scholarly journals Equatorial Jets in Decaying Shallow-Water Turbulence on a Rotating Sphere

2007 ◽  
Vol 64 (9) ◽  
pp. 3340-3353 ◽  
Author(s):  
Yuji Kitamura ◽  
Keiichi Ishioka
Keyword(s):  
Wave Packet ◽  
Shallow Water ◽  
Equatorial Region ◽  
Equatorial Waves ◽  
Mean Flow ◽  
Wave Interactions ◽  
Rotating Sphere ◽  
Flow Acceleration ◽  
Water Turbulence ◽  
Ensemble Experiments

Abstract Ensemble experiments of decaying shallow-water turbulence on a rotating sphere are performed to confirm the robustness of the emergence of an equatorial jet. While previous studies have reported that the equatorial jets emerging in shallow-water turbulence are always retrograde, predominance of a prograde jet, although less likely, was also found in the present ensemble experiments. Furthermore, a zonal-mean flow induced by wave–wave interactions was examined using a weak nonlinear model to investigate the acceleration mechanisms of the equatorial jet. The second-order acceleration is induced by the Rossby and mixed Rossby–gravity waves and its mechanisms can be categorized into two types. First, the local meridional wavenumber of a Rossby wave packet propagating toward the equator increases because of meridional variation of the Rossby deformation radius and/or the retrograde zonal-mean flow, resulting in a dissipation of the wave packet in the equatorial region. This mechanism always contributes to retrograde acceleration of an equatorial jet. Another mechanism is derived from the tilting of equatorial waves due to meridional shear of the zonal-mean flow. In this case, zonal-mean flow acceleration contributes to the intensification of a given basic flow.

scholarly journals Mechanism for the Formation of Equatorial Superrotation in Forced Shallow-Water Turbulence with Newtonian Cooling

2015 ◽  
Vol 72 (4) ◽  
pp. 1466-1483 ◽  
Author(s):  
Izumi Saito ◽  
Keiichi Ishioka
Keyword(s):  
Statistical Analysis ◽  
Structural Change ◽  
Shallow Water ◽  
Nonlinear Theory ◽  
Mean Flow ◽  
Rotating Sphere ◽  
Absolute Value ◽  
Acceleration Mechanism ◽  
Numerical Studies ◽  
Water Turbulence

Abstract Forced shallow-water turbulence on a rotating sphere with Newtonian cooling is examined with the aim of elucidating the mechanism of the robust formation of equatorial superrotation reported by R. K. Scott and L. M. Polvani. It is shown that the Newtonian cooling term distorts the structure of the Hough modes. This distortion can be visualized as either the westward or eastward tilting of the equiphase line with increasing absolute value of latitude; the structural change of the Hough modes leads to the acceleration of the zonal-mean flow. A statistical analysis based on a weak-nonlinear theory predicts that stochastically excited Hough modes generate a prograde equatorial jet, the profile of which is quantitatively consistent with that of the ensemble-averaged zonal-mean flow obtained in nonlinear time evolutions. The predicted prograde equatorial jet originates mainly from the acceleration produced by Rossby modes, the equiphase line of which is tilted westward by the Newtonian cooling term. This tilt of the equiphase line of the Hough modes is clarified and a comparison between the acceleration mechanism presented in the present paper and that in other numerical studies in which equatorial superrotation emerges is made.

Spontaneous formation of equatorial jets in freely decaying shallow water turbulence

1999 ◽  
Vol 11 (5) ◽  
pp. 1272-1274 ◽  
Author(s):  
R. Iacono ◽  
M. V. Struglia ◽  
C. Ronchi
Keyword(s):  
Shallow Water ◽  
Spontaneous Formation ◽  
Water Turbulence

Critical layers in accelerating two-layer flows

1988 ◽  
Vol 197 ◽  
pp. 429-451 ◽  
Author(s):  
Donald B. Altman
Keyword(s):  
Laboratory Experiments ◽  
Single Mode ◽  
Shear Instability ◽  
Mean Flow ◽  
Velocity Measurements ◽  
Interfacial Wave ◽  
Flow Acceleration ◽  
Critical Layers ◽  
The Mean ◽  
Processing Software

