scholarly journals The Art of Identifying Equatorial Waves

2021 ◽  
Author(s):  
Peter Knippertz ◽  
Juliana Dias ◽  
Andreas H. Fink ◽  
Maria Gehne ◽  
George Kiladis ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Deep Convection ◽  
Water System ◽  
Wave Theory ◽  
Lead Times ◽  
Linear Wave ◽  
Equatorial Waves ◽  
Easterly Waves ◽  
Advantages And Disadvantages ◽  
Shallow Water System

<div> <div> <div> <div> <p>Equatorial waves are synoptic- to planetary-scale propagating disturbances at low latitudes with frequencies from a few days to several weeks. Here this term includes Kelvin waves, equatorial Rossby waves, mixed-Rossby gravity waves, and inertio-gravity waves, which are closely related to linear wave theory, but also tropical disturbances, African easterly waves, and the intraseasonal Madden-Julian Oscillation. These waves can couple with deep convection, leading to a substantial modulation of rainfall. Recent work has shown that equatorial waves are amongst the dynamical features internal to the troposphere with the longest intrinsic predictability and that some models forecast them with an exploitable level of skill at lead times of up to a few weeks.</p> <p>A number of methods have been developed to identify and objectively isolate equatorial waves, both in (usually satellite) observations and in model fields. Most of these rely on (or at least refer to) the adiabatic, frictionless linearized primitive equations or shallow water system on the tropical beta plane. Common ingredients to these methods are longitude-time filtering (Fourier or wavelet) and/or projections onto predefined empirical or theoretical dynamical patterns. This paper aims to give an overview of the different methods to isolate the waves and their structures, to discuss underlying assumptions, to provide a systematic comparison, and to reveal advantages and disadvantages of each method. This way this study helps to optimally choose an approach suited to a given problem at hand and to avoid misuse and misinterpretation of the results.</p> </div> </div> </div> </div>

Modulation of Shallow-Water Equatorial Waves due to a Varying Equivalent Height Background

2013 ◽  
Vol 70 (9) ◽  
pp. 2726-2750 ◽  
Author(s):  
Juliana Dias ◽  
Pedro L. Silva Dias ◽  
George N. Kiladis ◽  
Maria Gehne
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Water System ◽  
Phase Speed ◽  
Asymptotic Solutions ◽  
Height Anomaly ◽  
Equatorial Waves ◽  
Moist Convection ◽  
Horizontal Structure ◽  
Shallow Water System

Abstract The dynamics of convectively coupled equatorial waves (CCEWs) is analyzed in an idealized model of the large-scale atmospheric circulation. The model is composed of a linear rotating shallow-water system with a variable equivalent height, or equivalent gravity wave speed, which varies in space. This model is based on the hypothesis that moist convection acts to remove convective instability, therefore modulating the equivalent height of a shallow-water system. Asymptotic solutions are derived in the case of a small perturbation around a constant coefficient, which is assumed to be a mean moist equivalent height derived from satellite observations. The first-order solutions correspond to the free normal modes of the linear shallow-water system and the second-order flow is derived solving a perturbation eigenvalue problem. The asymptotic solutions are documented in the case of a zonally varying equivalent height and for wavenumbers and frequencies that are consistent with observations of CCEWs. This analysis shows that the dynamics of the secondary divergence and its impact on the full divergence varies mode by mode. For instance, for a negative equivalent height anomaly, which is interpreted as a moister background, the secondary divergence is nearly in phase with the primary divergence in the case of Kelvin waves—in contrast to mixed Rossby–gravity waves where the secondary divergence acts to attenuate the primary divergence. While highly idealized, the modeled waves share some features with observations, providing a mechanism for the relationship between CCEWs phase speed, amplitude, and horizontal structure.

Equilibrium dynamics in a forced-dissipative f-plane shallow-water system

1994 ◽  
Vol 280 ◽  
pp. 369-394 ◽  
Author(s):  
Li Yuan ◽  
Kevin Hamilton
Keyword(s):  
Energy Spectrum ◽  
Shallow Water ◽  
Gravity Waves ◽  
Water System ◽  
Water Model ◽  
Dimensional System ◽  
Linear Potential ◽  
Two Dimensional ◽  
Equilibrium Dynamics ◽  
Shallow Water System

