scholarly journals Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory

2020 ◽  
Vol 1 (1) ◽  
pp. 111-125
Author(s):  
Volkmar Wirth
Keyword(s):  
Ray Tracing ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Local Source ◽  
General Tendency ◽  
Theoretical Concepts ◽  
Model Configuration ◽  
Longitudinal Sector ◽  
Current Context ◽  
Dissipative Model

Abstract. Ray paths of stationary Rossby waves emanating from a local midlatitude source are usually refracted equatorward. However, this general tendency for equatorward propagation is mitigated by the presence of a midlatitude jet that acts as a zonal waveguide. This opens up the possibility of circum-global teleconnections and quasi-resonance, which suggests that the ability to guide a wave in the zonal direction is an important jet property. This paper investigates waveguidability of idealized midlatitude jets in a barotropic model on the sphere. A forced-dissipative model configuration with a local source for Rossby waves is used in order to quantify waveguidability by diagnosing the latitudinal distribution of waviness in a longitudinal sector far downstream of the forcing. Systematic sensitivity experiments show that waveguidability increases smoothly with increasing jet amplitude and with decreasing jet width. This result is contrasted with the predictions from two idealized theoretical concepts based on (1) ray tracing as derived from Wentzel–Kramers–Brillouin (WKB) theory and (2) a sharp jet with a zonally oriented front of potential vorticity. The existence of two so-called turning latitudes, which is the key diagnostic for a zonal waveguide according to ray tracing theory, turns out to be a poor predictor for the dependence of waveguidability on jet amplitude and jet width obtained in the numerical simulations. By contrast, the meridional gradient of potential vorticity correlates fairly well with the diagnosed waveguidability. The poor predictions from ray tracing are not surprising, because the underlying WKB assumptions are not satisfied in the current context. The failure of WKB is traced back to the properties of the underlying equations, and a heuristic argument is presented to elucidate the potential of the potential vorticity (PV) gradient to act as a proxy for waveguidability.

Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory

2020 ◽  
Author(s):  
Volkmar Wirth
Keyword(s):  
Ray Tracing ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Local Source ◽  
General Tendency ◽  
Theoretical Concepts ◽  
Model Configuration ◽  
Longitudinal Sector ◽  
Current Context ◽  
Dissipative Model

<p>Ray paths of stationary Rossby waves emanating from a local mid-latitude source are usually refracted equatorward. However, this general tendency for equatorward propagation is mitigated by the presence of a midlatitude jet which acts as a zonal waveguide. This opens the possibility for circum-global teleconnections and quasi-resonance, which suggests that the ability of a jet to guide a wave in the zonal direction is an important property.</p><p>This paper investigates waveguidability of idealized midlatitude jets in a barotropic model on the sphere. A forced-dissipative model configuration with a local source for Rossby waves is used in order to quantify waveguidability by diagnosing the latitudinal distribution of waviness in a longitudinal sector far downstream of the forcing. Systematic sensitivity experiments show that waveguidability increases smoothly with increasing jet amplitude and with decreasing jet width. This result is contrasted with the predictions from two idealized theoretical concepts based (1) on ray tracing as derived from WKB theory and (2) on a sharp jet with a zonally oriented front of potential vorticity. The existence of two so-called turning latitudes, which is the key diagnostic for a zonal waveguide according to ray tracing theory, turns out to be a poor predictor for the dependence of waveguidability on jet amplitude and jet width obtained in the numerical simulations. By contrast, the meridional gradient of potential vorticity correlates fairly well with the diagnosed waveguidability. The poor prediction from ray tracing is not surprising, because the underlying WKB assumptions are not satisfied in the current context.</p>

scholarly journals Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory

2020 ◽  
Author(s):  
Volkmar Wirth
Keyword(s):  
Ray Tracing ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Local Source ◽  
General Tendency ◽  
Theoretical Concepts ◽  
Model Configuration ◽  
Longitudinal Sector ◽  
Current Context ◽  
Dissipative Model

