Benoit Cushman-Roisin

Westward Motion of Mesoscale Eddies

Abstract Since the pioneering work of Nof, the determination of the westward drift of mesoscale eddies under the planetary (beta) effect has been a recurrent theme in mesoscale oceanography, and several different formulae have been proposed in the literature. Here, recpatiulation is sought, and, within the confines of a single-layer model, a generalized formula is derived. Although it is similar to Nofs, the present formula is established from a modified definition and with fewer assumptions. It also recaptiulates all other formulae for the one-layer model and applies to a wide variety of situations, including cases when the vortex develops a wake of Rossby waves or undergoes axismmetrization. Following the derivation of the formula, a physical interpretation clarifies the migration mechanism, which can be divided between a self-induced propulsion and a reaction from the displaced ambient fluid. Numerical simulations with primitive and geostrophic equations validate the formula for a variety of length sc...

Northern Adriatic Response to a Wintertime Bora Wind Event

During winters, the northern Adriatic Sea experiences frequent, intense cold-air outbreaks that drive oceanic heat loss and imprint complex but predictable patterns in the underlying waters. This strong, reliable forcing makes this region an excellent laboratory for observational and numerical investigations of air-sea interaction, sediment and biological transport, and mesoscale wind-driven flow. Narrow sea surface wind jets, commonly known as “bora,” occur when cold, dry air spills through gaps in the Dinaric Alps (the mountain range situated along the Adriatics eastern shore). Horizontal variations in these winds drive a mosaic of oceanic cyclonic and anticyclonic cells that draw coastal waters far into the middle basin. The winds also drive intense cooling and overturning, producing a sharp front between dense, vertically homogenous waters (North Adriatic Dense Water, or NAdDW) in the north and the lighter (colder, fresher), stratified waters of the Po River plume. Once subducted at the front, the NAdDW flows southward in a narrow vein following the isobaths (contours of constant depth) of the Italian coast. In addition to governing the basins general circulation, these processes also influence sediment transport and modulate biological and optical variability

SOLUTION OF THE MILD-SLOPE WAVE PROBLEM BY ITERATION

Iterative solution procedures for solving the complete mild-slope wave (combined refractiondiffraction) equation are developed. Existing models for investigating wave refraction-diffraction in coastal areas have one of two main problems: (i) Some of the physics is lost as they resort to approximate solutions (e.g. parabolic approximations). Thus they are inappropriate in many situations. (ii) If all of the physics is to be incorporated, the problem defies computer solution except for extremely small domains (approximately 10 wavelengths), chiefly because the matrix equation associated with numerical discretization of the complete problem does not normally lend itself to solution by iteration. This paper describes the construction of iterative models that overcome both problems. First, a modified equation with an identical solution but which lends itself to iterative procedures is formulated, and the conjugate gradient method is used. A second, more rapidly converging algorithm is obtained by preconditioning. It is shown that the algorithms can be conveniently implemented on regions much larger than those handled by conventional models, without compromising the physics of the equation. Further, they can be efficiently run in either the linear or nonlinear mode. Comparisons of model results with laboratory data and other numerical and analytical solutions are found to be excellent for several cases. The procedures thus enable the engineer to expand the scope of the mild-slope equation. As an example, an experiment is performed to demonstrate the sensitivity of the wavefield to the location of a breakwater in a region with complex bathymetry.

Frontal Geostrophic Dynamics

Abstract From the primitive equations simplified dynamics are derived that apply to frontal situations in which interface slopes are important. The formalism, which eliminates inertial motions, is not Unlike the derivation of the quasi-geostrophic equation. The difference is two-fold: while quasi-geostrophic dynamics apply for length scales on the order of the deformation radius with limitation to small interface variations, frontal geostrophic dynamics apply for finite interface variations but only at length scales large compared to the deformation radius (three or more times). When the length scale is on the order of the deformation radius and, simultaneously, the interface variations are finite, inertial oscillations cannot be filtered out, and the primitive equations ought to be retained. In a reduced-gravity context, frontal geostrophic dynamics yield a single equation for the upper-layer depth. Although this equation is cubic in the depth variable, it is nonetheless considerably simpler than the pri...

A 3D finite-element model of the Adriatic tides

A 3D finite-element numerical model is applied to the Adriatic Sea to simulate its tidal motions. This fully nonlinear model includes a free surface, very realistic topography, and an advanced turbulence closure. Comparison with available tidal elevations at coastal stations and with tidal ellipses at a few locations in the open sea demonstrates that the model simulations are highly accurate. The results are then used to determine the 3D distribution of the tidal residual currents. D 2002 Published by Elsevier Science B.V.