The equilibrium dynamics in a homogeneous forced-dissipative f-plane shallow-water system is investigated through numerical simulations. In addition to classical two-dimensional turbulence, inertio-gravity waves also exist in this system. The dynamics is examined by decomposing the full flow field into a dynamically balanced potential-vortical component and a residual ‘free’ component. Here the potential-vortical component is defined as part of the flow that satisfies the gradient-wind balance equation and that contains all the linear potential vorticity of the system. The residual component is found to behave very nearly as linear inertio-gravity waves. The forcing employed is a mass and momentum source balanced so that only the large-scale potential-vortical component modes are directly excited. The dissipation is provided by a linear relaxation applied to the large scales and by an eighth-order linear hyperdiffusion. The statistical properties of the potential-vortical component in the fully developed flow were found to be very similar to those of classical two-dimensional turbulence. In particular, the energy spectrum of the potential-vortical component at scales smaller than the forcing is close to the ∼ k−3 expected for a purely two-dimensional system. Detailed analysis shows that the downscale enstrophy cascade into any wavenumber is dominated by very elongated triads involving interactions with large scales. Although not directly forced, a substantial amount of energy is found in the inertio-gravity modes and interactions among inertio-gravity modes are principally responsible for transferring energy to the small scales. The contribution of the inertio-gravity modes to the flow leads to a shallow tail at the high-wavenumber end of the total energy spectrum. For parameters roughly appropriate for the midlatitude atmosphere (notably Rossby number ∼ 0.5), the break between the roughly ∼ k−3 regime and this shallower regime occurs at scales of a few hundred km. This is similar to the observed mesoscale regime in the atmosphere. The nonlinear interactions among the inertio-gravity modes are extremely broadband in spectral space. The implications of this result for the subgrid-scale closure in the shallow-water model are discussed.

scholarly journals Surface manifestation of stochastically excited internal gravity waves

2021 ◽  
Author(s):  
Daniel Lecoanet ◽  
Matteo Cantiello ◽  
Evan H Anders ◽  
Eliot Quataert ◽  
Louis-Alexandre Couston ◽  
...  
Keyword(s):  
Transfer Function ◽  
Gravity Waves ◽  
Massive Stars ◽  
Theoretical Calculations ◽  
Low Frequency ◽  
Wave Theory ◽  
Internal Gravity Waves ◽  
Finite Width ◽  
Linear Wave ◽  
Surface Manifestation

Abstract Recent photometric observations of massive stars show ubiquitous low-frequency ‘red-noise’ variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red-noise. Theoretical calculations using linear wave theory by Shiode et al (2013) and Lecoanet et al (2019) predict IGWs should manifest at the surface as regularly-spaced peaks associated with standing g-modes. In light of the apparent discrepancy between these theories and simulations/observations, we test the theories with simplified 2D numerical simulations of wave generation by convection. The simulations agree with the transfer function calculations presented in Lecoanet et al (2019), demonstrating that the transfer function correctly models linear wave propagation. However, there are differences between our simulations and the g-mode amplitude predictions of Shiode et al (2013). This is because that work did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we again find good agreement between theory and simulations. This paper verifies the theoretical approach of Lecoanet et al (2019) and strengthens their conclusion that internal gravity waves generated by core convection do not have a surface manifestation consistent with observed low-frequency variability of massive stars.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

scholarly journals The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

2000 ◽  
Vol 18 (10) ◽  
pp. 1316-1324 ◽  
Author(s):  
S.-D. Zhang ◽  
F. Yi ◽  
J.-F. Wang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Packets ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Nonlinear Propagation ◽  
Waves And Tides ◽  
Time Variations ◽  
Isothermal Atmosphere

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

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 Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part II: Shear Flow with a Critical Level

2010 ◽  
Vol 67 (3) ◽  
pp. 694-712 ◽  
Author(s):  
Ji-Young Han ◽  
Jong-Jin Baik
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Wind Direction ◽  
Critical Level ◽  
Deep Convection ◽  
Vertical Wind Shear ◽  
Finite Depth ◽  
Vertical Displacement ◽  
Two Dimensions ◽  
Three Dimensions

Abstract Convectively forced mesoscale flows in a shear flow with a critical level are theoretically investigated by obtaining analytic solutions for a hydrostatic, nonrotating, inviscid, Boussinesq airflow system. The response to surface pulse heating shows that near the center of the moving mode, the magnitude of the vertical velocity becomes constant after some time, whereas the magnitudes of the vertical displacement and perturbation horizontal velocity increase linearly with time. It is confirmed from the solutions obtained in present and previous studies that this result is valid regardless of the basic-state wind profile and dimension. The response to 3D finite-depth steady heating representing latent heating due to cumulus convection shows that, unlike in two dimensions, a low-level updraft that is necessary to sustain deep convection always occurs at the heating center regardless of the intensity of vertical wind shear and the heating depth. For deep heating across a critical level, little change occurs in the perturbation field below the critical level, although the heating top height increases. This is because downward-propagating gravity waves induced by the heating above, but not near, the critical level can hardly affect the flow response field below the critical level. When the basic-state wind backs with height, the vertex of V-shaped perturbations above the heating top points to a direction rotated a little clockwise from the basic-state wind direction. This is because the V-shaped perturbations above the heating top is induced by upward-propagating gravity waves that have passed through the layer below where the basic-state wind direction is clockwise relative to that above.

Sign in / Sign up

Export Citation Format

Share Document