Topographic Rossby waves in a rough-bottomed ocean

1973 ◽  
Vol 61 (3) ◽  
pp. 583-607 ◽  
Author(s):  
Peter Rhines ◽  
Francis Bretherton
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Bottom Topography ◽  
Rapid Change ◽  
Computer Experiments ◽  
Exceptional Case ◽  
Analytical Models ◽  
Energy Propagation ◽  
Resonant Interactions ◽  
Sea Bed

The object is to predict the nature of small-amplitude long-period oscillations of a homogeneous rotating fluid over a ‘sea bed’ that is nowhere level. Analytically, we are limited to special choices of bottom topography, such as sinusoidal corrugations or an undulating continental slope, so long as the topographic restoring effect equals or exceeds that due to planetary curvature (the beta-effect). (Very slight topographic features, on the other hand, provide weak, resonant interactions between Rossby waves.)Integral properties of the equations, and computer experiments reported elsewhere, verify the following results found in the analytical models: typical frequencies of oscillation are [lsim ]fδ, where f is the Coriolis frequency and δ measures the fractional height of the bottom bumps; an initially imposed flow pattern of large scale will rapidly shrink in scale over severe roughness (even the simplest analytical model shows this rapid change in spatial structure with time); and energy propagation can be severely reduced by roughness of the medium, the energy velocity being of order fδa, where a is the horizontal topographic scale (although in an exceptional case, the sinusoidal bottom, the group velocity remains finite for vanishingly small values of a).

scholarly journals On the Arrest of Inverse Energy Cascade and the Rhines Scale

2007 ◽  
Vol 64 (9) ◽  
pp. 3312-3327 ◽  
Author(s):  
Semion Sukoriansky ◽  
Nadejda Dikovskaya ◽  
Boris Galperin
Keyword(s):  
Rossby Wave ◽  
Large Scale ◽  
Rossby Waves ◽  
Characteristic Length ◽  
Unsteady Flows ◽  
Energy Propagation ◽  
Dimensional Parameter ◽  
Inverse Energy Cascade ◽  
Energy Sink ◽  
Spectral Ranges

Abstract The notion of the cascade arrest in a β-plane turbulence in the context of continuously forced flows is revised in this paper using both theoretical analysis and numerical simulations. It is demonstrated that the upscale energy propagation cannot be stopped by a β effect and can only be absorbed by friction. A fundamental dimensional parameter in flows with a β effect, the Rhines scale, LR, has traditionally been associated with the cascade arrest or with the scale that separates turbulence and Rossby wave–dominated spectral ranges. It is shown that rather than being a measure of the inverse cascade arrest, LR is a characteristic of different processes in different flow regimes. In unsteady flows, LR can be identified with the moving energy front propagating toward the decreasing wavenumbers. When large-scale energy sink is present, β-plane turbulence may attain several steady-state regimes. Two of these regimes are highlighted: friction-dominated and zonostrophic. In the former, LR does not have any particular significance, while in the latter, the Rhines scale nearly coincides with the characteristic length associated with the large-scale friction. Spectral analysis in the frequency domain demonstrates that Rossby waves coexist with turbulence on scales smaller than LR thus indicating that the Rhines scale cannot be viewed as a crossover between turbulence and Rossby wave ranges.

Large-scale Rossby waves in the Antarctic stratosphere

2010 ◽  
Vol 16 (5) ◽  
pp. 5-11
Author(s):  
A.V. Agapitov ◽  
◽  
A.V. Grytsai ◽  
D.A. Salyuk ◽  
◽  
...  
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
The Antarctic

scholarly journals Opportunistic Large Array Propagation Models: A Comprehensive Survey

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4206
Author(s):  
Farhan Nawaz ◽  
Hemant Kumar ◽  
Syed Ali Hassan ◽  
Haejoon Jung
Keyword(s):  
Energy Efficient ◽  
Large Scale ◽  
Performance Metrics ◽  
Experimental Studies ◽  
Cooperative Transmission ◽  
Analytical Models ◽  
Future Research ◽  
Large Array ◽  
Propagation Models ◽  
Comprehensive Survey

