A Note on the Reflection of Low-Frequency Equatorial Rossby Waves from Realistic Western Boundaries

1987 ◽  
Vol 17 (11) ◽  
pp. 1944-1949 ◽  
Author(s):  
John D. McCalpin
Keyword(s):  
Rossby Waves ◽  
Low Frequency ◽  
Equatorial Rossby Waves

scholarly journals Reflection and Transmission of Equatorial Rossby Waves*

2005 ◽  
Vol 35 (3) ◽  
pp. 363-373 ◽  
Author(s):  
Michael A. Spall ◽  
Joseph Pedlosky
Keyword(s):  
Incident Energy ◽  
Rossby Waves ◽  
Low Frequency ◽  
Kelvin Waves ◽  
Western Boundary ◽  
Incident Flux ◽  
Western Basin ◽  
Wind Event ◽  
Wind Events ◽  
Equatorial Rossby Waves

Abstract The interaction of equatorial Rossby waves with a western boundary perforated with one or more narrow gaps is investigated using a shallow-water numerical model and supporting theory. It is found that very little of the incident energy flux is reflected into eastward-propagating equatorial Kelvin waves provided that at least one gap is located within approximately a deformation radius of the equator. Because of the circulation theorem around an island, the existence of a second gap off the equator reduces the reflection of short Rossby waves and enhances the transmission of the incident energy into the western basin. The westward energy transmitted past the easternmost island is further reduced upon encountering islands to the west, even if these islands are located entirely within the “shadow” of the easternmost island. A localized patch of wind forcing was also used to generate low-frequency Rossby waves for cases with island configurations representative of the western equatorial Pacific. For both idealized islands and a coastline based on the 200-m isobath, the amount of incident energy reflected into Kelvin waves depends on both the duration of the wind event and the meridional decay scale of the anomalous winds. For wind events of 2-yr duration with a meridional decay scale of 700 km, the reflected energy is 37% of the incident flux, and the energy transmitted into the Indian Ocean is approximately 10% of the incident flux, very close to that predicted by previous theories. For shorter wind events or winds confined more closely to the equator the reflected energy is significantly less.

scholarly journals Influence of the Barotropic Mean Flow on the Width and the Structure of the Atlantic Equatorial Deep Jets

2014 ◽  
Vol 44 (9) ◽  
pp. 2485-2497 ◽  
Author(s):  
Martin Claus ◽  
Richard J. Greatbatch ◽  
Peter Brandt
Keyword(s):  
Rossby Waves ◽  
Current System ◽  
Low Frequency ◽  
Water Model ◽  
Kelvin Wave ◽  
Mean Flow ◽  
The North ◽  
Basin Mode ◽  
The Mean ◽  
Equatorial Rossby Waves

Abstract A representation of an equatorial basin mode excited in a shallow-water model for a single high-order baroclinic vertical normal mode is used as a simple model for the equatorial deep jets. The model is linearized about both a state of rest and a barotropic mean flow corresponding to the observed Atlantic Equatorial Intermediate Current System. It was found that the eastward mean flow associated with the North and South Intermediate Counter Currents (NICC and SICC, respectively) effectively shields the equator from off-equatorial Rossby waves. The westward propagation of these waves is blocked, and focusing on the equator due to beta dispersion is prevented. This leads to less energetic jets along the equator. On the other hand, the westward barotropic mean flow along the equator reduces the gradient of absolute vorticity and hence widens the cross-equatorial structure of the basin mode. Increasing lateral viscosity predominantly affects the width of the basin modes’ Kelvin wave component in the presence of the mean flow, while the Rossby wave is confined by the flanking NICC and SICC. Independent of the presence of the mean flow, the application of sufficient lateral mixing also hinders the focusing of off-equatorial Rossby waves, which is hence an unlikely feature of a low-frequency basin mode in the real ocean.

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>

scholarly journals Trapped Planetary (Rossby) Waves Observed in the Indian Ocean by Satellite Borne Altimeters

2017 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor
Keyword(s):  
Indian Ocean ◽  
Rossby Waves ◽  
Low Frequency ◽  
Propagation Speed ◽  
Wave Theory ◽  
Planetary Waves ◽  
Sea Surface ◽  
Trapped Wave ◽  
The Indian Ocean ◽  
Frequency Variations

