scholarly journals Stability Criterion for the Centrifugal Instability of Surface Intensified Anticyclones

2019 ◽  
Vol 49 (3) ◽  
pp. 827-849 ◽  
Author(s):  
Eunok Yim ◽  
Alexandre Stegner ◽  
Paul Billant
Keyword(s):  
Turbulent Viscosity ◽  
Maximum Velocity ◽  
Stability Limit ◽  
Velocity Profiles ◽  
Instability Criterion ◽  
Marginal Stability ◽  
Vertical Wavelength ◽  
Centrifugal Instability ◽  
Wide Range ◽  
Anticyclonic Eddies

AbstractWe investigate the linear stability of intense baroclinic anticyclones, with a particular focus on the centrifugal (inertial) instability. Various vertical and radial velocity profiles are studied. The vertical profiles are such that the velocity is maximum at the surface. These profiles correspond to oceanic eddies such as submesoscale mixed-layer eddies or intense mesoscale eddies in the upper thermocline. The results show that the main characteristics of the centrifugal instability (growth rate, vertical wavelength) depend weakly on the baroclinic structure of the anticyclone. The dominant azimuthal wavenumber is for small Burger number (Bu) and for higher Bu, where Bu is the square root of the ratio of the deformation radius over the characteristic eddy radius where the velocity is maximum. The marginal stability limits of the centrifugal instability for the different velocity profiles collapse approximately on a single curve in the parameter space (Ro, Bu), where is the Rossby number, with being the maximum velocity. By means of an asymptotic analysis for short vertical wavelength, an explicit prediction for the marginal stability limit is derived for a wide range of velocity profiles. We then suggest to use, for most of oceanic anticyclones, the instability criterion valid for a Gaussian eddy: where is the Ekman number, H is the eddy depth, and ν is the turbulent viscosity at the ocean surface. Some baroclinic anticyclones can remain stable even if they have a core region of negative absolute vorticity provided that they are small enough. This formula explains the few observations of intense anticyclonic eddies having a negative core vorticity around .

Organized structures in turbulent Taylor-Couette flow

1984 ◽  
Vol 143 ◽  
pp. 429-449 ◽  
Author(s):  
A. Barcilon ◽  
J. Brindley
Keyword(s):  
Couette Flow ◽  
Eigenvalue Problems ◽  
Annular Region ◽  
Circular Cylinders ◽  
Coherent Motion ◽  
Marginal Stability ◽  
Centrifugal Instability ◽  
Wide Range ◽  
Taylor Couette ◽  
Taylor Couette Flow

A simple mathematical model is constructed to describe the regime of flow, extending over a wide range of values of Taylor number, in which turbulent Taylor–Couette flow in the annular region between two coaxial circular cylinders is characterized by the coexistence of steady coherent motion on two widely separated scales. These scales of motion, corresponding to the gap width of the annular region and to a boundary-layer thickness, are each identified as the consequence of a centrifugal instability, and are described as Taylor vortices and Görtler vortices respectively.The assumption that both scales of motion are near marginal stability gives a closure to a pair of coupled eigenvalue problems, and the results of a linear analysis are shown to be in good agreement with many features of experimental observations.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

Investigation on a Type of Flow Control to Weaken Unsteady Separated Flows by Unsteady Excitation in Axial Flow Compressors

2004 ◽  
Author(s):  
Xin-Qian Zheng ◽  
Xiao-Bo Zhou ◽  
Sheng Zhou
Keyword(s):  
Wide Spectrum ◽  
Excitation Frequency ◽  
Axial Flow ◽  
Maximum Velocity ◽  
Excitation Amplitude ◽  
High Order Scheme ◽  
Wide Range ◽  
Optimal Excitation ◽  
Suction And Blowing ◽  
Axial Flow Compressors

By solving unsteady Reynolds-averaged 2-D N-S equations discretized by a high-order scheme, the results showed that the disordered unsteady separated flow could be effectively controlled by periodic suction and blowing in a wide range of incidence, resulting in enhancement of time-averaged aerodynamic performances. The effects of unsteady excitation frequency, amplitude and excitation location were investigated in detail. The effective excitation frequency spans a wide spectrum and there is an optimal excitation frequency that is nearly equal to the Characteristic frequency of vortex shedding. Excitation amplitude exhibits a threshold value (nearly 10% in term of the ratio of maximum velocity of periodic suction and blowing to the velocity of free flow) and an optimal value (nearly 35%). The optimal excitation location is just upstream of the separation point. We also explored feasible unsteady actuators by utilizing upstream wake for constraining unsteady separation in axial flow compressors.

