Search Results

You are looking at 1 - 10 of 26 items for

  • Author or Editor: Peter Brandt x
  • Refine by Access: All Content x
Clear All Modify Search
Angelo Rubino and Peter Brandt

Abstract

Aspects of the dynamics of warm-core eddies evolving in a deep ocean are investigated using the results of laboratory experiments and numerical simulations. The vortices, produced experimentally in a system brought to solid body rotation by rapidly lifting a bottomless cylinder containing freshwater immersed in a salty ambient fluid, show clearly the presence of inertial oscillations: deepenings and contractions, shoalings and expansions, alternate during an exact inertial period. These pulsations, though predicted analytically and simulated numerically, had never been measured before for surface eddies having aspect ratios, as well as Rossby and Burger numbers, typical of geophysical warm-core eddies. The spatial structure of the vortex radial and tangential velocity components is analyzed using the experimental results and numerical simulations carried out by means of a layered, nonlinear, reduced-gravity frontal model. It is found that, while the dependence of the vortex radial velocity on the vortex radius evolves toward linearity as time elapses, different spatial structures seem to be possible for the vortex tangential velocity dependence. This behavior, which strongly differs from the “pulson” dynamics, is instead consistent with recently found analytical solutions of the nonlinear, reduced-gravity shallow-water equations describing the dynamics of warm-core eddies on an f plane.

Full access
Angelo Rubino, Peter Brandt, and Katrin Hessner

Abstract

New analytical, circular eddy solutions of the nonlinear, reduced-gravity, shallow-water equations in a rotating system are presented. While previous analytical solutions were limited to the description of pulsons, which are oscillating, frontal, warm-core eddies with paraboloidic shape and linear velocity components, the new solutions describe more general radial structures of eddy shape and azimuthal velocity. In particular, the new solutions, which contain as a subset the circular pulson solution, also allow for the description of circular, frontal, warm-core eddies with small azimuthal velocities at their periphery and/or with motionless cores, which are frequently observed characteristics of warm-core eddies in the World Ocean.

Full access
Martin Claus, Richard J. Greatbatch, and Peter Brandt

Abstract

A representation of an equatorial basin mode excited in a shallow-water model for a single high-order baroclinic vertical normal mode is used as a simple model for the equatorial deep jets. The model is linearized about both a state of rest and a barotropic mean flow corresponding to the observed Atlantic Equatorial Intermediate Current System. It was found that the eastward mean flow associated with the North and South Intermediate Counter Currents (NICC and SICC, respectively) effectively shields the equator from off-equatorial Rossby waves. The westward propagation of these waves is blocked, and focusing on the equator due to beta dispersion is prevented. This leads to less energetic jets along the equator. On the other hand, the westward barotropic mean flow along the equator reduces the gradient of absolute vorticity and hence widens the cross-equatorial structure of the basin mode. Increasing lateral viscosity predominantly affects the width of the basin modes’ Kelvin wave component in the presence of the mean flow, while the Rossby wave is confined by the flanking NICC and SICC. Independent of the presence of the mean flow, the application of sufficient lateral mixing also hinders the focusing of off-equatorial Rossby waves, which is hence an unlikely feature of a low-frequency basin mode in the real ocean.

Full access
Angelo Rubino, Sergey Dotsenko, and Peter Brandt

Abstract

Intrinsic oscillations of stable geophysical surface frontal currents of the unsteady, nonlinear, reduced-gravity shallow-water equations on an f plane are investigated analytically and numerically. For frictional (Rayleigh) currents characterized by linear horizontal velocity components and parabolic cross sections, the primitive equations are reduced to a set of coupled nonlinear ordinary differential equations. In the inviscid case, two periodic analytical solutions of the nonlinear problem describing 1) the inertially reversing horizontal displacement of a surface frontal current having a fixed parabolic cross section and 2) the cross-front pulsation of a coastal current emerging from a motionless surface frontal layer are presented. In a linear and in a weakly nonlinear context, analytical expressions for field oscillations and their frequency shift relative to the inertial frequency are presented. For the fully nonlinear problem, solutions referring to a surface frontal coastal current are obtained analytically and numerically. These solutions show that the currents oscillate always superinertially, the frequency and the amplitude of their oscillations depending on the magnitude of the initial disturbance and on the squared current Rossby number. In a linear framework, it is shown that disturbances superimposed on the surface frontal current are standing waves within the bounded region, the frequencies of which are inertial/superinertial for the first mode/higher modes. In the same frame, a zeroth mode, which could be interpreted as the superposition of an inertial wave on a background vorticity field, would formally yield subinertial frequencies. For surface frontal currents affected by Rayleigh friction, it is shown that the magnitude of the mean current decays according to a power law and that the oscillations decay faster, because this decay follows an exponential law. Implications of the intrinsic oscillations and of their rapid dissipation for the near-inertial motion in an active ambient ocean are discussed.

