Showing papers on "Rossby radius of deformation published in 1993"

The Annual Wind-driven Rossby Wave in the Subthermocline Equatorial Pacific

Abstract: The annual cycle of temperature in the subthermocline equatorial Pacific is studied using a new compilation of historical hydrographic profiles. The observations have several characteristics suggestive of a vertically propagating, first meridional mode (l=1) long-wavelength Rossby wave: phase lines that slope downward from east to west indicative of upward and westward phase propagation amplitude maxima parallel to phase lines, and nearly symmetric off-equatorial maxima of annual amplitude. Estimates of zonal wavenumber, vertical wavenumber, and the location of maxima of isotherm displacements are consistent with those of the l = 1 Rossby wave. A solution to a linear continuously stratified model, driven by a version of the observed annual wind field, confirms this interpretation. The solution is dominated by a vertically propagating, l = 1 Rossby wave. The wave is generated primarily by the westward-propagating component of the equatorial zonal wind field; it carries energy along WKB ray paths i...

Geostrophic velocity and transport variability in the Brazil-Malvinas Confluence

Abstract: This paper presents the results from a study of the dynamics of the Brazil-Malvinas Confluence in the southwestern Atlantic based on data collected with an array of inverted echo sounders. Dynamic height series were obtained at 10 different sites for a period of 15 months. The data are analyzed in terms of dynamic height, geostrophic velocities and transports. The large variability previously inferred from satellite observations is observed in the dynamic height field of the surface, relative to 100 m, and is attributed to changes in the latitude of separation, the meandering of the Confluence front towards the east, and eddy generation. The eddy circulation observed is both cyclonic and anticyclonic. These eddies are observed both between the southward edge of the Brazil Current and the northward edge of the Malvinas Current and superimposed to the main flows. The diameter of the eddies is two to three times the Rossby Radius of deformation. The highest observed values of the geostrophic velocities (102 cm s −1 at 36.5°S and −61 to −62 cm s −1 at 37.6°S) are associated with the large shear in frontal situations. The northward penetration of the Malvinas Current occurs during 1988 and 1990 during the southern hemisphere winter. This is in agreement woth results from a previous deployment, satellite observations and model results. The Brazil Current transport is at 35.2 and 36.5°S, −24 Sv towards the south and −20 Sv between 37.7 and 38°S (reference 1000 m). The transport of the Brazil Current return at 35.2°S is of the same value as the southward flow: 24 Sv. For the Malvinas Current, the estimates indicate a northward transport of 5 Sv at 37.7°S (reference 1000 m). These values are considered as a lower limit. The array captured only about half the flow due to the location of the deployments, and only the baroclinic component. The transport should be at least doubled to compensate the value obtained for the Malvinas return flow at the same latitudes, −24 Sv.

Rossby Vortices, Spiral Structures, Solitons: Astrophysics and Plasma Physics in Shallow Water Experiments

