scholarly journals The spin-up of a linearly stratified fluid in a sliced, circular cylinder

2016 ◽  
Vol 806 ◽  
pp. 254-303
Author(s):  
R. J. Munro ◽  
M. R. Foster
Keyword(s):  
Circular Cylinder ◽  
Rossby Waves ◽  
Rotation Axis ◽  
A Priori ◽  
Propagation Speed ◽  
Stratified Fluid ◽  
Decay Rates ◽  
The Waves ◽  
Western Half ◽  
Good Agreement

A linearly stratified fluid contained in a circular cylinder with a linearly sloped base, whose axis is aligned with the rotation axis, is spun-up from a rotation rate $\unicode[STIX]{x1D6FA}-\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}$ to $\unicode[STIX]{x1D6FA}$ (with $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}\ll \unicode[STIX]{x1D6FA}$) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number $S$ is not small, then that spin-up looks quite different from that reported by Pedlosky & Greenspan (J. Fluid Mech., vol. 27, 1967, pp. 291–304) for $S=0$. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height $S^{-1/2}$ above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al.Phys. Fluids A, vol. 2, 1990, pp. 150–159 and Munro & Foster Phys. Fluids, vol. 26, 2014, 026603, for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom $S^{-1/2}$ region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with $S$ as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large $S$, and vertical vortices are found to occur only for Rossby numbers comparable to $E^{1/2}$, where $E$ is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

Stratified wake of a tilted cylinder. Part 2. Lee internal waves

2012 ◽  
Vol 699 ◽  
pp. 198-215 ◽  
Author(s):  
Patrice Meunier
Keyword(s):  
Circular Cylinder ◽  
Internal Waves ◽  
Bluff Body ◽  
Theoretical Study ◽  
Horizontal Cylinder ◽  
Quantitative Prediction ◽  
Dispersive Waves ◽  
Lee Waves ◽  
The Waves ◽  
Good Agreement

AbstractThis experimental, numerical and theoretical study considers the lee internal waves generated by the wake of a circular cylinder, whose axis is tilted with respect to a stable density gradient. The main difference with the case of a horizontal cylinder is that the lee waves contain a large axial velocity, which are located in a row of lobes extending downstream from the cylinder. At small tilt angles, the wavelength is equal to $2\lrm{\pi} U/ N$, $U$ being the velocity of the cylinder and $N$ the Brunt–Väisälä frequency, which can be explained by the fact that the group velocity of the waves is small. The amplitude of the waves can be predicted using the Lighthill theory for dispersive waves applied to the case of a tilted bluff body. The flow around the cylinder is modelled empirically in order to reach a quantitative prediction in good agreement with the experimental and numerical results. The spatial structure of the predicted internal waves is qualitatively correct although some discrepancies arise because the advection by the flow around the cylinder is neglected.

scholarly journals Could hydrodynamic Rossby waves explain the westward drift?

2018 ◽  
Vol 474 (2213) ◽  
pp. 20180119 ◽  
Author(s):  
O. P. Bardsley
Keyword(s):  
Rossby Waves ◽  
Rotation Axis ◽  
Outer Core ◽  
Momentum Equation ◽  
Energy Propagation ◽  
Initial Value ◽  
Core Mantle Boundary ◽  
Novel Theory ◽  
The Waves ◽  
Westward Drift

A novel theory for the origin of the westward drift of the Earth’s magnetic field is proposed, based upon the propagation of hydrodynamic Rossby waves in the liquid outer core. These waves have the obscure property that their crests always progress eastwards—but, for a certain subset, energy can nevertheless be transmitted westwards. In fact, this subset corresponds to sheet-like flow structures, extended in both the axial and radial directions, which are likely to be preferentially excited by convective upwellings in the Earth’s rapidly rotating outer core. To enable their analysis, the quasi-geostrophic (QG) approximation is employed, which assumes horizontal motions to be independent of distance along the rotation axis, yet accounts for variations in the container height (i.e. the slope of the core–mantle boundary). By projecting the momentum equation onto flows of a QG form, a general equation governing their evolution is derived, which is then adapted for the treatment of two initial value problems—in both Cartesian and spherical geometries—which demonstrate the preference for westward energy propagation by the waves in question. The merits of this mechanism as an explanation for westward drift are discussed.