Enabled by the fifth-generation (5G) and beyond 5G communications, large-scale deployments of Internet-of-Things (IoT) networks are expected in various application fields to handle massive machine-type communication (mMTC) services. Device-to-device (D2D) communications can be an effective solution in massive IoT networks to overcome the inherent hardware limitations of small devices. In such D2D scenarios, given that a receiver can benefit from the signal-to-noise-ratio (SNR) advantage through diversity and array gains, cooperative transmission (CT) can be employed, so that multiple IoT nodes can create a virtual antenna array. In particular, Opportunistic Large Array (OLA), which is one type of CT technique, is known to provide fast, energy-efficient, and reliable broadcasting and unicasting without prior coordination, which can be exploited in future mMTC applications. However, OLA-based protocol design and operation are subject to network models to characterize the propagation behavior and evaluate the performance. Further, it has been shown through some experimental studies that the most widely-used model in prior studies on OLA is not accurate for networks with networks with low node density. Therefore, stochastic models using quasi-stationary Markov chain are introduced, which are more complex but more exact to estimate the key performance metrics of the OLA transmissions in practice. Considering the fact that such propagation models should be selected carefully depending on system parameters such as network topology and channel environments, we provide a comprehensive survey on the analytical models and framework of the OLA propagation in the literature, which is not available in the existing survey papers on OLA protocols. In addition, we introduce energy-efficient OLA techniques, which are of paramount importance in energy-limited IoT networks. Furthermore, we discuss future research directions to combine OLA with emerging technologies.

scholarly journals Rossby Waves in Astrophysics

2021 ◽  
Vol 217 (1) ◽  
Author(s):  
T. V. Zaqarashvili ◽  
M. Albekioni ◽  
J. L. Ballester ◽  
Y. Bekki ◽  
L. Biancofiore ◽  
...  
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Magnetic Activity ◽  
Future Research ◽  
Rotating Stars ◽  
Spatial And Temporal Scales ◽  
Physical Role ◽  
Astrophysical Objects ◽  
Exoplanetary Atmospheres ◽  
Rapidly Rotating Stars

AbstractRossby waves are a pervasive feature of the large-scale motions of the Earth’s atmosphere and oceans. These waves (also known as planetary waves and r-modes) also play an important role in the large-scale dynamics of different astrophysical objects such as the solar atmosphere and interior, astrophysical discs, rapidly rotating stars, planetary and exoplanetary atmospheres. This paper provides a review of theoretical and observational aspects of Rossby waves on different spatial and temporal scales in various astrophysical settings. The physical role played by Rossby-type waves and associated instabilities is discussed in the context of solar and stellar magnetic activity, angular momentum transport in astrophysical discs, planet formation, and other astrophysical processes. Possible directions of future research in theoretical and observational aspects of astrophysical Rossby waves are outlined.

Waves, jets and vortices: Regime transitions in shallow water turbulence

2021 ◽  
Author(s):  
Nikos Bakas
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Rossby Waves ◽  
Phase Speed ◽  
Critical Value ◽  
Turbulent Regime ◽  
Wave Regime ◽  
Frequency Spectra ◽  
Spectra Analysis ◽  
Zonal Jets