A series of laboratory experiments on accelerating two-layer shear flows over topography is described. The mean flow reverses at the interface of the layers, forcing a critical layer to occur there. It is found that for a sufficiently thin interface, a slowly growing recirculating region, the ‘acceleration rotor’, develops on the interfacial wave at mean-flow Richardson numbers of O(0.5). This, in turn, can induce a secondary dynamical shear instability on the trailing edge of the wave. A single-mode, linear, two-layer numerical model reproduces many features of the acceleration rotor if mean-flow acceleration and bottom forcing are included. Velocity measurements are obtained from photographs using image processing software developed for the automated reading of particle-streak photographs. Typical results are shown.

scholarly journals Shallow Water Magnetohydrodynamics in Plasma Astrophysics. Waves, Turbulence, and Zonal Flows

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 314 ◽  
Author(s):  
Arakel Petrosyan ◽  
Dmitry Klimachkov ◽  
Maria Fedotova ◽  
Timofey Zinyakov
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Fundamental Problem ◽  
Flow Behavior ◽  
Magnetohydrodynamic Equations ◽  
Plasma Astrophysics ◽  
Wave Interactions ◽  
Zonal Flows ◽  
New Applications ◽  
The Universe

The purpose of plasma astrophysics is the study and description of the flow of rotating plasma in order to understand the evolution of various objects in the universe, from stars and planetary systems to galaxies and galaxy clusters. A number of new applications and observations have appeared in recent years and actualized the problem of studying large-scale magnetohydrodynamic flows, such as a thin layer under the convective zone of the sun (solar tachocline), propagation of accreting matter in neutron stars, accretion disks in astrophysics, dynamics of neutron star atmospheres, and magnetoactive atmospheres of exoplanets tidally locked with their host star. The article aims to discuss a fundamental problem in the description and study of multiscale astrophysical plasma flows by studying its general properties characterizing different objects in the universe. We are dealing with the development of geophysical hydrodynamic ideas concerning substantial differences in plasma flow behavior due to the presence of magnetic fields and stratification. We discuss shallow water magnetohydrodynamic equations (one-layer and two-layer models) and two-dimensional magnetohydrodynamic equations as a basis for studying large-scale flows in plasma astrophysics. We discuss the novel set of equations in the external magnetic field. The following topics will be addressed: Linear theory of magneto-Rossby waves, three-wave interactions and related parametric instabilities, zonal flows, and turbulence.

Integrated Motor/Propulsor Duct Optimization for Increased Vehicle and Propulsor Performance

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Stephen A. Huyer ◽  
Amanda Dropkin
Keyword(s):  
Fluid Dynamics ◽  
Computational Study ◽  
Mean Flow ◽  
Design Constraint ◽  
Propulsive Efficiency ◽  
Flow Acceleration ◽  
Blade Row ◽  
Total Vehicle ◽  
Stator Blade ◽  
Thrust And Torque

This paper presents a computational study to better understand the underlying fluid dynamics associated with various duct shapes and the resultant impact on both total vehicle drag and propulsor efficiency. A post-swirl propulsor configuration (downstream stator blade row) was selected with rotor and stator blade number kept constant. A generic undersea vehicle hull shape was chosen and the maximum shroud radius was required to lie within this body radius. A cylindrical rim-driven electric motor capable of generating a specific horsepower to achieve the design operational velocity required a set volume that established a design constraint limiting the shape of the duct. Individual duct shapes were designed to produce constant flow acceleration from upstream of the rotor blade row to downstream of the stator blade row. Ducts producing accelerating and decelerating flow were systematically examined. The axisymmetric Reynolds Averaged Navier–Stokes (RANS) version of fluent® was used to study the fluid dynamics associated with a range of accelerated and decelerated duct flow cases as well as provide the base total vehicle drag. For each given duct shape, the propeller blade design code, PBD 14.3, was used to generate an optimized rotor and stator. To provide fair comparisons, the maximum rotor radius was held constant with similar circulation distributions intended to generate equivalent amounts of thrust. Computations predicted that minimum vehicle drag was produced with a duct that produced zero mean flow acceleration. Ducted designs generating accelerating or decelerating flow increased drag. However, propulsive efficiency based exclusively on blade thrust and torque was significantly increased for accelerating flow through the duct and reduced for decelerating flow cases. Full 3D RANS flow simulations were then conducted for select test cases to quantify the specific blade, hull, and shroud forces and highlight the increased component drag produced by an operational propulsor, which reduced overall propulsive efficiency. From these results, a final optimized design was proposed.