Abstract: 1. Introduction.- 2. The Natural Phenomena Simulated in Rotating Shallow Water Experiments.- 2.1 Length, Rotation Velocity, and Lifetime of the Structures.- 2.2 Large-Scale, Long-Lived Rossby Vortices in the Atmospheres of Giant Planets. The Cyclone-Anticyclone Asymmetry.- 2.3 Rossby Vortices in the Oceans.- 2.3.1 Open Sea Vortices.- 2.3.2 Rings of the Gulf Stream and the Kuroshio Current.- 2.3.3 Internal Thermoclinic Vortices (Lenses).- 2.4 Spiral Structures in Galaxies.- 3. Common Features of the Simulated Natural Phenomena.- 3.1 Quasi-Two-Dimensionality.- 3.2 Structure Generation by Flows with Horizontal Velocity Shear.- 3.3 Horizontal Dimensions Exceeding the Characteristic Rossby Radius.- 4. Physical Prerequisites of the Laboratory Simulation of Large-Scale Rossby Vortices and Galactic Spiral Structures.- 4.1 The Analogy Between Two-Dimensional Gas Dynamics and the Dynamics of Shallow Water.- 4.1.1 Theory.- 4.1.2 Experiment.- 4.2 Principal Similarity Parameters in Nature and Experiment.- 5. Physical Basis for the Experimental Investigation of Rossby Solitons and Laboratory Simulation of Drift Vortices and Solitons in Magnetized Plasma.- 5.1 Two-Dimensional Motion of Charged Particles in Magnetized Plasma and Particles in Rotating Shallow Water.- 5.2 General Nonlinear Equation for Drift Motion.- 5.3 Linear Rossby Waves and Plasma Drift Waves.- 5.4 Linear Packet of Rossby Waves and the Time of its Dispersion Decay. Definition of a Soliton.- 5.5 Nonlinear Rossby Waves: Vortices and Solitons.- 5.6 Viscous Damping of Rossby Vortices.- 6. Experimental Configurations.- 6.1 Geometry and Rotation Regime of the Vessels for the Observation of Rossby Solitons.- 6.2 Techniques for Local Generation of Rossby Vortices.- 6.3 Devices for Generating Rossby Vortices by Counterflows.- 6.4 Devices for the Simulation of Galactic Spiral Structures.- 6.5 Diagnostic Techniques.- 7. Laboratory Simulation of Rossby Vortices and Solitons in Planetary Atmospheres and Oceans.- 7.1 Generation of Rossby Vortex Chains by Zonal Counterflows in Rotating Shallow Water. The Cyclone-Anticyclone Asymmetry.- 7.2 Self-Organizing Solitary Anticyclonic Rossby Vortex in Zonal Flows as a Model of Jovian Great Red Spot.- 7.3 Regularity in the Generation of Chains with Different Numbers of Vortices and the Problems of Uniqueness and Stationarity of the JGRS.- 7.4 Two- and Three-Dimensional Models of the JGRS.- 7.5 Alternative JGRS Laboratory Models.- 7.6 Stationary Rossby Vortices in Flows and the Blocking Phenomenon.- 8. Laboratory Simulation of Galactic Spiral Structures.- 8.1 Generation of Spiral Structures in Differentially Rotating Shallow Water.- 8.2 Spiral-Vortex Structures.- 8.3 The Common Mechanism Generating Solitary Rossby Vortices in Planetary Atmospheres and Spirals in Galaxies.- 8.4 Asymmetrical and Outbranching Spirals.- 8.5 The Influence of Viscosity and Friction.- 8.6 Laboratory Simulation and Astronomical Observations. Predictions for Astronomers.- 9. Rossby Vortices and Solitons in Free Motion.- 9.1 A Short History of the Experiments.- 9.2 Rossby Solitons in the Laboratory and Their Properties.- 9.3 Collisions of Rossby Vortices.- 9.4 Cyclone-Anticyclone Asymmetry.- 9.5 Quasi-Two-Dimensionality of Rossby Vortices. The Non-Principal Role of Viscosity.- 9.6 Vortex-Wave Dualism.- 9.7 Comparison between Experiment and Theory.- 10. Solitonic Model of Natural Vortices.- 10.1 Solitonic Model of the JGRS and Other Large-Scale, Long-Lived Vortices in Planetary Atmospheres.- 10.2 An Alternative Model of the JGRS: Numerical Calculation.- 10.3 Solitonic Vortices in the Oceans.- 11. Dipolar Rossby Vortices.- 11.1 Preliminary Experiments.- 11.2 Dipolar Vortex Decay for Moderate Liquid Depths.- 11.3 Solitonic Properties of Dipolar Vortices for Large Liquid Depths.- 12. Shallow-Water Simulation of Drift Vortices and Solitons in Magnetized Plasma.- 12.1 Prediction of Drift Soliton Properties Based on Shallow-Water Simulation. Drawbacks of the "Purely Wave" Concept.- 12.2 Vortical Mechanism for the Enhanced Diffusion of Plasma Across a Strong Magnetic Field.- 13. Conclusion.- S. Supplements.- References.

Characteristics of the summer 1987 flow field in the Ionian Sea

Abstract: We present an extensive analysis of the first complete data set in the northern Ionian Sea collected during the Physical Oceanography of the Eastern Mediterranean (POEM) general circulation survey of September 1987. A four water mass structure of the basin is found to be represented by a first internal baroclinic Rossby radius of deformation of 11.8 km. The horizontal correlation scales decrease with depth, and the subsurface flow is dominated by anticyclonic gyres. Large-scale circulation trends of the temperature and salinity covariance matrices are compensated below 200 m, and only the gyre scales (∼100 km) persist at intermediate and deep levels. The empirical orthogonal functions of the data set show that an horizontal scale separation exists between the first and higher vertical modes of the dynamic height field.