<p>Forced-dissipative beta-plane turbulence in a single-layer shallow-water fluid has been widely considered as a simplified model of planetary turbulence as it exhibits turbulence self-organization into large-scale structures such as robust zonal jets and strong vortices. In this study we perform a series of numerical simulations to analyze the characteristics of the emerging structures as a function of the planetary vorticity gradient and the deformation radius. We report four regimes that appear as the energy input rate ε of the random stirring that supports turbulence in the flow increases. A homogeneous turbulent regime for low values of ε, a regime in which large scale Rossby waves form abruptly when ε passes a critical value, a regime in which robust zonal jets coexist with weaker Rossby waves when ε passes a second critical value and a regime of strong materially coherent propagating vortices for large values of ε. The wave regime which is not predicted by standard cascade theories of turbulence anisotropization and the vortex regime are studied thoroughly. Wavenumber-frequency spectra analysis shows that the Rossby waves in the second regime remain phase coherent over long times. The coherent vortices are identified using the Lagrangian Averaged Deviation (LAVD) method. The statistics of the vortices (lifetime, radius, strength and speed) are reported as a function of the large scale parameters. We find that the strong vortices propagate zonally with a phase speed that is equal or larger than the long Rossby wave speed and advect the background turbulence leading to a non-dispersive line in the wavenumber-frequency spectra.</p>

Topographic Rossby Waves in the Abyssal South China Sea

2021 ◽  
Author(s):  
QI QUAN ◽  
ZHONGYA CAI ◽  
GUANGZHEN JIN ◽  
ZHIQIANG LIU
Keyword(s):  
South China Sea ◽  
Group Velocity ◽  
South China ◽  
Large Scale ◽  
Rossby Waves ◽  
Western Boundary ◽  
Horizontal Shear ◽  
Boundary Current ◽  
China Sea ◽  
Topographic Rossby Waves

AbstractTopographic Rossby waves (TRWs) in the abyssal South China Sea (SCS) are investigated using observations and high-resolution numerical simulations. These energetic waves can account for over 40% of the kinetic energy (KE) variability in the deep western boundary current and seamount region in the central SCS. This proportion can even reach 70% over slopes in the northern and southern SCS. The TRW-induced currents exhibit columnar (i.e., in-phase) structure in which the speed increases downward. Wave properties such as the period (5–60 days), wavelength (100–500 km), and vertical trapping scale (102–103 m) vary significantly depending on environmental parameters of the SCS. The TRW energy propagates along steep topography with phase propagation offshore. TRWs with high frequencies exhibit a stronger climbing effect than low-frequency ones and hence can move further upslope. For TRWs with a certain frequency, the wavelength and trapping scale are dominated by the topographic beta, whereas the group velocity is more sensitive to the internal Rossby deformation radius. Background circulation with horizontal shear can change the wavelength and direction of TRWs if the flow velocity is comparable to the group velocity, particularly in the central, southern, and eastern SCS. A case study suggests two possible energy sources for TRWs: mesoscale perturbation in the upper layer and large-scale background circulation in the deep layer. The former provides KE by pressure work, whereas the latter transfers the available potential energy (APE) through baroclinic instability.

scholarly journals Stellar mass spectrum within massive collapsing clumps

2018 ◽  
Vol 611 ◽  
pp. A89 ◽  
Author(s):  
Yueh-Ning Lee ◽  
Patrick Hennebelle
Keyword(s):  
Large Scale ◽  
Equations Of State ◽  
Initial Conditions ◽  
Peak Position ◽  
Density Fluctuations ◽  
Initial Mass Function ◽  
Analytical Models ◽  
Numerical Resolution ◽  
Tidal Forces ◽  
The Imf

Context. Understanding the origin of the initial mass function (IMF) of stars is a major problem for the star formation process and beyond. Aim. We investigate the dependence of the peak of the IMF on the physics of the so-called first Larson core, which corresponds to the point where the dust becomes opaque to its own radiation. Methods. We performed numerical simulations of collapsing clouds of 1000 M⊙ for various gas equations of state (eos), paying great attention to the numerical resolution and convergence. The initial conditions of these numerical experiments are varied in the companion paper. We also develop analytical models that we compare to our numerical results. Results. When an isothermal eos is used, we show that the peak of the IMF shifts to lower masses with improved numerical resolution. When an adiabatic eos is employed, numerical convergence is obtained. The peak position varies with the eos, and using an analytical model to infer the mass of the first Larson core, we find that the peak position is about ten times its value. By analyzing the stability of nonlinear density fluctuations in the vicinity of a point mass and then summing over a reasonable density distribution, we find that tidal forces exert a strong stabilizing effect and likely lead to a preferential mass several times higher than that of the first Larson core. Conclusions. We propose that in a sufficiently massive and cold cloud, the peak of the IMF is determined by the thermodynamics of the high-density adiabatic gas as well as the stabilizing influence of tidal forces. The resulting characteristic mass is about ten times the mass of the first Larson core, which altogether leads to a few tenths of solar masses. Since these processes are not related to the large-scale physical conditions and to the environment, our results suggest a possible explanation for the apparent universality of the peak of the IMF.

