A unified moisture mode theory for the Madden Julian Oscillation and the Boreal Summer Intraseasonal Oscillation

The Madden Julian Oscillation (MJO) and the Boreal Summer Intraseasonal Oscillation (BSISO) are fundamental modes of variability in the tropical atmosphere on the intraseasonal time scale. A linear model, using a moist shallow water equation set on an equatorial beta plane, is developed to provide a unified treatment of the two modes and to understand their growth and propagation over the Indian Ocean. Moisture is assumed to increase linearly with longitude and to decrease quadratically with latitude. Solutions are obtained through linear stability analysis, considering the gravest (n = 1) meridional mode with nonzero meridional velocity. Anomalies in zonal moisture advection and surface fluxes are both proportional to those in zonal wind, but of opposite sign. With observation-based estimates for both effects, the zonal advection dominates, and drives the planetary-scale instability. With a sufficiently small meridional moisture gradient, the horizontal structure exhibits oscillations with latitude and a northwest-southeast horizontal tilt in the northern hemisphere, qualitatively resembling the observed BSISO. As the meridional moisture gradient increases, the horizontal tilt decreases and the spatial pattern transforms toward the “swallowtail” structure associated with the MJO, with cyclonic gyres in both hemispheres straddling the equatorial precipitation maximum. These results suggest that the magnitude of the meridional moisture gradient shapes the horizontal structures, leading to the transformation from the BSISO-like tilted horizontal structure to the MJO-like neutral wave structure as the meridional moisture gradient changes with the seasons. The existence and behavior of these intraseasonal modes can be understood as a consequence of phase speed matching between the equatorial mode with zero meridional velocity (analogous to the dry Kelvin wave) and a local off-equatorial component that is characterized by considering an otherwise similar system on an f-plane.

On the Formulation of Nonreflecting Boundary Conditions for Turbomachinery Configurations: Part I — Theory and Implementation

With unsteady flow simulations of industrial turbomachinery configurations becoming more and more affordable there is a growing need for accurate inlet and outlet boundary conditions as numerical reflections alone can lead to incorrect trends in engine efficiency, noise and aeroelastic analysis parameters. This is the first of two papers on the formulation of unsteady boundary conditions which have been implemented for both time-domain and frequency-domain solvers. Giles’ original idea for steady solvers to formulate the boundary condition in terms of characteristics generalizes to frequency-domain solvers. The boundary condition drives the value of the incoming characteristics to ideal values that are computed using the modal decomposition of linearized 2D Euler flows. The present paper explains how to generalize 2D nonreflecting boundary conditions to real 3D annular domains by applying them in certain conical rotational surfaces. For a flow with zero radial component and an annular boundary that is perpendicular to the machine axis, these surfaces are the cylindrical streamsurfaces. For more general flows and geometries, however, there is no natural choice for the rotational surfaces. In this paper, two choices are discussed: the surfaces that are generated by the boundary normals and those that are defined by the circumferentially averaged meridional velocity. The impact of the boundary condition on the stability of the harmonic-balance solver is analyzed by studying the pseudo-time evolution of certain energy integrals. For a model problem which consists of a small disturbance of an inviscid flow, the increase or decrease of this energy integral is shown to be directly related to the normal characteristic variables along the boundary. This shows that the actual boundary condition should be formulated as a control problem for the normal characteristics. Moreover, the application of the harmonic balance solver to a simple duct configuration with prescribed disturbances demonstrates that using the characteristics based on the meridional velocity may prevent the solver from converging. In contrast, the 2D theory can be formulated in a different surface without impairing the robustness of the overall approach. These findings are illustrated by a simple test case. The impact of the choice of the rotational surface for the 2D theory is studied for various duct segments and a low-pressure turbine configuration in the second paper. There it is shown that applying the 2D theory to the meridional-velocity surfaces may be advantageous in that it leads to more accurate results.