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

PIV Analysis of Dynamic Velocity Profiles in Non-Newtonian Drilling Fluids Exposed to Oscillatory Motion

2018 ◽  
Author(s):  
Maduranga Amaratunga ◽  
Roar Nybø ◽  
Rune W. Time
Keyword(s):  
Low Frequency ◽  
Velocity Profiles ◽  
Liquid Column ◽  
Oscillatory Motion ◽  
Velocity Shear ◽  
Drilling Fluids ◽  
Cross Sectional ◽  
Low Frequencies ◽  
Wide Range ◽  
Dynamic Velocity

Drilling fluids experience a wide range of shear rates and oscillatory motion while circulating through the well and also during the operations for solids control. Therefore, it is important to investigate the influence of oscillatory fields on the velocity profiles, shear rate and resulting rheological condition of non-Newtonian polymers, which are additives in drilling fluids. In this paper, we present the dynamic velocity profiles within both Newtonian (deionized water) and non-Newtonian liquids (Polyanionic Cellulose – PAC) exposed to oscillatory motion. A 15 cm × 15 cm square cross-sectional liquid column was oscillated horizontally with very low frequencies (0.75–1.75 Hz) using a laboratory made oscillating table. The dynamic velocity profiles at the bulk of the oscillating liquid column were visualized by the Particle Image Velocimetry (PIV) method, where the motion of fluid is optically visualized using light scattering “seeding” particles. Increased frequency of oscillations lead to different dynamic patterns and ranges of velocity-shear magnitudes. The experiments are part of a comprehensive study aimed at investigating the influence of low frequency oscillations on particle settling in non-Newtonian drilling fluids. It is discussed, how such motion imposed on polymeric liquids influences both flow dynamics as well as local settling velocities of cuttings particles.

Experimental Studies of Pressure Drop and Flow Instability in Evaporative Micro-Channels

2008 ◽  
Author(s):  
Hee Joon Lee ◽  
Dongyao Liu ◽  
Shi-Chune Yao
Keyword(s):  
Pressure Drop ◽  
Flow Instability ◽  
Experimental Studies ◽  
Bond Number ◽  
Effective Length ◽  
Instability Criterion ◽  
Micro Channel ◽  
Micro Channels ◽  
Wide Range ◽  
Channel Systems

Experiments were conducted on evaporative micro-channel systems of water, containing 48 parallel channels of 353 μm hydraulic diameter. The general correlation of two-phase pressure drop for an initial design purpose of evaporative micro-channel systems reported in [1] has been validated. For the water boiling in micro-channels, flow instability was observed. The instability criterion, proposed by Kandlikar [2], is able to predict the water experimental results. However, further examination of his criterion revealed that it can not predict the results of Brutin and Tadrist’s data of n-pentane. This is because the Bond number of water is 0.01, but 0.33 for n-pentane. As a result, the growing bubble of n-pentane may not cover the whole length of the micro-channel. A general expression of the effective length of squeezed bubbles in micro-channel was established for fluids at a wide range of Bond number. Using this proposed effective length, the Brutin and Tadrist’s experimental instability data can also be predicted satisfactorily.

Formation of Anticyclones above Topographic Depressions

2021 ◽  
Vol 51 (1) ◽  
pp. 207-228
Author(s):  
Aviv Solodoch ◽  
Andrew L. Stewart ◽  
James C. McWilliams
Keyword(s):  
Energy Distribution ◽  
Numerical Simulations ◽  
North Atlantic ◽  
Potential Vorticity ◽  
Circulation Pattern ◽  
Nonlinearity Parameter ◽  
Wide Range ◽  
Anticyclonic Eddies ◽  
Topographic Depressions ◽  
Pv Gradient