Linearly stratified, rotating flow over long ridges in a channel

1986 ◽  
Vol 318 (1544) ◽  
pp. 411-438 ◽  
Keyword(s):  
Rotation Axis ◽  
Rectangular Cross Section ◽  
Lower Boundary ◽  
Quantitative Agreement ◽  
Stratified Fluid ◽  
Minor Role ◽  
Geometrical Parameters ◽  
Laboratory System ◽  
Coriolis Parameter ◽  
Good Agreement

The flow of a rotating, linearly stratified fluid over a long symmetric ridge in a channel is investigated experimentally. The laboratory apparatus consists of a long channel of rectangular cross section. The upper bounding surface is a transparent, horizontal plane; the lower boundary is a horizontal flexible belt. The belt serves as a false bottom of the channel and is translated parallel to its long axis. Topographic features are mounted on the belt and are towed through a salt-stratified fluid which is otherwise at rest relative to a rotating observer; the channel rests on a rotating table whose rotation axis is vertical. The most important dimensionless parameters governing the motion are the Rossby and Ekman numbers, a stratification parameter defined as the ratio of the Brunt-Vaisala frequency to the Coriolis parameter, and the geometrical parameters defining the aspect ratio of the ridge, the ridge height to channel depth ratio and the ridge to channel width ratios. An analysis is presented that demonstrates the conditions under which centrifugal effects can be neglected in such laboratory experiments. The analysis also shows the conditions under which the laboratory flows should be a good approximation to the quasigeostrophic potential vorticity equations and attendant boundary conditions for the oceans and atmosphere. This analysis is made for a general three-dimensional topographic feature; i.e. it is not restricted to a long ridge. The laboratory system seems to be an excellent vehicle for modelling oceanic flows but does not properly reproduce a non-Boussinesq term in the atmospheric equation. An analysis for an infinitely long ridge is presented. The predictions so obtained are in good qualitative agreement with the experiments. The quantitative agreement, for the range of parameters considered however, is shown to be poor and this is attributed to neglecting the effects of the lateral bounding surfaces. The experiments demonstrate that for fixed rotation, stratification and free stream speed, the streakline deflection caused by the topography decays with height. For such experiments the flow in the lower levels for positive upward rotation deflects to the left before reaching the ridge, then continues to deflect to the left on the upwind side of the ridge before beginning a rightward drift slightly upstream of the mountain crest. 1 his rightward drift continues on the downwind side of the ridge and well downstream ot the ridge itself before reaching a maximum shift, from which a leftward drift again begins. Increased rotation, other parameters being held fixed, provides stronger horizontal streakhne deflections. Stronger stratification, other parameters being fixed leads to stronger downslope winds and possibly flow separation in the lee. Various charactenstics of the flow field, such as the distance upstream to which substantial streakline curvature is observed, are measured as functions of the various system parameters; comparisons with the infinite ridge theory are also made The downstream motion is accompanied by lee waves for the major portion of the parameter space examined. The amplitude of these waves is shown to decrease with increased rotation other parameters being held fixed. Some non-rotating experiments and these are shown to be in good agreement with the model of Long (1955) and the measured wavelengths are found to be in good agreement with linear theory and laboratory measurements made by other investigators. Measurements of Queney (1947) are presented which show that the horizontal wavelenghts of the waves decrease for increased rotation, other parameters being fixed. A flow regime map based on the observed structure of the vertical wave motion is developed and it is shown that for the range of parameters considered, rotation plays only a minor role, if any.

Mixing induced by oscillatory stratified flow past a right-circular cylinder

1995 ◽  
Vol 284 ◽  
pp. 1-21 ◽  
Author(s):  
M. J. A. M. Perera ◽  
H. J. S. Fernando ◽  
D. L. Boyer
Keyword(s):  
Circular Cylinder ◽  
Potential Energy ◽  
Stratified Flow ◽  
Stratified Fluid ◽  
Rate Of Change ◽  
Buoyancy Flux ◽  
Eddy Diffusivities ◽  
Flow Past ◽  
Rectangular Basin ◽  
Good Agreement

