Search Results

You are looking at 1 - 10 of 23 items for

  • Author or Editor: Peter Brandt x
  • 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
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
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

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
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
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
Katrin Hessner, Angelo Rubino, Peter Brandt, and Werner Alpers

Abstract

The dynamics of the Rhine outflow plume in the proximity of the river mouth is investigated by using remote sensing data and numerical simulations. The remote sensing data consist of 41 synthetic aperture radar (SAR) images acquired by the First and Second European Remote Sensing satellites ERS-1 and ERS-2 over the outflow region of the river Rhine. Most of them show sea surface signatures of oceanic phenomena, for example, surface current and wind variations, ship wakes, and oil slicks. In particular, in 36 of these images pronounced frontal features are visible as narrow zones of mainly enhanced, sometimes enhanced/reduced radar backscatter that can be associated with the Rhine surface front. Within the area enclosed by the frontal line, large zones characterized by a lower radar backscatter than in the outer area are often visible. The analysis of the ERS SAR images suggests that the form and the location of the frontal features are mainly linked to the semidiurnal tidal phase in the outflow region, although their variability suggests also that they weakly depend on river discharge, residual currents, and neap-spring tidal cycle. In order to test this observational hypothesis, the results obtained from the analysis of the ERS SAR images are compared with the results obtained from the numerical simulation of the hydrodynamics of the Rhine outflow region carried out using a two-layer, frontal model, which is based on the nonlinear, hydrostatic shallow-water equations on an f plane. The model is forced by prescribing tidal and residual currents and river discharge at the open boundaries. Several simulations are performed by varying the values of these forcing parameters. The numerical results corroborate the observational conjecture: It is found that the form and the location of the simulated interface outcropping lines in the proximity of the river mouth are mainly determined by the semidiurnal tidal phase in the outflow region and that river discharge, residual currents, and neap-spring tidal cycle contribute only secondarily to their determination. Inserting the simulated surface velocity field into a simple radar-imaging model that relates the modulation of the backscattered radar power to the surface velocity convergence in radar look direction, narrow, elongated bands of enhanced radar backscatter emerge near the model frontal line while patches of low radar backscatter appear within the simulated Rhine plume area. The consistency of the model results with the results obtained from the analysis of the SAR images enables one to infer a mean spatial and temporal evolution of the Rhine outflow plume over a semidiurnal tidal cycle from the analysis of spaceborne SAR images acquired during different tidal cycles over the Rhine outflow area and suggests the possibility of using numerical modeling, in conjunction with the analysis of spaceborne measurements, for monitoring the oceanic variability in the Rhine outflow area.

Full access
Franz Philip Tuchen, Peter Brandt, Martin Claus, and Rebecca Hummels

Abstract

Besides the zonal flow that dominates the seasonal and long-term variability in the equatorial Atlantic, energetic intraseasonal meridional velocity fluctuations are observed in large parts of the water column. We use 15 years of partly full-depth velocity data from an equatorial mooring at 23°W to investigate intraseasonal variability and specifically the downward propagation of intraseasonal energy from the near-surface into the deep ocean. Between 20 and 50 m, intraseasonal variability at 23°W peaks at periods between 30 and 40 days. It is associated with westward-propagating tropical instability waves, which undergo an annual intensification in August. At deeper levels down to about 2000 m considerable intraseasonal energy is still observed. A frequency–vertical mode decomposition reveals that meridional velocity fluctuations are more energetic than the zonal ones for periods < 50 days. The energy peak at 30–40 days and at vertical modes 2–5 excludes equatorial Rossby waves and suggests Yanai waves to be associated with the observed intraseasonal energy. Yanai waves that are considered to be generated by tropical instability waves propagate their energy from the near-surface west of 23°W downward and eastward to eventually reach the mooring location. The distribution of intraseasonal energy at the mooring position depends largely on the dominant frequency and the time, depth, and longitude of excitation, while the dominant vertical mode of the Yanai waves plays only a minor role. Observations also show the presence of weaker intraseasonal variability at 23°W below 2000 m that cannot be associated with tropical instability waves.

Full access