How white is the sky?

<p>The energy spectrum of atmospheric horizontal motions has been extensively studied in observations and numerical simulations. Its canonical shape includes a transition from the -3 power law at synoptic scale to -5/3 power law at mesoscale. The transition is taking place at scales around 500 km that can be seen as the scale where energy associated with quasi-linear inertia-gravity waves exceeds the balanced (or Rossby wave) energy. In contrast to the horizontal spectrum, the spectrum of kinetic energy of vertical motions is poorly known since the vertical motion is not an observed quantity of the global observing system and vertical kinetic energy spectra from non-hydrostatic models are difficult to validate.</p> <p>Traditionally, vertical velocities associated with the Rossby and gravity waves have been treated separately using the quasi-geostrophic omega equations and polarization relations for the stratified Boussinesq fluid in the (x,z) plane, respectively. In the tropics, the Rossby and gravity  wave regimes are difficult to separate and their frequency gap, present in the extra-tropics, is filled with the Kelvin and mixed Rossby-gravity waves. A separate treatment of the Rossby and gravity wave regimes makes it challenging to quantify energies of their vertical motions and vertical momentum fluxes. A unified treatment and wave interactions is performed by high-resolution non-hydrostatic models but their understanding requires the toolkit of theory. </p> <p>This contribution presents a unified framework for the derivation of vertical velocities of the Rossby and inertia-gravity waves and associated kinetic energy spectra. Expressions for the Rossby and gravity wave vertical velocities are derived using the normal-mode framework in the hydrostatic atmosphere that can be considered applicable up to the scale around 10 km. The derivation involves the analytical evaluation of divergence of the horizontal wind associated with the Rossby and inertia-gravity eigensolutions of the linearized primitive equations. The new framework is applied to the global analysis data of the ECMWF system. Results confirm that the tropical vertical kinetic energy spectra associated with inertia-gravity waves are on average indeed white. Deviations from the white spectrum are discussed for latitude and altitude bands.</p>

Faster and Slower Soliton Phase Shift: Oceanic Waves Affected by Earth Rotation

This research paper investigates the accuracy of a novel computational scheme (Khater II method) by applying this new technique to the fractional nonlinear Ostrovsky (FNO) equation. The accuracy of the obtained solutions was verified by employing the Adomian decomposition (AD) and El Kalla (EK) methods. The AD and EK methods are considered as two of the most accurate semi-analytical schemes. The FNO model is a modified version of the well-known Korteweg–de Vries (KdV) equation that considers the effects of rotational symmetry in space. However, in the KdV model, solutions to the KdV equations substitute this effect with radiating inertia gravity waves, and thus this impact is ignored. The analytical, semi-analytical, and accuracy between solutions are represented in some distinct plots. Additionally, the paper’s novelty and its contributions are demonstrated by comparing the obtained solutions with previously published results.

2-Day Westward-Propagating Inertio-Gravity Waves during GoAmazon

The dynamical and thermodynamical features of Amazonian 2-day westward-propagating inertia-gravity waves (WIG) are examined. On the basis of a linear regression analysis of satellite brightness temperature and data from the 2014-15 Observations and Modeling of the Green Ocean Amazon (GoAmazon) field campaign, it is shown that Amazonian WIG waves exhibit structure and propagation characteristics consistent with the n=1 WIG waves from shallow water theory. These WIG waves exhibit a pronounced seasonality, with peak activity occurring from March to May and a minimum occurring from June to September. Evidence is shown that mesoscale convective systems over the Amazon are frequently organized in 2-day WIG waves. Results suggest that many of the Amazonian WIG waves come from pre-existing 2-day waves over the Atlantic, which slow down when coupled with the deeper, more intense convection over tropical South America. In contrast to WIG waves that occur over the ocean, Amazonian 2-day WIG waves exhibit a pronounced signature in surface temperature, moisture, and heat fluxes.

The signature of the tropospheric gravity wave background in observed mesoscale motion

How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. This study diagnoses profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC4A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area-equivalent radius. This functional dependence is also confirmed in reanalysis data and a global, freely evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite-observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia–gravity waves may be more relevant as a convection-modulating factor. The analytic relationship between energy spectra and divergence amplitudes proposed in this article, if confirmed by future studies, could be used to design better external forcing methods for regional models.

Diverse solitary and Jacobian solutions in a continually laminated fluid with respect to shear flows through the Ostrovsky equation

In this paper, the generalized Jacobi elliptical functional (JEF) and modified Khater (MK) methods are employed to find the soliton, breather, kink, periodic kink, and lump wave solutions of the Ostrovsky equation. This model is considered as a mathematical modification model of the Korteweg-de Vries (KdV) equation with respect to the effects of background rotation. The solitary solutions of the well-known mathematical model (KdV equation) usually decay and are replaced by radiating inertia gravity waves. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Many distinct solutions are obtained through the employed computational schemes. Moreover, some solutions are sketched in 2D, 3D, and contour plots. The effective and powerful of the two used computational schemes are tested. Furthermore, the accuracy of the obtained solutions is examined through a comparison between them and that had been obtained in previously published research.

The signature of the tropospheric gravity wave background in observed mesoscale motion

<p>How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. We diagnose profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC<sup>4</sup>A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area equivalent radius. This functional dependence is also confirmed in reanalysis data and a global freely-evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia-gravity waves may be more relevant as a convection-modulating factor. We propose an analytic relationship between energy spectra and divergence amplitudes, which, if confirmed by future studies, could be used to design better external forcing methods for regional models.</p>

Wind-driven Oscillations in the Meridional Overturning Circulation near the equator

<p>Numerical model studies have shown the meridional overturning circulation (MOC) to exhibit variability on near-inertial timescales, and also indicate a region of enhanced variability on the equator. We present an analysis of a set of integrations of a global configuration of a numerical ocean model, which show very large amplitude oscillations in the MOCs in the Atlantic, Indian and Pacific oceans confined to the equatorial region. The amplitude of these oscillations is proportional to the width of the ocean basin, typically about 100 (200) Sv in the Atlantic (Pacific). We show that these oscillations are driven by surface winds within 10°N/S of the equator, and their periods (typically 4-10 days) correspond to a small number of low mode equatorially trapped planetary waves. Furthermore, the oscillations can be well reproduced by idealised wind-driven simulations linearised about a state of rest. Zonally integrated linearised equations of motion are solved using vertical normal modes and equatorial meridional modes representing Yanai and inertia-gravity waves. Idealised simulations capture between 85% and 95% of the variance of matching time-series segments diagnosed from the NEMO integrations. Similar results are obtained for the corresponding modes in the Atlantic and Indian Oceans. Our results raise questions about the roles of inertia-gravity waves near the equator in the vertical transfer of heat and momentum and whether these transfers will be explicitly resolved by ocean models or need to be parametrised.</p>