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 Uniform Asymptotics for the Linear Kelvin Wave in Spherical Geometry

2008 ◽  
Vol 65 (2) ◽  
pp. 655-660 ◽  
Author(s):  
John P. Boyd ◽  
Cheng Zhou
Keyword(s):  
Asymptotic Approximation ◽  
Rossby Waves ◽  
Spherical Geometry ◽  
Uniform Asymptotics ◽  
Kelvin Wave ◽  
Beta Plane ◽  
Zonal Wavenumber ◽  
Equatorial Wave ◽  
Wave Limit ◽  
Two Parameters

Abstract The Kelvin wave is the gravest eigenmode of Laplace’s tidal equation. It is widely observed in both the ocean and the atmosphere. In the absence of mean currents, the Kelvin wave depends on two parameters: the zonal wavenumber s (always an integer) and Lamb’s parameter ε. An asymptotic approximation valid in the limit s2 + ε ≫ 1 is derived that generalizes the usual “equatorial wave” limit that ε → ∞ for fixed s. Just as shown for Rossby waves two decades ago, the width of the Kelvin wave is (ε + s2)−1/4 rather than ε−1/4 as in the classical equatorial beta-plane approximation.

Steady radiating baroclinic vortices in vertically sheared flows

2021 ◽  
Author(s):  
Georgi Sutyrin ◽  
Jonas Nycander ◽  
Timour Radko
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Vertical Shear ◽  
Alternative Mechanism ◽  
Beta Plane ◽  
Subtropical Oceans ◽  
Baroclinic Vortices ◽  
Favorable Conditions

<p>Baroclinic vortices embedded in a large-scale vertical shear are examined. We describe a new class of steady propagating vortices that radiate Rossby waves but yet do not decay. This is possible since they can extract available potential energy (APE) from a large-scale vertically sheared flow, even though this flow is linearly stable. The vortices generate Rossby waves which induce a meridional vortex drift and an associated heat flux explained by an analysis of pseudomomentum and pseudoenergy. An analytical steady solution is considered for a marginally stable flow in a two-layer model on the beta-plane, where the beta-effect is compensated by the potential vorticity gradient (PVG) associated with the meridional slope of the density interface. The compensation occurs in the upper layer for an upper layer westward flow (an easterly shear) and in the lower layer for an upper layer eastward flow (the westerly shear). The theory is confirmed by numerical simulations indicating that for westward flows in subtropical oceans, the reduced PVG in the upper layer provides favorable conditions for eddy persistence and long-range propagation. The drifting and radiating vortex is an alternative mechanism besides baroclinic instability for converting background APE to mesoscale energy. </p>

scholarly journals Effect of Overturning Circulation on Long Equatorial Waves: A Low-Frequency Cutoff

2018 ◽  
Vol 75 (5) ◽  
pp. 1721-1739 ◽  
Author(s):  
Amanda Back ◽  
Joseph A. Biello
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Meridional Circulation ◽  
Low Frequency ◽  
Hadley Cell ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Background Flow ◽  
Overturning Circulation ◽  
Equatorial Wave

Zonally long tropical waves in the presence of a large-scale meridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscale moist dynamics (IMMD) theory. The model consists of a system of shallow-water equations describing barotropic and first baroclinic vertical modes coupled to one another by the zonally symmetric, time-independent background circulation. To isolate the effects of the meridional circulation alone, an idealized background flow is chosen to mimic the meridional and vertical components of the flow of the Hadley cell; the background flow meridionally converges and rises at the equator. The resulting linear eigenvalue problem is a generalization of the long-wave-scaled version of Matsuno’s equatorial wave problem with the addition of meridional and vertical advection. The results demonstrate that the meridional circulation couples equatorially trapped baroclinic Rossby waves to planetary, barotropic free Rossby waves. The meridional circulation also causes the Kelvin wave to develop an equatorially trapped barotropic component, imparting a westward-tilted vertical structure to the wave. The total energy of the linear system is positive definite, so all waves are shown to be neutrally stable. A critical layer exists at latitudes where the meridional background flow vanishes, resulting in a minimum frequency cutoff for physically feasible waves. Therefore, linear Matsuno waves with periods longer than the vertical transport time of the meridional circulation do not exist in the equatorial waveguide. This implies a low-frequency cutoff for long equatorial waves.

Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves

1989 ◽  
Vol 202 ◽  
pp. 149-176 ◽  
Author(s):  
Satoshi Sakai
Keyword(s):  
Gravity Waves ◽  
Rossby Waves ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Kelvin Wave ◽  
Layer System ◽  
Geostrophic Balance ◽  
New Type ◽  
Frontal Instability ◽  
Zero Phase

An ageostrophic version of Phillips’ model is studied. All instabilities found are systematically interpreted in terms of resonance of wave components. The instability occurs if there is a pair of wave components which propagate in the opposite direction to the basic flow and these wave components have almost the same Doppler-shifted frequency. A new instability, identified as a resonance between the Kelvin wave and the Rossby waves, is found at Froude number F ≈ 0.7. The Rossby waves are almost completely in geostrophic balance while the ageostrophic Kelvin wave is the same as in a one-layer system. Doppler shifting matches frequencies which would otherwise be very different. This instability is presumably the mechanism of the frontal instability observed by Griffiths & Linden (1982) in a laboratory experiment. Ageostrophic, baroclinic instability with non-zero phase speed is also observed in the numerical calculation. This instability is caused by resonance between different geostrophic modes.