Rossby waves in the Pacific Ocean extracted from Geosat altimeter data

Abstract: Rossby waves have been detected in the northeast Pacific in time series of in situ hydrographic data, but the limited geographic coverage of such data has restricted the search for Rossby waves to small regions. Two years of continuous Geosat altimetry data were used here to extract the signatures of Rossby waves from the entire Pacific Ocean. This relatively long time series of global data presents an excellent opportunity to examine the surface expression of large-scale ocean phenomena such as Rossby waves. For this analysis the Pacific Ocean was divided into 10-degree square regions, and Rossby waves defined by the Rossby wave dispersion relation were fit to the Geosat data in each region. Rossby waves fit to each 10-degree region were separated by Fourier components in wavenumber space, with frequencies determined by the dispersion relation. Barotropic and first mode baroclinic Rossby waves were fit separately to the Geosat data. Rossby wave amplitudes from the least-squares fit were plotted ...

On the behaviour of baroclinic waves undergoing horizontal deformation. II: Error-bound amplification and Rossby wave diagnostics

Abstract: An expression for the maximum possible amplification of a baroclinic wave with zero potential vorticity, undergoing horizontal deformation, is obtained. This amplification provides an estimate of the growth of hypothetical analysis errors for such a system. For the geophysically relevant flows considered in detail in this paper, strain rates of ±1 × 10−5 s−1 cause a 28% reduction in the logarithmic amplification over a 48-hour period. If the effects of phase changes of water are simulated by halving the brunt-Vaisala frequency, all growth rates are larger, but strain rated of ±1 × 10−5s−1 now cause a 34% reduction logarithmic amplification. Notably, this corresponds to an 81% reduction in actual amplification. For all strain rates the increase in non-modal growth associated with lowering the Richardson number is found to be less than for norma-mode-type baroclinic waves. To understand why particular initial zonal wavelengths and vertical phase shifts optimize growth in this time-dependent basic state, new diagnostics are developed. The diagnostics are based on a mathematical model of Bretherton's qualitative description of baroclinic instability in terms of two counter-propagating Rossy waves. They provide a viewpoint from which growth results form the product of a scale term, which is proportional to the wind strength induced at opposing boundaries, and a phase term, which is maximized when the upper wave is 90° up shear of the lower Rossby wave. The perspective leads to a simple explanation of why strain affects amplification and how this effect depends on the static stability. Furthermore, it provides simple methods, based on diagnosed amplitudes of neglected 2nd and 3rd order nonlinear terms, for forecasting when linear prediction become misleading. To assess how dynamic constraints associated with the time dependence of a basis flow affect its stability, it proves useful to define a new quantity, the ‘potential maximal wave amplification’, which is the amplification that would arise if at each instant the flow was adiabatically and mass preservingly rearranged so that the Rossby waves defining the boundary buoyancy distribution were always optimally configured for growth. The results presented here also show that time-dependent systems which do not support normal modes can amplify certain wavelengths more than other, and hence be likely to impart the corresponding horizontal structures onto arbitrarily shaped initial disturbances. Such scale selection is linked to the relationship between the horizontal morphology of a Rossby wave and the strength of the wind it can induce at vertically distant points. The effect of strain on sets of flows is also found to depend on the mean meridional wave number of such flows. Notably, if this mean meridional wave number is increased to values near the short-wave cut-off for instability, the presence of strain can actually enhance growth. In narrow baroclinic jets, such as those found off ice edges in polar regions, barotropic modes often grow faster than baroclinic modes in unstrained flow. A comparison with the effects of strain on barotropic instability shows that frontogenetic strain damps barotropic growth much more than baroclinic growth. The result may be important to theories of polar-low genesis.