Full access
Angelo Rubino, Katrin Hessner, and Peter Brandt

Abstract

Aspects of the decay of stable frontal warm-core eddies in the deep ocean are investigated using a new numerical layered “frontal” model that solves the nonlinear, reduced-gravity, shallow-water equations for a horizontally inhomogeneous, viscous fluid on an f plane. After a discussion on aspects of the numerical techniques implemented to allow for the eddy expansions and contractions at the sea surface, for the first time the capability of a numerical model of reproducing the evolution of analytical nonstationary frontal vortices is explored. This step is necessary, as far as different phenomena related to the dynamics of these oceanic features are to be studied numerically. In fact the comparison between numerical and analytical inviscid solutions allows for a quantification of the numerical dissipation affecting the simulated solutions. This dissipation is found to be very small in this numerical model: The simulated lifetimes are larger than those of most of the frontal eddies observed in the World Ocean. On this basis, the eddy decay due to interfacial (linear and quadratic) friction, harmonic horizontal momentum diffusion, as well as linear ambient-water entrainment is investigated. It is found that interfacial friction represents a much more efficient mechanism than horizontal diffusion and water entrainment in inducing the eddy decay as well as in damping the eddy pulsations. It is thus suggested that internal wave radiation due to vortex pulsation can represent a relevant mechanism for the dissipation of the vortex energy in a stratified ambient ocean only episodically. Finally, a critical discussion about the appropriateness of the different approximations assumed in the investigation is presented. In particular, the appropriateness of the reduced-gravity assumption is discussed. Results are consistent with those obtained analytically in the frame of the frontal-geostrophic theory: Although the effect of an active ambient layer on the vortex dynamics is found to be virtually absent only for unrealistically large water depths, it appears that the reduced-gravity model describes warm-core eddies acceptably for values of the ratio between maximum vortex thickness and total water depth typical for Gulf Stream rings.

Full access
Angelo Rubino, Sergey Dotsenko, and Peter Brandt

Abstract

For the first time, an analytical theory and a very high-resolution, frontal numerical model, both based on the unsteady, nonlinear, reduced-gravity shallow water equations on a β plane, have been used to investigate aspects of the migration of homogeneous surface, frontal warm-core eddies on a β plane. Under the assumption that, initially, such vortices are surface circular anticyclones of paraboloidal shape and having both radial and azimuthal velocities that are linearly dependent on the radial coordinate (i.e., circular pulsons of the first order), approximate analytical expressions are found that describe the nonstationary trajectories of their centers of mass for an initial stage as well as for a mature stage of their westward migration. In particular, near-inertial oscillations are evident in the initial migration stage, whose amplitude linearly increases with time, as a result of the unbalanced vortex initial state on a β plane. Such an initial amplification of the vortex oscillations is actually found in the first stage of the evolution of warm-core frontal eddies simulated numerically by means of a frontal numerical model initialized using the shape and velocity fields of circular pulsons of the first order. In the numerical simulations, this stage is followed by an adjusted, complex nonstationary state characterized by a noticeable asymmetry in the meridional component of the vortex’s horizontal pressure gradient, which develops to compensate for the variations of the Coriolis parameter with latitude. Accordingly, the location of the simulated vortex’s maximum depth is always found poleward of the location of the simulated vortex’s center of mass. Moreover, during the adjusted stage, near-inertial oscillations emerge that largely deviate from the exactly inertial ones characterizing analytical circular pulsons: a superinertial and a subinertial oscillation in fact appear, and their frequency difference is found to be an increasing function of latitude. A comparison between vortex westward drifts simulated numerically at different latitudes for different vortex radii and pulsation strengths and the corresponding drifts obtained using existing formulas shows that, initially, the simulated vortex drifts correspond to the fastest predicted ones in many realistic cases. As time elapses, however, the development of a β-adjusted vortex structure, together with the effects of numerical dissipation, tend to slow down the simulated vortex drift.

Full access
Peter Brandt, Angelo Rubino, and Jürgen Fischer

Abstract

The analysis of high-resolution oceanographic data referring to velocity measurements carried out by means of a vessel-mounted acoustic Doppler current profiler on 12 November 2000 in the equatorial Atlantic, at 44°W between 4.5° and 6°N, reveals the presence of three large-amplitude internal solitary waves superimposed on the velocity field associated with the North Equatorial Countercurrent (NECC). These waves were found in the deep ocean, more than 500 km off the continental shelf and far from regions of topographic variations. They propagated toward the north-northeast, strongly inclined with respect to the main axis of the NECC and perpendicular to the Brazilian shelf, as well as to the North Brazil Current, and were characterized by maximum horizontal velocities of about 2 m s−1 and maximum vertical velocities of about 20 cm s−1. The large magnitudes of the measured velocities indicate that the observed waves represent disturbances evolving in a strongly stratified ocean. The distance separating the waves (about 70 km) indicates that the observed features cannot be considered as elements of a single train of internal solitary waves. The waves consist, instead, of truly disconnected, pulselike intense solitary disturbances. This behavior, which strongly differs from that typically observed for trains of tidally generated internal solitary waves, indicates that different mechanisms were possibly involved in their generation and/or evolution.