Tidal dynamics in the northern Adriatic Sea

Tides in the northern Adriatic Sea are investigated using two distinct numerical models. First, a two-dimensional (2-D) finite difference model is implemented with very high horizontal resolution (556 m) to simulate the northern Adriatic. After calibration of open boundary conditions the model gives very satisfactory results: The averaged vectorial difference between observed and simulated elevations is <1.3 cm for each of the seven major tidal constituents. Next, a 3-D finite element model is applied to the entire sea in order to provide a better simulation of the tidal currents in the vicinity of the open boundary of the first model. Results show that the northern Adriatic behaves like a narrow rotating channel in which the instantaneous sea surface elevation (SSE) contours are aligned with the depth-averaged velocity vectors and in which the SSE is always higher to the right of the local current. These features emphasize the rotational character that tides can exhibit in a relatively small basin. Wave fitting to the current elevation structure shows that semidiurnal tidal constituents are well represented with a system of two frictionless Kelvin waves (incident and reflected). In contrast, the diurnal constituents are best described as a topographic wave propagating across, not along, the basin, from the Croatian coast to the Italian shore. Despite this obvious disparity the semidiurnal and diurnal tides can be understood as distinct members of a single family of linear waves, which exist under the combined actions of gravity and topography.

On the Influence of a Lower Layer on the Propagation of Nonlinear Oceanic Eddies

Abstract The one-layer, reduced-gravity, also called equivalent-barotropic, model has been widely used in countless applications. Although its validity is based on the assumption that a second, lower layer is sufficiently deep to be dynamically inactive, the question of how deep that second layer ought to be has not yet received thorough examination. When one considers the importance of the two processes excluded from the reduced-gravity model, namely barotropic motion and baroclinic instability, the conventional choice of a second layer much deeper than the first might be too simplistic. A scaling analysis aimed at covering all two-layer regimes, geostrophic as well as ageostrophic, leads to a double criterion, requiring that the total depth of fluid be much larger than either of two values. These values, resulting from f-plane and β-plane dynamics, apply to the shorter and longer scales, respectively. A number of numerical experiments on the propagation of eddies on the β-plane with various eddy radii a...

A General Theory for Equivalent Barotropic Thin Jets

Abstract The so-called thin-jet approximation, in which variations along the jet axis are assumed gradual in comparison with variations normal to the axis, allows the calculations of along- and cross-axis structures to be decoupled. The result is a nonlinear equation, with one lesser spatial dimension, governing the meandering of the jet. Here a new such “path equation” is constructed in the context of a one-layer, reduced-gravity model. The formalism retains two distinct physical processes: a vortex-induction mechanism, originating from the jet curvature, that causes meanders to travel downstream (i.e., usually eastward), and the planetary (beta) effect, induced by meridional displacements, that gives the meanders the allure of Rossby waves and generates a westward (i.e., usually upstream) propagation. After a brief comparison with previous path equations, analytical solutions of the new equation are explored, including solitons and other exact nonlinear wave forms. The presentation concludes with numeri...

Two-Layer Geostrophic Dynamics. Part I: Governing Equations

Abstract Although the quasigeostrophic formalism has been a cornerstone in oceanographic modeling for over four decades, studies have shown time and time again that other geostrophic, but non-quasigeostrophic, regimes can also exist. These include a particular class of regimes representative of oceanic fronts and frontal eddies. The task undertaken here is the clarification and investigation of the possible geostrophic regimes, quasigeostrophic and otherwise, of a two-layer mean. To simplify the analysis, attention is restricted to a system on the midlatitude beta plane, above a flat bottom and below a rigid lid. Under the assumption of a small Rossby number, geostrophic regimes are sought, and the set of primitive equations is reduced to two prognostic equations, one for each of the barotropic and baroclinic pressure fields. These equations share with the quasigeostrophic equations the absence of inertia-gravity waves, but their greater range of validity allows order-one variations in the upper-layer dep...

Northern Adriatic Sea

The northern Adriatic Sea is the northernmost region of the Mediterranean Sea, extending as far North as 45°47′N and bounded by the Italian peninsula to the West and the Balkans to the East (Figure 5–1). It is a shallow sub-basin of the Adriatic whose southern open boundary is arbitrarily taken as the 100-m isobath, approximately located North of 43°20′N. The northern and western coasts of the northern Adriatic are generally sandy, and the nearby land is flat (alluvial plains). In contrast, the eastern coast is rugged and mountainous, including numerous islands, inlets, bays and coves. Note that only the open northern Adriatic is considered in this chapter, excluding the waters enclosed by the northern Croatian islands (e.g., Rijeka Bay), which are discussed in section 6.3 of this book.