AbstractLong-lived anticyclonic eddies (ACs) have been repeatedly observed over several North Atlantic basins characterized by bowl-like topographic depressions. Motivated by these previous findings, the authors conduct numerical simulations of the spindown of eddies initialized in idealized topographic bowls. In experiments with one or two isopycnal layers, it is found that a bowl-trapped AC is an emergent circulation pattern under a wide range of parameters. The trapped AC, often formed by repeated mergers of ACs over the bowl interior, is characterized by anomalously low potential vorticity (PV). Several PV segregation mechanisms that can contribute to the AC formation are examined. In one-layer experiments, the dynamics of the AC are largely determined by a nonlinearity parameter ϵ that quantifies the vorticity of the AC relative to the bowl’s topographic PV gradient. The AC is trapped in the bowl for low , but for moderate values () partial PV segregation allows the AC to reside at finite distances from the center of the bowl. For higher , eddies freely cross the topography and the AC is not confined to the bowl. These regimes are characterized across a suite of model experiments using ϵ and a PV homogenization parameter. Two-layer experiments show that the trapped AC can be top or bottom intensified, as determined by the domain-mean initial vertical energy distribution. These findings contrast with previous theories of mesoscale turbulence over topography that predict the formation of a prograde slope current, but do not predict a trapped AC.

Design of a Kind of Non-Resonant Linear Piezoelectric Motor

2013 ◽  
Vol 459 ◽  
pp. 418-423 ◽  
Author(s):  
Xi Fu Chen ◽  
Wei Qing Huang ◽  
Ji Quan Luo ◽  
Jing Jing Xu
Keyword(s):  
Optimization Design ◽  
Maximum Velocity ◽  
Piezoelectric Motor ◽  
Element Analysis ◽  
Mechanism Model ◽  
Flexible Arm ◽  
Wide Range ◽  
Piezoelectric Motors ◽  
Amplification Mechanism ◽  
Trajectory Equation

A type of drive foot with displacement amplification was proposed based on analysis of the friction drive principle of the non-resonant linear piezoelectric motors. Firstly, the displacement amplification mechanism of the drive foot was carried on and the elliptical trajectory equation of the drive tip was deduced through the mechanism model of the drive foot. The optimization design of main structure parameters was conducted with finite element analysis software to analyze the influences of displacement amplification. The simulation results showed that the maximum magnification factor can be obtained when H(the thickness of flexible arm) is 0.8mm and θ (the flexible angle) is 12°. A linear piezoelectric motor prototype was designed and fabricated, the experimental results indicated that this kind of motor can run steadily in a wide range (the operation bandwidth is beyond 1kHz) and that the thrust can be 0.35N and the maximum velocity can be 2.5mm/s when the operation frequency is 4kHz and the operation voltage is 90V.

Experimental Study on Mean Velocity Profiles Under Wave-Current Interactions

2008 ◽  
Author(s):  
Jinhai Zheng ◽  
Tongfei Li ◽  
Yixin Yan ◽  
Jinchun Hu
Keyword(s):  
River Estuary ◽  
Maximum Velocity ◽  
Velocity Profiles ◽  
Yangtze River Estuary ◽  
Current Profile ◽  
Linear Superposition ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Law ◽  
A Current

A series of experiments are carried out in a laboratory flume for combined wave-current flows, to investigate the characteristics of vertical structure of current profile in a wave-current co-existing water areas. Changes induced in the mean velocity profiles are considered for a range of wave heights, wave periods, water depths and flow velocities which are based on those typical data in the Yangtze River Estuary, China. Preliminary tests are conducted on the unidirectional current and on the wave alone. These show that the current mean velocity profiles agree well with the logarithmic law, and that the waves are approximated closely by the Stokes’ second-order theory. For the combined wave and current tests, the mean velocity profiles generally differ from those suggested by a linear superposition of wave and current velocities. In the case of waves following a current, the velocity distributions exhibit a relatively greater velocity near the bed and a smaller velocity above a certain depth relative to the logarithmic law, and the maximum velocity is observed at a lower location. In the case of wave opposing a current, the velocity distributions depart from the logarithmic law with a relatively smaller velocity near the bed and a greater velocity above a certain depth. Experimental data can be used to validate the theoretical or mathematical models associated with the combined wave-current motions.

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