Interannual to decadal variability in subtropical circulation transport in the south Indian Ocean

<p><span>This study estimates variability in meridional velocity and transport of the subtropical circulation in the south Indian Ocean using in-situ hydrographic observations, satellite altimetry and two reanalysis products for the period from 2006 to 2017. Previous studies used the zonal difference of satellite sea surface height (SSH) between the western and eastern parts of the basin as an index to variability in basinwide meridional geostrophic transport.</span> <span>This study estimates </span><span>meridional geostrophic velocity in the upper 1800 m from in-situ observations and compares results with SSH variability.</span><span> Results show that zonal SSH difference represents a surface trapped variability in meridional velocity, the amplitude of which is large in the upper 250 m and decreases to zero at about 1000 m depth. Zonal SSH difference is significantly correlated with zonally integrated meridional transport relative to 1000 m depth. It is likely that wind variability both in the south Indian Ocean and tropical Pacific Ocean is responsible for this surface trapped variability, as is suggested by past studies. Results of this study also show meridional velocity variability at subsurface, which peaks in magnitude at about 400 to 800 m depth and is not correlated with zonal SSH difference. Waves radiated from the eastern boundary are possibly responsible for the generation of this subsurface flow, but detailed forcing mechanisms are not known in this study. This subsurface flow can contribute to interannual variability in mode water transport and warrants a further study.</span></p>

Numerical Simulation of Flow through Vaneless Diffuser

Flow through vaneless diffuser in the centrifugal compressor stage is studied at varied flow conditions using finite volume method based commercial code, ANSYS CFX. The contour of static pressure, stagnation pressure, absolute velocity, as well as meridional velocity divulges the nature of flow that happens in the centrifugal compressor stage. Circumferential non-uniformity due “jet-wake” formation is seen at the impeller exit. These lead to mixing of fluid having varied energy levels which happens within the vaneless diffuser. Total pressure rises along the radius ratio and its distribution is higher near the shroud for all flow conditions. Absolute velocity reduces along radius ratio as area of the flow passage increase indicating diffusion. The meridional velocity is seen as non-uniform at Ф = 0.15 but, it is uniform at diffuser exit at Ф = 0.25.

Deep Intraseasonal Variability in the Central Equatorial Atlantic

Besides the zonal flow that dominates the seasonal and long-term variability in the equatorial Atlantic, energetic intraseasonal meridional velocity fluctuations are observed in large parts of the water column. We use 15 years of partly full-depth velocity data from an equatorial mooring at 23°W to investigate intraseasonal variability and specifically the downward propagation of intraseasonal energy from the near-surface into the deep ocean. Between 20 and 50 m, intraseasonal variability at 23°W peaks at periods between 30 and 40 days. It is associated with westward-propagating tropical instability waves, which undergo an annual intensification in August. At deeper levels down to about 2000 m considerable intraseasonal energy is still observed. A frequency–vertical mode decomposition reveals that meridional velocity fluctuations are more energetic than the zonal ones for periods < 50 days. The energy peak at 30–40 days and at vertical modes 2–5 excludes equatorial Rossby waves and suggests Yanai waves to be associated with the observed intraseasonal energy. Yanai waves that are considered to be generated by tropical instability waves propagate their energy from the near-surface west of 23°W downward and eastward to eventually reach the mooring location. The distribution of intraseasonal energy at the mooring position depends largely on the dominant frequency and the time, depth, and longitude of excitation, while the dominant vertical mode of the Yanai waves plays only a minor role. Observations also show the presence of weaker intraseasonal variability at 23°W below 2000 m that cannot be associated with tropical instability waves.