A series of laboratory experiments was performed to investigate the overall mixing characteristics of oscillatory stratified flow past an isolated topography. The experiments were conducted by oscillating a right-circular cylinder in an otherwise quiescent linearly stratified fluid contained in a rectangular basin. The mixing was largely confined to the turbulent ‘core’ region around the cylinder. This mixed fluid was then injected into the fluid interior of the basin by numerous intrusive tongues. These intrusions were accompanied by return currents of unmixed stratified fluid into the turbulent core. The overall effect of this mixing process was to increase the potential energy of the fluid in the basin. An expression is derived to relate the rate of change of potential energy of the system to the basin-averaged buoyancy flux. This formula was then used to calculate the mean buoyancy flux from measurements of the rate of change of potential energy of the fluid system. Basin-averaged diapycnal eddy diffusivities for the experiments were evaluated and the results were found to be in good agreement with the predictions of a heuristic model based on the energetics of the mixing. Observations on the spreading of intrusions and the evolution of the density field are also presented.

scholarly journals MAX-DOAS observations of aerosols, formaldehyde and nitrogen dioxide in the Beijing area: comparison of two profile retrieval approaches

2015 ◽  
Vol 8 (2) ◽  
pp. 941-963 ◽  
Author(s):  
T. Vlemmix ◽  
F. Hendrick ◽  
G. Pinardi ◽  
I. De Smedt ◽  
C. Fayt ◽  
...  
Keyword(s):  
Standard Deviation ◽  
A Priori ◽  
Systematic Bias ◽  
Aerosol Extinction ◽  
Data Set ◽  
Near Surface ◽  
Beijing Area ◽  
Least Squares Fit ◽  
Relative Differences ◽  
Good Agreement

Abstract. A 4-year data set of MAX-DOAS observations in the Beijing area (2008–2012) is analysed with a focus on NO2, HCHO and aerosols. Two very different retrieval methods are applied. Method A describes the tropospheric profile with 13 layers and makes use of the optimal estimation method. Method B uses 2–4 parameters to describe the tropospheric profile and an inversion based on a least-squares fit. For each constituent (NO2, HCHO and aerosols) the retrieval outcomes are compared in terms of tropospheric column densities, surface concentrations and "characteristic profile heights" (i.e. the height below which 75% of the vertically integrated tropospheric column density resides). We find best agreement between the two methods for tropospheric NO2 column densities, with a standard deviation of relative differences below 10%, a correlation of 0.99 and a linear regression with a slope of 1.03. For tropospheric HCHO column densities we find a similar slope, but also a systematic bias of almost 10% which is likely related to differences in profile height. Aerosol optical depths (AODs) retrieved with method B are 20% high compared to method A. They are more in agreement with AERONET measurements, which are on average only 5% lower, however with considerable relative differences (standard deviation ~ 25%). With respect to near-surface volume mixing ratios and aerosol extinction we find considerably larger relative differences: 10 ± 30, −23 ± 28 and −8 ± 33% for aerosols, HCHO and NO2 respectively. The frequency distributions of these near-surface concentrations show however a quite good agreement, and this indicates that near-surface concentrations derived from MAX-DOAS are certainly useful in a climatological sense. A major difference between the two methods is the dynamic range of retrieved characteristic profile heights which is larger for method B than for method A. This effect is most pronounced for HCHO, where retrieved profile shapes with method A are very close to the a priori, and moderate for NO2 and aerosol extinction which on average show quite good agreement for characteristic profile heights below 1.5 km. One of the main advantages of method A is the stability, even under suboptimal conditions (e.g. in the presence of clouds). Method B is generally more unstable and this explains probably a substantial part of the quite large relative differences between the two methods. However, despite a relatively low precision for individual profile retrievals it appears as if seasonally averaged profile heights retrieved with method B are less biased towards a priori assumptions than those retrieved with method A. This gives confidence in the result obtained with method B, namely that aerosol extinction profiles tend on average to be higher than NO2 profiles in spring and summer, whereas they seem on average to be of the same height in winter, a result which is especially relevant in relation to the validation of satellite retrievals.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

The role of the Pacific Decadal Oscillation and ocean-atmosphere interactions in driving United States heatwaves

2021 ◽  
Author(s):  
Sem Vijverberg ◽  
Dim Coumou
Keyword(s):  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Causal Link ◽  
Causal Mechanism ◽  
Temperature Forecast ◽  
The Pacific ◽  
Ocean Atmosphere ◽  
The Waves