Full access
Vasiliy Vlasenko, Peter Brandt, and Angelo Rubino

Abstract

The horizontal and vertical structure of large-amplitude internal solitary waves propagating in stratified waters on a continental shelf is investigated by analyzing the results of numerical simulations and in situ measurements. Numerical simulations aimed at obtaining stationary, solitary wave solutions of different amplitudes were carried out using a nonstationary model based on the incompressible two-dimensional Euler equations in the frame of the Boussinesq approximation. The numerical solutions, which refer to different density stratifications typical for midlatitude continental shelves, were obtained by letting an initial disturbance evolve according to the numerical model. Several intriguing characteristics of the structure of the simulated large-amplitude internal solitary waves like, for example, wavelength–amplitude and phase speed–amplitude relationship as well as form of the locus of zero horizontal velocity emerge, consistent with those obtained previously using stationary Euler models. The authors’ approach, which tends to exclude unstable oceanic internal solitary waves as they are filtered out during the evolution process, was also employed to perform a detailed comparison between model results and characteristics of large-amplitude internal solitary waves found in high-resolution in situ data acquired north and south of the Strait of Messina, in the Mediterranean Sea. From this comparison the importance of using higher-order theoretical models for a detailed description of large-amplitude internal solitary waves observed in the real ocean emerge. Implications of the results showing the complexity related to a possible inversion of sea surface manifestations of oceanic internal solitary waves into characteristics of the interior ocean dynamics are finally discussed.

Full access
Peter Brandt, Angelo Rubino, Werner Alpers, and Jan O. Backhaus

Abstract

A new numerical two-layer model is presented, which describes the generation of internal tidal bores and their disintegration into internal solitary waves in the Strait of Messina. This model is used to explain observations made by the synthetic aperture radar (SAR) from the European Remote Sensing satellites ERS 1 and ERS 2. The analysis of available ERS 1/2 SAR data of the Strait of Messina and adjacent sea areas show that 1) northward as well as southward propagating internal waves are generated in the Strait of Messina, 2) southward propagating internal waves are observed more frequently than northward propagating internal waves, 3) sea surface manifestations of southward as well as northward propagating internal waves are stronger during periods where a strong seasonal thermocline is known to be present, 4) southward propagating internal bores are released from the sill between 1 and 5 hours after maximum northward tidal flow and northward propagating internal bores are released between 2 and 6 hours after maximum southward tidal flow, and 5) the spatial separation between the first two internal solitary waves of southward propagating wave trains is smaller in the period from July to September than in the period from October to June.

The numerical two-layer model is a composite of two models consisting of 1) a hydrostatic “generation model,” which describes the dynamics of the water masses in the region close to the strait’s sill, where internal bores are generated, and 2) a weakly nonhydrostatic “propagation model,” which describes the dynamics of the water masses outside of the sill region where internal bores may disintegrate into internal solitary waves. Due to a technique for movable lateral boundaries, the generation model is capable of simulating the dynamics of a lower layer that may intersect the bottom topography. The proposed generation–propagation model depends on one space variable only, but it retains several features of a fully three-dimensional model by including a realistic channel depth and a realistic channel width. It is driven by semidiurnal tidal oscillations of the sea level at the two open boundaries of the model domain.

Numerical simulations elucidate several observed characteristics of the internal wave field in the Strait of Messina, such as north–south asymmetry, times of release of the internal bores from the strait’s sill, propagation speeds, and spatial separations between the first two solitary waves of internal wave trains.

Full access
Martin Claus, Richard J. Greatbatch, Peter Brandt, and John M. Toole

Abstract

The equatorial deep jets (EDJs) are a ubiquitous feature of the equatorial oceans; in the Atlantic Ocean, they are the dominant mode of interannual variability of the zonal flow at intermediate depth. On the basis of more than 10 years of moored observations of zonal velocity at 23°W, the vertically propagating EDJs are best described as superimposed oscillations of the 13th to the 23rd baroclinic modes with a dominant oscillation period for all modes of 1650 days. This period is close to the resonance period of the respective gravest equatorial basin mode for the dominant vertical modes 16 and 17. It is argued that since the equatorial basin mode is composed of linear equatorial waves, a linear reduced-gravity model can be employed for each baroclinic mode, driven by spatially homogeneous zonal forcing oscillating with the EDJ period. The fit of the model solutions to observations at 23°W yields a basinwide reconstruction of the EDJs and the associated vertical structure of their forcing. From the resulting vertical profile of mean power input and vertical energy flux on the equator, it follows that the EDJs are locally maintained over a considerable depth range, from 500 to 2500 m, with the maximum power input and vertical energy flux at 1300 m. The strong dissipation closely ties the apparent vertical propagation of energy to the vertical distribution of power input and, together with the EDJs’ prevailing downward phase propagation, requires the phase of the forcing of the EDJs to propagate downward.

Full access