Abstract. Using 20 years of accurately calibrated, high resolution, observations of Sea Surface Height Anomalies (SSHA) by satellite ‎borne altimeters we show that in the Indian Ocean south of the Australian coast the low frequency variations of SSHA are ‎dominated by westward propagating, trapped, i.e. non-harmonic, planetary waves. Our results demonstrate that the ‎meridional-dependent amplitudes of the SSHA are large only within a few degrees of latitude next to the South-Australian ‎coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the ‎amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signals is analyzed by ‎employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely ‎between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The ‎estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of ‎harmonic Rossby (Planetary) waves by 140 % to 200 %. In contrast, the theory of trapped Rossby (Planetary) waves in a ‎domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase ‎speeds.‎

Synthesis of Vortex Rossby Waves. Part II: Vortex Motion and Waves in the Outer Waveguide

2015 ◽  
Vol 72 (10) ◽  
pp. 3958-3974 ◽  
Author(s):  
Israel Gonzalez ◽  
Amaryllis Cotto ◽  
Hugh E. Willoughby
Keyword(s):  
Nonlinear Model ◽  
Rossby Waves ◽  
Critical Radius ◽  
Vortex Motion ◽  
Low Frequency ◽  
Wave Interaction ◽  
Linear Acceleration ◽  
Propagation Speed ◽  
Large Radius ◽  
Subsequent Work

Abstract Beta, the meridional gradient of planetary vorticity, causes tropical cyclones to propagate poleward and westward at approximately 2 m s−1. In a previous shallow-water linear model, the simulated vortex accelerated without limit, ostensibly because beta forced a free linear mode. In the analogous nonlinear model, wave–wave interaction limited the propagation speed. Subsequent work based upon the asymmetric balance (AB) approximation was unable to replicate the linear result. The present barotropic nondivergent model replicates the linear beta gyres as a streamfunction dipole with a uniform southeasterly ventilation flow across the vortex. The simulated storm accelerates to unphysical, but finite, speeds that are limited by vorticity filamentation. In the analogous nonlinear model, nonlinearly forced wavenumber-1 gyres have opposite phase to the linear gyres so that their ventilation flow counteracts advection by the linear gyres to limit the overall vortex speed to approximately 3 m s−1. A bounded mean vortex with zero circulation at large radius must contain an outer annulus of anticyclonic vorticity to satisfy the circulation theorem. The resulting positive mean vorticity gradient constitutes an outer waveguide that supports downstream-propagating, very-low-frequency vortex Rossby waves. It is confined between an inner critical radius where the waves are absorbed and an outer turning point where they are reflected. Vorticity filamentation at the critical radius limits the beta-drift acceleration. The original unlimited linear acceleration stemmed from too-weak dissipation caused by second-order diffusion applied to velocity components instead of vorticity. Fourth-order diffusion and no outer waveguide in the Rankine-like vortex of the AB simulations plausibly explain the different results.

scholarly journals Propagation properties of Rossby waves for latitudinal β-plane variations of <I>f</I> and zonal variations of the shallow water speed

2012 ◽  
Vol 30 (5) ◽  
pp. 849-855 ◽  
Author(s):  
C. T. Duba ◽  
J. F. McKenzie
Keyword(s):  
Shallow Water ◽  
Group Velocity ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Wave Number ◽  
Coriolis Parameter ◽  
Propagation Properties ◽  
Wave Normal ◽  
Water Speed

Abstract. Using the shallow water equations for a rotating layer of fluid, the wave and dispersion equations for Rossby waves are developed for the cases of both the standard β-plane approximation for the latitudinal variation of the Coriolis parameter f and a zonal variation of the shallow water speed. It is well known that the wave normal diagram for the standard (mid-latitude) Rossby wave on a β-plane is a circle in wave number (ky,kx) space, whose centre is displaced −β/2 ω units along the negative kx axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. This form of anisotropy (arising from the latitudinal y variation of f), combined with the highly dispersive nature of the wave, gives rise to a group velocity diagram which permits eastward as well as westward propagation. It is shown that the group velocity diagram is an ellipse, whose centre is displaced westward, and whose major and minor axes give the maximum westward, eastward and northward (southward) group speeds as functions of the frequency and a parameter m which measures the ratio of the low frequency-long wavelength Rossby wave speed to the shallow water speed. We believe these properties of group velocity diagram have not been elucidated in this way before. We present a similar derivation of the wave normal diagram and its associated group velocity curve for the case of a zonal (x) variation of the shallow water speed, which may arise when the depth of an ocean varies zonally from a continental shelf.

scholarly journals Tropical Wave Driving of the Annual Cycle in Tropical Tropopause Temperatures. Part II: Model Results