Abstract. Ray paths of stationary Rossby waves emanating from a local mid-latitude source are usually refracted equatorward. However, this general tendency for equatorward propagation is mitigated by the presence of a midlatitude jet which acts as a zonal waveguide. This opens the possibility for circum-global teleconnections and quasi-resonance, which suggests that the ability to guide a wave in the zonal direction is an important jet property. This paper investigates waveguidability of idealized midlatitude jets in a barotropic model on the sphere. A forced-dissipative model configuration with a local source for Rossby waves is used in order to quantify waveguidability by diagnosing the latitudinal distribution of waviness in a longitudinal sector far downstream of the forcing. Systematic sensitivity experiments show that waveguidability increases smoothly with increasing jet amplitude and with decreasing jet width. This result is contrasted with the predictions from two idealized theoretical concepts based on (1) ray tracing as derived from Wenztel-Kramers-Brillouin (short: WKB) theory and (2) a sharp jet with a zonally oriented front of potential vorticity. The existence of two so-called turning latitudes, which is the key diagnostic for a zonal waveguide according to ray tracing theory, turns out to be a poor predictor for the dependence of waveguidability on jet amplitude and jet width obtained in the numerical simulations. By contrast, the meridional gradient of potential vorticity correlates fairly well with the diagnosed waveguidability. The poor predictions from ray tracing are not surprising, because the underlying WKB assumptions are not satisfied in the current context. The failure of WKB is traced back to the properties of the underlying equations, and a heuristic argument is presented to elucidate the potential of the PV gradient to act as a proxy for waveguidability.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

2009 ◽  
Vol 66 (6) ◽  
pp. 1735-1748 ◽  
Author(s):  
W. T. M. Verkley
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Rossby Waves ◽  
Coriolis Parameter ◽  
Beta Plane ◽  
Propagating Waves ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity ◽  
The One

Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

A regime perspective on jet and blocking dynamics in CMIP6

2021 ◽  
Author(s):  
Joshua Dorrington
Keyword(s):  
Potential Vorticity ◽  
Climate Models ◽  
Rossby Waves ◽  
Climate Model ◽  
Atmospheric Dynamics ◽  
Interdecadal Variability ◽  
Model Ensemble ◽  
Atlantic Region ◽  
Non Linear ◽  
Jet Structure

<p>Weather over the Euro-Atlantic region during winter is highly variable, with rich and chaotic internal atmospheric dynamics. In particular, the non-linear breaking of Rossby waves irreversibly mixes potential vorticity contours and so triggers shifts in the latitude of the eddy driven jet and establishes persistent anticyclonic blocking events. The concept of atmospheric regimes captures the tendency for blocks – and for the jet – to persist in a small number of preferred locations. Regimes then provide a non-linear basis through which model deficiencies, interdecadal variability and forced trends in the Euro-Atlantic circulation can be studied.</p><p>A drawback of past regime approaches is that they were unable to easily capture both the dynamics of the jet and of blocking anticyclones simultaneously. In this work we apply a recently developed regime framework, which is able to capture both these important aspects while reducing sampling variability, to the CMIP6 climate model ensemble. We analyse both the historical variability and biases of blocking and jet structure in this latest generation of climate models, and make new estimates of the anthropogenic forced trend over the coming century.</p><p> </p>

scholarly journals Potential Vorticity of the Madden–Julian Oscillation

2012 ◽  
Vol 69 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Chidong Zhang ◽  
Jian Ling
Keyword(s):  
Potential Vorticity ◽  
Diabatic Heating ◽  
Rossby Waves ◽  
Early Stage ◽  
Relative Vorticity ◽  
Dynamical Structure ◽  
Madden Julian Oscillation ◽  
Convective Envelope ◽  
Convective Initiation ◽  
Pv Generation

Abstract This study explores the extent to which the dynamical structure of the Madden–Julian oscillation (MJO), its evolution, and its connection to diabatic heating can be described in terms of potential vorticity (PV). The signature PV structure of the MJO is an equatorial quadrupole of cyclonic and anticyclonic PV that tilts westward and poleward. This PV quadrupole is closely related to positive and negative anomalies in precipitation that are in a swallowtail pattern extending eastward along the equator and splitting into off-equatorial branches westward. Two processes dominate the generation of MJO PV. One is linear, involving MJO diabatic heating alone. The other is nonlinear, involving diabatic heating and relative vorticity of perturbations spectrally outside the MJO domain but spatially constrained to the MJO convective envelope. The MJO is thus partially a self-sustaining system and partially a consequence of scale interaction of MJO-constrained stochastic processes. Convective initiation of the MJO over the Indian Ocean features a swallowtail pattern of negative anomalous precipitation and associated anticyclonic PV anomalies at the early stage, and increasing cyclonic PV generation straddling the equator in the midtroposphere due to increasing positive anomalies in precipitation. These lead to the swallowtail pattern in positive anomalous precipitation and the associated PV quadrupole that signifies the fully developed MJO. The equatorial Kelvin and Rossby waves bear PV structures distinct from that of the MJO. They contribute insignificantly to the structure and generation of MJO PV. Solely based on the PV analysis, a hypothesis is proposed that the fundamental dynamics of the MJO depends on neither Kelvin nor Rossby waves.