Current variability and upwelling along the north shore of Baie des Chaleurs

Abstract: The circulation and temperature variability along the north shore of Baie des Chaleurs is investigated from the first extensive set of moored current‐meter data. Instruments were deployed from July to December of 1985, 1986 and 1987 at three locations. The moorings were placed within an internal Rossby radius of deformation of the coast and the sites had a total alongshore separation distance of 100 km. The currents were primarily directed alongshore and the variability was dominated by the tides. The tidal amplitudes were 0.05–0.25 m s‐1 in contrast to low‐frequency (periods above 1 d) speeds that were typically <0.04 m s‐1. The mean residual currents ranged from 0.01–0.1 m s‐1 and are shown to dominate the advective displacement of passive particles for periods above 5 d. The mean circulation was westward in summer but reversed in early autumn in the outer half of the bay. The westward flow is believed to be an extension of the Gaspe Current. A reduction in the strength of the Gaspe Current, co...

Rossby Number or Rotation Period

Abstract: It is shown that the scaling of rotation periods by a color-dependent parameter (turnover time) improves substantially the observed activity- period relations only for single, main sequence, solar type stars with 0.5 ≲ B − V ≲ 0.8. For other single main sequence stars and for single giants activity indices correlate equally well with rotation period and the Rossby number, or show no correlation with either parameter.

Observations on the long-period variability of the Gulf Stream downstream of Cape Hatteras

Abstract: To examine the long-period variability of the Gulf Stream, sea level residuals relative to a 2-year mean sea level in the Gulf Stream downstream of Cape Hatteras (between 75 deg W and 60 deg W longitude) are used. Residuals, as derived from Geosat altimetry between November 1986 and December 1988, were gridded in space and time at a temporal resolution of 10 days and spatial resolution of 1/4 deg. Complex empirical orthogonal function (CEOF) analysis was applied to the data set to extract the spatially correlated signal with the original data subsampled to 1/2 deg. In addition to determining the space-time scales and propagation characterisitics of the different modes, wavenumber-frequency spectral techniques were used to separate the variability into propagating and stationary components. The CEOF technique applied to the data set indicated that the first four CEOF modes accounted for 60% of the variability and were found to be above the noise leve 99% of the time. CEOF 1 was associated with westward propagation at 5 km/d at a wavelength of 2000 km and eastward propagation at 1-2 km/d centered at a 500-km wavelength. This first CEOF is in good agreement with thin-jet equivalent barotropic models which predict westward propagation for wavelengths greater than 1130 km. A deflection of the wavelike pattern at 65 deg W also indicates a possible topographic effect. A simple scaling of the effect of topography indicates that for length scales longer than the internal Rossby radius of deformation, the topographic term is at least of the same order of magnitude as the beta effect. The second CEOF was more broadbanded in wavenumber space, with eastward propagation occurring in a wavenumber-frequency band between 300 and 1400 km and 0.5 and 2.0 cycles/yr. The third CEOF is similar in structure to the first, but with less energy. CEOF 4 was clearly identifiable with higher frequencies than the first three with westward propagation at 4 km/d. The spatial location of this mode along with the westward propagation indicates possible influences from eddy-stream interactions. Thus topography, Rossby wave dynamics and eddy-stream interactions all appear to have a significant role in determining the space-time scales and propagation properties of the long-period response of sea level in the Gulf Stream.

Seasonal variations in equatorial Atlantic Ocean zonal volume transport at 28°W

Abstract: Zonal volume transport is examined over the upper 150 m of the water column at 28°W, using the Seasonal Response of the Equatorial Atlantic experiment moored current meter data at 0.75°S, 0.0°, and 0.75°N and a time domain empirical orthogonal function (EOF) analysis to improve spatial and temporal resolution. Gaussian distributions are fit to the mean volume transports per unit width and the fluctuations about these means that are found to be represented by a single EOF mode. The mean volume transport is distributed symmetrically both about the equator and about 75 m depth, with a meridional scale width of 101 km and a magnitude of 20.3 Sv. The standard deviation for the fluctuations is 4.7 Sv, and in contrast to the mean the fluctuations are confined to above 100 m depth, with a larger meridional scale width. The scale width for the mean is consistent with an inertial scale associated with conservation of potential vorticity, while the scale width for the fluctuations is consistent with an equatorial Rossby radius of deformation associated with equatorially trapped waves. These findings support a hypothesis that different physical processes are controlling the volume transport, as integrated from the surface across the Equatorial Undercurrent, over different time scales. On the time scale of the record length average, inertial dynamics appear to be controlling, while on the time scales of the seasonal fluctuations, linear equatorial long-wave dynamics appear to be controlling. However, given the limited record length, there are insufficient degrees of freedom to test this hypothesis statistically.