Meridional Heat Advection due to Mixed Rossby Gravity Waves in the Equatorial Indian Ocean

This study examines heat advection due to mixed Rossby gravity waves in the equatorial Indian Ocean using moored buoy observations at (0°, 80.5°E) and (0°, 90°E) and an ocean general circulation model (OGCM) output. Variability associated with mixed Rossby gravity waves is defined as that at periods of 10–30 days, where both observations and the OGCM results show high energy in meridional velocity and meridional gradient of temperature. The 10–30-day variability in meridional velocity causes convergence of heat flux onto the equator, the net effect of which amounts to 2.5°C month−1 warming at the depth of the thermocline. Detailed analysis shows that the wave structure manifested in temperature and velocity is tilted in the x–z plane, which causes the phase lag between meridional velocity and meridional temperature gradient to be a half cycle on the equator and results in sizable thermocline warming. An experiment with a linear continuously stratified model shows that the contributions of many baroclinic modes, and the right zonal wavelength of wind forcing, are essential in generating the correct wave structure. It is also shown that contributions of mixed Rossby gravity waves to cross-equatorial heat transport are negligible, as temperature variability associated with this wave mode has a node on the equator.

Reply to “Comments on ‘On the Steadiness of Separating Meandering Currents’”

The authors thank Nof et al. for their comments on the authors’ paper “On the steadiness of separating meandering currents.” The authors’ paper was motivated by a series of papers by Nof et al. Under a certain set of conditions (reduced gravity, steady state, no meridional velocity at outflow, and parallel outflow), Nof et al. showed that a separating and retroflecting frictionless current cannot be steady because of a momentum imbalance. The main conclusion of the authors’ paper was that they agree with the Nof et al. result that a momentum imbalance exists and extended the proof to all possible configurations of retroflecting currents, even including friction. The authors’ results point to a new mechanism for the generation of variability in the ocean that is not related to dynamical instability of the flow. The main claim in the comments is that the authors incorrectly argued in the appendix that the steady-state solutions presented by Nof et al. in several papers fulfill the extra constraint u2 = g′h. In the original paper, the authors showed that it follows from the geostrophic assumption stated implicitly in all these Nof et al. papers, because the flow is assumed to be parallel. Nof et al. now argue that the flow is only approximately geostrophic in all Nof et al. papers. The authors show in this reply that for steady weakly meandering outflows approximate geostrophy does lead to a momentum imbalance paradox as Nof et al. claim. However, for a steady strongly meandering outflow, approximate geostrophy is not enough and one has to use the method explored by van Leeuwen and De Ruijter to derive a momentum imbalance paradox.

Modification of Long Equatorial Rossby Wave Phase Speeds by Zonal Currents

Previously unaddressed aspects of how equatorial currents affect long Rossby wave phase speeds are investigated using solutions of the shallow-water equations linearized about quasi-realistic currents. Modification of the background potential vorticity (PV) gradient by curvature in the narrow equatorial currents is shown to play a role comparable to the Doppler shift emphasized by previous authors. The important variables are the meridional projections of mean-current features onto relevant aspects of the wave field. As previously shown, Doppler shifting of long Rossby waves is determined by the projection of the mean currents onto the wave’s squared zonal-velocity and pressure fields. PV-gradient modification matters only to the extent that it projects onto the wave field’s squared meridional velocity. Because the zeros of an equatorial wave’s meridional velocity are staggered relative to those of the zonal velocity and pressure, and because the meridional scales of the equatorial currents are similar to those of the low-mode Rossby waves, different parts of the current system dominate the advective and PV-gradient modification effects on a single mode. Since the equatorial symmetry of classical equatorial waves alternates between symmetric and antisymmetric with increasing meridional mode number, the currents produce opposite effects on adjacent modes. Meridional mode 1 is slowed primarily by a combination of eastward advection by the Equatorial Undercurrent (EUC) and the PV-gradient decrease at the peaks of the South Equatorial Current (SEC). The mode-2 phase speed, in contrast, is increased primarily by a combination of westward advection by the SEC and the PV-gradient increase at the core of the EUC. Perturbation solutions are carried to second order in ε, the Rossby number of the mean current, and it is shown that this is necessary to capture the full effect of quasi-realistic current systems, which are asymmetric about the equator. Equatorially symmetric components of the current system affect the phase speed at O(ε), but antisymmetric components of the currents and distortions of the wave structures by the currents do not influence the phase speed until O(ε2).