Rotating Shallow-Water Models with Moist Convection

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Baroclinic Instability ◽  
Potential Temperature ◽  
Moist Convection ◽  
Mathematical Properties ◽  
Vertical Fluxes ◽  
Equivalent Potential ◽  
Shallow Water Models ◽  
Wave Emission ◽  
Rotating Shallow Water ◽  
Convective Fluxes

It is shown how the standard RSW can be ’augmented’ to include phase transitions of water. This chapter explains how to incorporate extra (convective) vertical fluxes in the model. By using Lagrangian conservation of equivalent potential temperature condensation of the water vapour, which is otherwise a passive tracer, is included in the model and linked to convective fluxes. Simple relaxational parameterisation of condensation permits the closure of the system, and surface evaporation can be easily included. Physical and mathematical properties of thus obtained model are explained, and illustrated on the example of wave scattering on the moisture front. The model is applied to ’moist’ baroclinic instability of jets and vortices. Condensation is shown to produce a transient increase of the growth rate. Special attention is paid to the moist instabilities of hurricane-like vortices, which are shown to enhance intensification of the hurricane, increase gravity wave emission, and generate convection-coupled waves.

scholarly journals Convectively Coupled Equatorial Waves. Part I: Horizontal and Vertical Structures

2007 ◽  
Vol 64 (10) ◽  
pp. 3406-3423 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian Hoskins ◽  
Julia Slingo
Keyword(s):  
Composite Structures ◽  
Wave Structure ◽  
Wave Theory ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Ambient Flow ◽  
Convectively Coupled Equatorial Waves ◽  
Eastern Hemisphere ◽  
Equatorial Wave

Abstract Multilevel 15-yr ECMWF Re-Analysis (ERA-15) and satellite-observed brightness temperature (Tb) data for the period May–October 1992 are used to examine the horizontal and vertical structures of convectively coupled equatorial waves. Dynamical waves are isolated using a methodology developed previously. Composite structures of convectively coupled equatorial waves are obtained using linear regression/correlation between convection (Tb) and dynamical structures. It is found that the relationship depends on the ambient flow and the nature of the convective coupling, and varies between off-equatorial- and equatorial-centered convection, different hemispheres, and seasons. The Kelvin wave structure in the Western Hemisphere is generally consistent with classic equatorial wave theory and has its convection located in the region of low-level convergence. In the Eastern Hemisphere the Kelvin wave tends to have convection in the region of enhanced lower-tropospheric westerlies and a tilted vertical structure. The Kelvin wave also tends to have a third peak in zonal wind amplitude at 500 hPa and exhibits upward propagation into the lower stratosphere. Lower-tropospheric westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave structures and their relationship with convection are consistent with classic equatorial wave theory and the implied lower-tropospheric convergences. In the Eastern Hemisphere the WMRG and R1 waves have first baroclinic mode structures in the vertical. However, in the Western Hemisphere, the R1 wave has a barotropic structure. In the Eastern Hemisphere the R1 wave, like the Kelvin wave, tends to have equatorial convection in the region of enhanced lower-level westerlies, suggesting that enhanced surface energy fluxes associated with these waves may play an important organizing role for equatorial convection in this warm-water hemisphere. In the upper troposphere, eastward-moving Rossby–gravity (EMRG) and n = 1 gravity waves are found in the Eastern Hemisphere, and eastward-moving WMRG and R1 waves are found in the Western Hemisphere, suggestive of Doppler shifting of waves by the ambient flow.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

scholarly journals Contributions of equatorial planetary waves and small-scale convective gravity waves to the 2019/20 QBO disruption

2021 ◽  
Author(s):  
Min-Jee Kang ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Reanalysis Data ◽  
Small Scale ◽  
Negative Wave ◽  
Quasi Biennial Oscillation ◽  
Wave Forcing ◽  
Equatorial Wave ◽  
Convective Gravity Waves

Abstract. In January 2020, unexpected easterly winds developed in the downward-propagating westerly quasi-biennial oscillation (QBO) phase. This event corresponds to the second QBO disruption in history, and it occurred four years after the first disruption that occurred in 2015/16. According to several previous studies, strong midlatitude Rossby waves propagating from the Southern Hemisphere (SH) during the SH winter likely initiated the disruption; nevertheless, the wave forcing that finally led to the disruption has not been investigated. In this study, we examine the role of equatorial waves and small-scale convective gravity waves (CGWs) in the 2019/20 QBO disruption using MERRA-2 global reanalysis data. In June–September 2019, unusually strong Rossby wave forcing originating from the SH decelerated the westerly QBO at 0°–5° N at ~50 hPa. In October–November 2019, vertically (horizontally) propagating Rossby waves and mixed Rossby–gravity (MRG) waves began to increase (decrease). From December 2019, contribution of the MRG wave forcing to the zonal wind deceleration was the largest, followed by the Rossby wave forcing originating from the Northern Hemisphere and the equatorial troposphere. In January 2020, CGWs provided 11 % of the total negative wave forcing at ~43 hPa. Inertia–gravity (IG) waves exhibited a moderate contribution to the negative forcing throughout. Although the zonal-mean precipitation was not significantly larger than the climatology, convectively coupled equatorial wave activities were increased during the 2019/20 disruption. As in the 2015/16 QBO disruption, the increased barotropic instability at the QBO edges generated more MRG waves at 70–90 hPa, and westerly anomalies in the upper troposphere allowed more westward IG waves and CGWs to propagate to the stratosphere. Combining the 2015/16 and 2019/20 disruption cases, Rossby waves and MRG waves can be considered the key factors inducing QBO disruption.

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