The Reflection of Unstable Baroclinic Waves and the Production of Mean Coastal Currents

Abstract: The problem of the reflection of unstable baroclinic waves from straight boundaries inclined with respect to latitude circles is studied. The basic flow in which the incident unstable wave is embedded is a flow with only vertical shear flowing parallel to the boundary. The analysis is done for a two-layer model on the β plane. For a wave packet centered on the most unstable wave, the reflection process produces two reflected modes, each trapped to the boundary. The trapping scale is of the order of the Rossby radius of deformation. This trapping occurs whenever the current is inclined with respect to a latitude circle, in which case all shears, no matter how small, will support unstable waves. It is argued that the trapped character of the reflected disturbance will produce a rectified current along the boundary with a net barotropic component.

First-order resonance in the reflection of baroclinic Rossby waves

Abstract: The nonlinear interaction between an incident and a reflected Rossby wave produces a steady flow parallel to the (non-zonal) reflecting wall and a transient flow oscillating at twice the frequency of the incident-reflected pair. If the transient forcing is resonant, i.e. a free Rossby wave, the resonant response must have zero amplitude at the wall in order to fulfil the boundary condition there; a straightforward expansion predicts a linear growth of its amplitude in the offshore direction y. Resonance is possible only if 0 < |sin α| ≤ , where α is the angle between the wall and the easterly direction. This requirement is met by several boundaries in the ocean. A simple graphical method to find a resonant triad is described.Using the method of multiple scales, it is shown that the wave amplitudes of the triad are slowly varying periodic functions of y, such that the energy flux of the triad through any plane parallel to the wall vanishes, as required by energy conservation. The waves participating in the resonant triad become wave packets. The three waves do not exchange energy in time due to the additional constraint on the motion imposed by the boundary condition at the wall. It is shown that the wave amplitudes cannot be slowly varying functions of v and time.As a possible oceanic application of the theoretical findings, the distance from the wall where one would expect to find large semi-annual amplitudes if annual Rossby waves are impinging on the boundary is of the order of 100 km. Motivated by similar studies (Plumb 1977; Mysak 1978), there are speculations on what would happen if three incident-reflected Rossby wave pairs (or modes) are taken, allowing each mode amplitude to be slowly varying in time.

Eddy Rossby wave frequency in β‐plane turbulence

Abstract: The concept of eddy viscosity is generalized to include an ‘‘eddy β‐term’’ that accounts for the effect of unresolved turbulence and Rossby waves on the resolved modes in the subgrid‐scale representation of β‐plane turbulence.

Nonlinear Rossby Waves and Their Interactions (I) ——Collision of Envelope Solitary Rossby Waves

Abstract: By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two envelope solitary Rossby waves. It is found that for a range of parameters, the collision interactions are envelope soliton-like in that the properties of the two envelope solitary waves change very little. For other parameters, new "inelastic" effects are observed, including speed changes, fission of envelope solitary waves and energy dispersion. It is also found that despite of the complexity of the interacting process, the energy of each wave is conserved.

Trapped internal gravity waves in a geostrophic boundary current

Abstract: The effect of a geostrophic boundary current on internal gravity waves is studied with a reduced-gravity model. We found that the boundary current not only modifies the coastal Kelvin wave, but also forms wave guides for short internal gravity waves. The combined effects of current shear, the boundary, and the slope of the interface create the trapping mechanism. These trapped internal gravity waves appear as groups of discrete zonal modes. They have wavelengths comparable to or shorter than the internal Rossby radius of deformation. Their phase speeds are close to that of the internal Kelvin wave. However, they can propagate both in, or opposite to, the direction of the Kelvin wave. The results of the present work suggest the possibility of finding an energetic internal gravity wave phenomenon with near-inertial frequency in a broad geostrophic boundary current.

