumental Behavior ◽  
Active Response ◽  
The Mean ◽  
Instrumental Control ◽  
Clear Condition

Infants aged 5–12 weeks were shown a silent colour film whose clarity/focus was contingent on their sucking on a dummy nipple. In the ‘suck-for-clear’ condition the mean rate of sucking increased significantly over baseline level, and decreased when the contingency shifted to ‘suck-for-blur’. When the initial condition was suck-for-blur, sucking rate remained close to baseline level (even after the shift to suck-for-clear). Time spent looking at the clear film increased in both conditions, but there was little change in looking at the blurred pictures. With the introduction of the contingency conditions patterns of looking at the clearing and cleared pictures changed, and looking at the cleared picture increased in the suck-for-clear but not the suck-for-blur condition. Asymmetry of the results indicates that infants are better able to use an active response for instrumental means than to inhibit a response to achieve instrumental control. Implications for the development of voluntary control of action are explored.

scholarly journals Influence of the Monsoon Trough on Westward-Propagating Tropical Waves over the Western North Pacific. Part II: Energetics and Numerical Experiments

2015 ◽  
Vol 28 (23) ◽  
pp. 9332-9349 ◽  
Author(s):  
Liang Wu ◽  
Zhiping Wen ◽  
Renguang Wu
Keyword(s):  
North Pacific ◽  
Numerical Experiments ◽  
Western North Pacific ◽  
Monsoon Trough ◽  
Water Model ◽  
Mean Flow ◽  
Horizontal Structure ◽  
Rotational Flows ◽  
The Mean ◽  
The Waves

Abstract Part I of this study examined the modulation of the monsoon trough (MT) on tropical depression (TD)-type–mixed Rossby–gravity (MRG) and equatorial Rossby (ER) waves over the western North Pacific based on observations. This part investigates the interaction of these waves with the MT through a diagnostics of energy conversion that separates the effect of the MT on TD–MRG and ER waves. It is found that the barotropic conversion associated with the MT is the most important mechanism for the growth of eddy energy in both TD–MRG and ER waves. The large rotational flows help to maintain the rapid growth and tilted horizontal structure of the lower-tropospheric waves through a positive feedback between the wave growth and horizontal structure. The baroclinic conversion process associated with the MT contributes a smaller part for TD–MRG waves, but is of importance comparable to barotropic conversion for ER waves as it can produce the tilted vertical structure. The growth rates of the waves are much larger during strong MT years than during weak MT years. Numerical experiments are conducted for an idealized MRG or ER wave using a linear shallow-water model. The results confirm that the monsoon background flow can lead to an MRG-to-TD transition and the ER wave amplifies along the axis of the MT and is more active in the strong MT state. Those results are consistent with the findings in Part I. This indicates that the mean flow of the MT provides a favorable background condition for the development of the waves and acts as a key energy source.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

The role of the Pacific Decadal Oscillation and ocean-atmosphere interactions in driving United States heatwaves

2021 ◽  
Author(s):  
Sem Vijverberg ◽  
Dim Coumou
Keyword(s):  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Causal Link ◽  
Causal Mechanism ◽  
Temperature Forecast ◽  
The Pacific ◽  
Ocean Atmosphere ◽  
The Waves

<p>Heatwaves can have devastating impact on society and reliable early warnings at several weeks lead time are needed. Heatwaves are often associated with quasi-stationary Rossby waves, which interact with sea surface temperature (SST). Previous studies showed that north-Pacific SST can provide long-lead predictability for eastern U.S. temperature, moderated by an atmospheric Rossby wave. The exact mechanisms, however, are not well understood. Here we analyze Rossby waves associated with heatwaves in western and eastern US. Causal inference analyses reveal that both waves are characterized by positive ocean-atmosphere feedbacks at synoptic timescales, amplifying the waves. However, this positive feedback on short timescales is not the causal mechanism that leads to a long-lead SST signal. Only the eastern US shows a long-lead causal link from SSTs to the Rossby wave. We show that the long-lead SST signal derives from low-frequency PDO variability, providing the source of eastern US temperature predictability. We use this improved physical understanding to identify more reliable long-lead predictions. When, at the onset of summer, the Pacific is in a pronounced PDO phase, the SST signal is expected to persist throughout summer. These summers are characterized by a stronger ocean-boundary forcing, thereby more than doubling the eastern US temperature forecast skill, providing a temporary window of enhanced predictability.</p>

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