Turbulent Flow of Water in Plane Curved Channels of Finite Depth

1963 ◽  
Vol 85 (3) ◽  
pp. 377-390 ◽  
Author(s):  
O. G. Brown ◽  
A. W. Marris
Keyword(s):  
Experimental Study ◽  
Shear Flow ◽  
Turbulent Flow ◽  
Finite Depth ◽  
Width Ratio ◽  
Mean Flow ◽  
Curved Channel ◽  
Flow Acceleration ◽  
Curved Channels ◽  
Convex Wall

An experimental study of turbulent flow in a plane curved channel of depth-to-width ratio 8:1 and mean radius-to-width ratio 1.83:1 by means of measured distributions of mean peripheral velocity and pressure and flow visualization methods using dye. It appears that due to the large depth-to-width ratio, the secondary flow, though appreciable, is apparent mainly in the end plate regions. Even so it has a pronounced effect on the flow near the inner (convex) wall. It appears that the sharp curvature is effective in quenching the turbulence of the entering rectilinear shear flow at the inner wall of the curved channel by causing a mean flow acceleration in this region. The study indicates that localized backflows can occur at the inner wall at the meeting of secondary and main flows under near-laminar conditions.

scholarly journals Nonlinear Saturation of Vertically Propagating Rossby Waves

2009 ◽  
Vol 66 (4) ◽  
pp. 915-934 ◽  
Author(s):  
Constantine Giannitsis ◽  
Richard S. Lindzen
Keyword(s):  
Wave Propagation ◽  
Channel Model ◽  
Plane Channel ◽  
Nonlinear Flow ◽  
Computational Domain ◽  
Mean Flow ◽  
Wave Interactions ◽  
Linear Solution ◽  
Wave Growth ◽  
Flow Interactions

Abstract The interaction between vertical Rossby wave propagation and wave breaking is studied in the idealized context of a beta-plane channel model. Considering the problem of propagation through a uniform zonal flow in an exponentially stratified fluid, where linear theory predicts exponential wave growth with height, the question is how wave growth is limited in the nonlinear flow. Using a numerical model, the authors examine the behavior of the flow as the bottom forcing increases through values bound to lead to a breakdown of the linear solution within the computational domain. Focusing on the equilibrium flow obtained for each value of the bottom forcing, an attempt is made to identify the mechanisms involved in limiting wave growth and examine in particular the importance of wave–wave interactions. The authors also examine the case in which forcing is continuously increasing with time so as to enhance effects peculiar to transiency; it does not significantly alter the main results. Wave–mean flow interactions are found to dominate the dynamics even for strong bottom forcing values. Ultimately, it is the modification of the mean flow that is found to limit the vertical penetration of the forced wave, through either increased wave absorption or downward reflection. Linear propagation theory is found to capture the wave structure surprisingly well, even when the total flow is highly deformed. Overall, the numerical results seem to suggest that wave–wave interactions do not have a strong direct effect on the propagating disturbance. Wave–mean flow interactions limit wave growth sufficiently that a strong additional nonlinear enstrophy sink, through downscale cascade, is not necessary. Quantitatively, however, wave–wave interactions, primarily among the lowest wavenumbers, prove important so as to sufficiently accurately determine the basic state and its influence on wave propagation.

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