The energy dispersion of magnetic Rossby waves has been investigated by applying the two-dimensional incompressible magnetohydrodynamic (MHD) equations in both uniform basic flow and basic magnetic field. The dispersion relation suggests that the magnetic Rossby waves can be divided into fast- and slow-propagating modes, respectively. The fast-propagating mode propagates eastward and is similar to the fast Alfvén waves. The energy dispersion speed is faster than the phase speed, which means the perturbation energy can lead the perturbations themselves to arrive downstream. The slow-propagating waves with smaller (larger) horizontal scales are similar to those of the slow Alfvén waves (Rossby waves). The zonal group velocity is slower than the zonal phase speed for the slow-propagating magnetic Rossby waves. For the slow-propagating waves that propagate eastward, this means that the perturbation energy may trigger new perturbations that are located upstream of the perturbations themselves. The group velocity vector is basically same as (opposite of) the wavevector for the fast-propagating (slow-propagating) magnetic Rossby waves that propagate eastward. The endpoints of the group velocity vectors and the wavevector multiplying a factor are located on a cycle in the wavenumber space. Due to the uniform basic flow and the uniform basic magnetic field, the energy dispersion paths (called rays) are straight lines. Along the straight-line rays, the wave action, wave energy, and amplitude keep their initial values, and the wave neither develops nor decays.
This paper investigates the impact of equatorial wind stress on the equatorial Ekman transport during the Indian Ocean Dipole (IOD) mature phase. The results show that the equatorial zonal wind stress directly drives the meridional motion of seawater at the upper levels. In normal years, the zonal wind stress south of the equator is easterly and that north of the equator is westerly, which contributes to southward Ekman transport at the upper levels to form the climatological Indian Ocean shallow meridional overturning circulation. During the years of positive IOD events, abnormal easterly winds near the equator bring southward Ekman transport south of the equator while they bring northward Ekman transport north of the equator. This causes the seawater to move away from the equator and hence induces upwelling near the equator, which forms a pair of small circulation cells that are symmetric about the equator at the upper levels (approximately 100 m deep). The abnormal circulation cell south (north) of the equator strengthens (weakens) the southward (southward) motion south (north) of the equator. During years with negative IOD events, the opposite occurs. In addition, during the mature period of IOD, the remote sea surface temperature anomaly (SSTA) such as El Niño–Southern Oscillation (ENSO) may exert some influence on Ekman transport anomaly near the equator during the mature period of IOD.
The dynamics of local thermal circulations (LTCs) are examined by constructing a linear theory based on Boussinesq equations in the planetary boundary layer (PBL). Linear theory arranges LTCs into a sixth-order partial differential equation of temperature, which can be solved by using the Fourier transform and inverse Fourier transform. The analytic solution suggests that the horizontal distribution of the temperature anomaly is basically determined by surface heating, while the vertical distribution of the temperature anomaly is a combination of exponential decay and an Ekman spiral. For shallow PBL cases where the Ekman elevation is much smaller than the vertical scale of motion, the higher-order partial differential terms that represent the Ekman spiral structure can be ignored so that the equations reduce to a second-order partial differential equation. Compared with the numerical results, this so-called low-order approximation does not induce dramatic errors in the temperature distribution. However, to avoid distortion in the forced atmospheric circulation, the eddy viscosity in the motion equations should be replaced with the Rayleigh form, which is the common practice in LTCs. For deep PBL cases where the Ekman elevation is comparable to the vertical scale of motion, both the exponential decay and Ekman spiral structure play roles in the forced atmospheric circulation. The most significant influence is that there exist three additional compensating forced circulation cells that surround the direct forced circulation cell.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.