Large scale perturbations in extratropical atmosphere—Part I: On rossby waves

Abstract: This study reexamines the propagation mechanism and geostrophic property of the classical two dimensional Rossby waves in a non-divergent barotropic atmosphere. It will be found that propagation of large scale atmospheric waves depends crucially on horizontal divergence. A small Rossby number in Rossby waves is not sufficient for the waves to have a small ageostrophic component, because the two dimensional classical Rossby waves do not manifest the geostrophic balance as good as observed in the atmosphere.

Rossby Vortices and Solitons in Free Motion

Abstract: The theory of anticyclonic vortical Rossby solitons has been discussed in Chap. 5. The solitonic concept of anticyclonic Rossby vortices has been used as a foundation for the theoretical solitonic models of the JGRS and similar long-lived vortices in the atmospheres of giant planets and in the oceans. The first consistent solitonic theory of the JGRS was proposed in 1976 (see below). In the light of these theoretical results, it appeared quite important to obtain a Rossby soliton in laboratory experiment. The present chapter describes how this problem was solved.

Study of nonlinear rossby waves in the atmosphere under semi-geostrophic approximation

Abstract: Under semi-geostrophic approximation the nonlinear ordinary differential equations are obtained for the motion inthe barotropic and baroclinic atmospheres with the effects of zonal shear basic flow and topographic forcing included.Two constraints are acquired of finite-amplitude periodic and solitary waves in the original model with the aid of thephase-plane geometric qualitative theory of a dynamic system defined by the differential equation.The explicit solutionof the nonlinear waves is found by means of the approximation method and some significant results are achieved.

Sea level variations due to equatorial Rossby waves associated with El Niño

Abstract: Interannual variations of sea level in the tropical Pacific are examined in relation to the El Nin˜o phenomenon. The amplitude of equatorial Rossby waves forced by wind and the sea level due to the waves are calculated from the analytical solutions in a two-layer reduced-gravity ocean model using filtered monthly wind data during the period 1961–87. Sea level variations with interannual periods at Truk, Ponape, and Majuro islands, located around 7°N, as well as at Rabaul, Honiara, and Funafuti in the South Pacific, are almost explained by Rossby waves remotely forced by winds. Reflected Rossby waves generated at the eastern coast of the Pacific may not significantly be effective. The interannual Rossby wave components of sea level are produced by odd meridional-mode waves excited from the equatorially symmetric component wind, which is composed of wind data in the same hemisphere as the studied sea level grid. Therefore, the Rossby components in the North Pacific are not affected by wind in the S...

Laboratory Simulation of Rossby Vortices and Solitons in Planetary Atmospheres and Oceans

Abstract: The experiments described in this chapter and in Chaps. 9–11 have been performed in the following succession. First, Rossby vortices and solitons were studied in a liquid rotating as a single body. In these experiments, the vortex under investigation was generated with a local pulsed (single-action) source and then propagated along the parallel in the free-travel regime through the rotating parabolic layer of shallow water. The lifetime of the vortex was limited by viscosity, apart from any other factors [7.1–3]. Next, experiments were carried out on generating Rossby vortices with stationary, axially symmetrical geostrophic counterflows. These experiments produced steadily drifting chains of vortices, from ten vortices in a chain when the flow velocity was low to one when it was high. This second series of experiments is of particular interest since it fits much better with the actual process of Rossby vortex generation by zonal flows in planetary atmospheres, therefore this series will be the first to be described. On the other hand, to elucidate the physical nature of the vortices in question one has to investigate them in their free-travel regime. Without such a study, it is impossible to tell whether there are any Rossby solitons among the observed vortices and whether they simulate plasma drift vortices and solitons. This series of experiments is described in Chaps. 9–11.

Rossby Number Dependence on Meander Dynamics of a Potential Vorticity Front

Abstract: Semi-geostrophic dynamics of jets are studied using a potential vorticity front in an equivalent barotropic model. Meandering processes of the front are examined in the thin-jet limit on a β-plane by a curvilinear coordinate system. For calculated along-front velocity fields, asymmetrical profiles are caused by meandering. This asymmetry of the velocity profile is enhanced as the Rossby number becomes large. Using the along-front velocity fields, the normal velocity of front is expressed so that the Rossby number is explicitly included. This expression can be rewritten in the form of the mKdV equation.