scholarly journals On the correlation between ozone and potential vorticity for large-scale Rossby waves

1997 ◽  
Vol 102 (D7) ◽  
pp. 8793-8804 ◽  
Author(s):  
Lars Peter Riishøjgaard ◽  
Erland Källén
Keyword(s):  
Potential Vorticity ◽  
Large Scale ◽  
Rossby Waves

scholarly journals Jets and Orography: Idealized Experiments with Tip Jets and Lighthill Blocking

2007 ◽  
Vol 64 (10) ◽  
pp. 3627-3639 ◽  
Author(s):  
P. B. Rhines
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Flow Acceleration ◽  
Westerly Flow ◽  
The Mean ◽  
Strong Control

Abstract This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on βa2/U, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, U (β is the meridional potential vorticity gradient, f is the Coriolis frequency, and a is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially β plumes, which are illustrated by their linear Green function. For large βa2/U, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, βa2/U ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, δh, relative to the mean fluid depth, H, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, δh/h ≪ aβ/f, that the f/h contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with βa2/U ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.

scholarly journals An Adiabatic Mechanism for the Reduction of Jet Meander Amplitude by Potential Vorticity Filamentation

2018 ◽  
Vol 75 (12) ◽  
pp. 4091-4106 ◽  
Author(s):  
Ben Harvey ◽  
John Methven ◽  
Maarten H. P. Ambaum
Keyword(s):  
Decay Rate ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Large Scale ◽  
Rossby Waves ◽  
Weather Forecasting ◽  
Single Layer ◽  
Jet Streams ◽  
Rapid Reduction ◽  
Simple Method

Abstract The amplitude of ridges in large-amplitude Rossby waves has been shown to decrease systematically with lead time during the first 1–5 days of operational global numerical weather forecasts. These models also exhibit a rapid reduction in the isentropic gradient of potential vorticity (PV) at the tropopause during the first 1–2 days of forecasts. This paper identifies a mechanism linking the reduction in large-scale meander amplitude on jet streams to declining PV gradients. The mechanism proposed is that a smoother isentropic transition of PV across the tropopause leads to excessive PV filamentation on the jet flanks and a more lossy waveguide. The approach taken is to analyze Rossby wave dynamics in a single-layer quasigeostrophic model. Numerical simulations show that the amplitude of a Rossby wave propagating along a narrow but smooth PV front does indeed decay transiently with time. This process is explained in terms of the filamentation of PV from the jet core and associated absorption of wave activity by the critical layers on the jet flanks, and a simple method for quantitatively predicting the magnitude of the amplitude reduction without simulation is presented. Explicitly diffusive simulations are then used to show that the combined impact of diffusion and the adiabatic rearrangement of PV can result in a decay rate of Rossby waves that is 2–4 times as fast as could be expected from diffusion acting alone. This predicted decay rate is sufficient to explain the decay observed in operational weather forecasting models.

scholarly journals Piecewise Potential Vorticity Inversion: Elementary Tests

2008 ◽  
Vol 65 (6) ◽  
pp. 2015-2024 ◽  
Author(s):  
Joseph Egger
Keyword(s):  
Potential Vorticity ◽  
Rossby Waves ◽  
Specific Problem ◽  
Analytic Solutions ◽  
One Dimensional ◽  
Barotropic Fluid ◽  
Wave Dynamics ◽  
Baroclinic Waves ◽  
Potential Vorticity Inversion ◽  
Wave Development

Abstract Piecewise potential vorticity inversion (PPVI) is widely accepted as a useful tool in atmospheric diagnostics. This method is thought to quantify the instantaneous interaction at a distance of anomalies of potential vorticity (PV) separated horizontally and/or vertically. Doubts with respect to the dynamical justification of PPVI are formulated. In particular, it is argued that the tendency of the inverted streamfunction must be determined in order to quantify far-field effects. Elementary tests of PPVI are conducted to clarify these points. First, PPVI is performed for the textbook case of linear Rossby waves in a one-dimensional barotropic fluid. Analytic solutions are presented for PPVI and the related tendency problem. It is found that PPVI does not contribute to an understanding of Rossby wave dynamics. On the other hand, PPVI turns out to be more useful when applied to confined PV extrema. Neither the application of PPVI to linear baroclinic waves in zonal shear flow nor the inversions of the related temperature anomalies at the boundaries help to better understand the wave development. It is concluded that PPVI with additional tendency calculations poses and solves a specific problem by retaining observed PV anomalies in one subdomain and removing them in others. The usefulness of the results with regard to the diagnosis of the observed state depends strongly on the flows considered and on the partitions chosen, which must comply with a simple rule.

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