Assessing the Multiple Pressure Source Hypothesis for the Sakurajima Volcano and Aira Caldera Magmatic System

2021 ◽  
Author(s):  
Robert Backhurst
Keyword(s):  
Numerical Modelling ◽  
Large Scale ◽  
Numerical Study ◽  
Deformation Source ◽  
Geodetic Data ◽  
Analytical Models ◽  
Magmatic System ◽  
Sakurajima Volcano ◽  
Subsurface Heterogeneity ◽  
Increased Risk

<p>Sakurajima, located on the southern rim of Aira caldera, is one of the most active volcanoes in Japan. From long term deformation trends, the volcano is showing an increased risk of large-scale eruption, emphasizing the need to better understand the magmatic system.</p><p>Deformation modelling, primarily using the Mogi method, has dominated the geodetic assessment history of Sakurajima. These methods, however, contain limitations, such as the assumption of a homogeneous crust, and have therefore not accurately depicted the magmatic system. Numerical modelling techniques have reduced this limitation by accounting for subsurface heterogeneity.</p><p>Analytical modelling studies have suggested multiple magmatic sources beneath Aira caldera and Sakurajima volcano, whilst the only numerical study undertaken so far indicated a single source. Here, we test the multiple deformation source hypothesis, whilst also incorporating subsurface heterogeneity and topography, using Finite Element (FE) numerical modelling, and geodetic data from Sakurajima.</p><p>Using a full 3D model geometry for Sakurajima and Aira caldera, preliminary forward modelling suggests a second deformation source produces our best fit to the measured geodetic data. Optimum results indicate a shallow prolate source 7-10 km below sea level (bsl), in addition to a deeper oblate source at ~13 km bsl. These preliminary findings produce greater shallow storage depths than the previous analytical models (3-6 km) and ties in with the trans-crustal magmatic system hypothesis.</p><p>Increasing our understanding of the Sakurajima magmatic system will enable improved interpretations of geodetic data prior to eruptions and will inform models for a range of similar volcanoes world-wide.</p>

Barotropic aspects of large-scale atmospheric turbulence

2020 ◽  
pp. 183-222
Author(s):  
Theodore G. Shepherd
Keyword(s):  
Atmospheric Turbulence ◽  
General Circulation ◽  
Large Scale ◽  
Rossby Waves ◽  
Wave Turbulence ◽  
Mean Flow ◽  
Zonal Flows ◽  
Atmospheric General Circulation ◽  
Scale Turbulence ◽  
Inertia Gravity Waves

The chapter begins with a phenomenological treatment of the observed atmospheric circulation. It then goes on to discuss how the barotropic model arises as a so-calledbalanced model of the slow, vorticity-driven dynamics, from the more general shallowwater model which also admits inertia-gravity waves. This is important because large-scale atmospheric turbulence exhibits aspects of both balanced and unbalanced dynamics. Because of the first-order importance of zonal flows in the atmospheric general circulation, the large-scale turbulence is highly inhomogeneous, and is shaped by the nature of the interaction between zonal flows and Rossby waves described eloquently by Michael McIntyre as a wave-turbulence jigsaw puzzle. This motivates a review of the barotropic theory of wave, mean-flow interaction, which is underpinned by the Hamiltonian structure of geophysical fluid dynamics.

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