2006 ◽  
Vol 63 (5) ◽  
pp. 1420-1431 ◽  
Author(s):  
W. A. Norton
Keyword(s):  
Annual Cycle ◽  
Rossby Waves ◽  
Lower Stratosphere ◽  
Equation Model ◽  
Stationary Waves ◽  
Mean Flow ◽  
Flux Divergence ◽  
Tropical Tropopause ◽  
Equatorial Rossby Waves ◽  
Tropical Heating

Abstract The atmospheric response to a localized distribution of tropical heating is examined in terms of the stationary waves excited and how these impact the mean flow near the tropical tropopause. This is done by examining nonlinear simulations of the Gill model with a primitive equation model that extends from the surface up into the stratosphere. The model produces strong cooling of zonal mean temperatures near the tropical tropopause when the heating is on the equator but weaker cooling with the heating at 15°N. The model shows that equatorial Rossby waves that penetrate the lower stratosphere and changes in EP flux divergence that correspond to the observed changes between December and August. It is suggested that ascent in the upper tropical troposphere is driven by vorticity advection or equivalently potential vorticity fluxes due to these equatorial Rossby waves, particularly when the heating is close to the equator. The model results provide support to the hypothesis that the annual cycle in tropical tropopause temperatures is a result of the annual variation in latitude of tropical heating and that equatorial Rossby waves are key in producing the response in the upper troposphere and lower stratosphere.

scholarly journals Instability of combined gravity-inertial-Rossby waves in atmospheres and oceans

2011 ◽  
Vol 29 (6) ◽  
pp. 997-1003 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Energy Exchange ◽  
Wave Speed ◽  
Rossby Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Ocean Dynamics ◽  
Stratified Medium ◽  
Instability Condition ◽  
Long Wavelength ◽  
Critical Latitude

Abstract. The properties of the instability of combined gravity-inertial-Rossby waves on a β-plane are investigated. The wave-energy exchange equation shows that there is an exchange of energy with the background stratified medium. The energy source driving the instability lies in the background enthalpy released by the gravitational buoyancy force. It is shown that if the phase speed of the westward propagating low frequency-long wavelength Rossby wave exceeds the Poincaré-Kelvin (or "equivalent" shallow water) wave speed, instability arises from the merging of Rossby and Poincaré modes. There are two key parameters in this instability condition; namely, the equatorial/rotational Mach (or Froude) number M and the latitude θ0 of the β-plane. In general waves equatorward of a critical latitude for given M can be driven unstable, with corresponding growth rates of the order of a day or so. Although these conclusions may only be safely drawn for short wavelengths corresponding to a JWKB wave packet propagating internally and located far from boundaries, nevertheless such a local instability may play a significant role in atmosphere-ocean dynamics.

scholarly journals Long-Wave Dynamics of Sea Level Variations during Indian Ocean Dipole Events

2009 ◽  
Vol 39 (5) ◽  
pp. 1115-1132 ◽  
Author(s):  
Dongliang Yuan ◽  
Hailong Liu
Keyword(s):  
Indian Ocean ◽  
Sea Level ◽  
Indian Ocean Dipole ◽  
Rossby Waves ◽  
Western Boundary ◽  
Kelvin Wave ◽  
Wave Pulse ◽  
Wave Dynamics ◽  
Long Wave ◽  
Equatorial Rossby Waves

Abstract Long-wave dynamics of the interannual variations of the equatorial Indian Ocean circulation are studied using an ocean general circulation model forced by the assimilated surface winds and heat flux of the European Centre for Medium-Range Weather Forecasts. The simulation has reproduced the sea level anomalies of the Ocean Topography Experiment (TOPEX)/Poseidon altimeter observations well. The equatorial Kelvin and Rossby waves decomposed from the model simulation show that western boundary reflections provide important negative feedbacks to the evolution of the upwelling currents off the Java coast during Indian Ocean dipole (IOD) events. Two downwelling Kelvin wave pulses are generated at the western boundary during IOD events: the first is reflected from the equatorial Rossby waves and the second from the off-equatorial Rossby waves in the southern Indian Ocean. The upwelling in the eastern basin during the 1997–98 IOD event is weakened by the first Kelvin wave pulse and terminated by the second. In comparison, the upwelling during the 1994 IOD event is terminated by the first Kelvin wave pulse because the southeasterly winds off the Java coast are weak at the end of 1994. The atmospheric intraseasonal forcing, which plays an important role in inducing Java upwelling during the early stage of an IOD event, is found to play a minor role in terminating the upwelling off the Java coast because the intraseasonal winds are either weak or absent during the IOD mature phase. The equatorial wave analyses suggest that the upwelling off the Java coast during IOD events is terminated primarily by western boundary reflections.

Sign in / Sign up

Export Citation Format

Share Document