<p>Heatwaves can have devastating impact on society and reliable early warnings at several weeks lead time are needed. Heatwaves are often associated with quasi-stationary Rossby waves, which interact with sea surface temperature (SST). Previous studies showed that north-Pacific SST can provide long-lead predictability for eastern U.S. temperature, moderated by an atmospheric Rossby wave. The exact mechanisms, however, are not well understood. Here we analyze Rossby waves associated with heatwaves in western and eastern US. Causal inference analyses reveal that both waves are characterized by positive ocean-atmosphere feedbacks at synoptic timescales, amplifying the waves. However, this positive feedback on short timescales is not the causal mechanism that leads to a long-lead SST signal. Only the eastern US shows a long-lead causal link from SSTs to the Rossby wave. We show that the long-lead SST signal derives from low-frequency PDO variability, providing the source of eastern US temperature predictability. We use this improved physical understanding to identify more reliable long-lead predictions. When, at the onset of summer, the Pacific is in a pronounced PDO phase, the SST signal is expected to persist throughout summer. These summers are characterized by a stronger ocean-boundary forcing, thereby more than doubling the eastern US temperature forecast skill, providing a temporary window of enhanced predictability.</p>

scholarly journals Trapped Planetary (Rossby) Waves Observed in the Indian Ocean by Satellite Borne Altimeters

2017 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor
Keyword(s):  
Indian Ocean ◽  
Rossby Waves ◽  
Low Frequency ◽  
Propagation Speed ◽  
Wave Theory ◽  
Planetary Waves ◽  
Sea Surface ◽  
Trapped Wave ◽  
The Indian Ocean ◽  
Frequency Variations

Abstract. Using 20 years of accurately calibrated, high resolution, observations of Sea Surface Height Anomalies (SSHA) by satellite ‎borne altimeters we show that in the Indian Ocean south of the Australian coast the low frequency variations of SSHA are ‎dominated by westward propagating, trapped, i.e. non-harmonic, planetary waves. Our results demonstrate that the ‎meridional-dependent amplitudes of the SSHA are large only within a few degrees of latitude next to the South-Australian ‎coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the ‎amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signals is analyzed by ‎employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely ‎between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The ‎estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of ‎harmonic Rossby (Planetary) waves by 140 % to 200 %. In contrast, the theory of trapped Rossby (Planetary) waves in a ‎domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase ‎speeds.‎

scholarly journals Validation of nine years of MOPITT V5 NIR using MOZAIC/IAGOS measurements: biases and long-term stability

2014 ◽  
Vol 7 (11) ◽  
pp. 3783-3799 ◽  
Author(s):  
A. T. J. de Laat ◽  
I. Aben ◽  
M. Deeter ◽  
P. Nédélec ◽  
H. Eskes ◽  
...  
Keyword(s):  
Near Infrared ◽  
Transport Model ◽  
A Priori ◽  
Validation Data ◽  
Chemistry Transport Model ◽  
Large Variability ◽  
Long Term Stability ◽  
Spatio Temporal ◽  
Good Agreement

Abstract. Validation results from a comparison between Measurement Of Pollution In The Troposphere (MOPITT) V5 Near InfraRed (NIR) carbon monoxide (CO) total column measurements and Measurement of Ozone and Water Vapour on Airbus in-service Aircraft (MOZAIC)/In-Service Aircraft for a Global Observing System (IAGOS) aircraft measurements are presented. A good agreement is found between MOPITT and MOZAIC/IAGOS measurements, consistent with results from earlier studies using different validation data and despite large variability in MOPITT CO total columns along the spatial footprint of the MOZAIC/IAGOS measurements. Validation results improve when taking the large spatial footprint of the MOZAIC/IAGOS data into account. No statistically significant drift was detected in the validation results over the period 2002–2010 at global, continental and local (airport) scales. Furthermore, for those situations where MOZAIC/IAGOS measurements differed from the MOPITT a priori, the MOPITT measurements clearly outperformed the MOPITT a priori data, indicating that MOPITT NIR retrievals add value to the MOPITT a priori. Results from a high spatial resolution simulation of the chemistry-transport model MOCAGE (MOdèle de Chimie Atmosphérique à Grande Echelle) showed that the most likely explanation for the large MOPITT variability along the MOZAIC-IAGOS profile flight path is related to spatio-temporal CO variability, which should be kept in mind when using MOZAIC/IAGOS profile measurements for validating satellite nadir observations.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

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