Glenn R. Flierl

New development in the MOCNESS, an apparatus for sampling zooplankton and micronekton

Four variants of the Multiple Opening/Closing Net and Environmental Sensing System (MOCNESS) have been constructed to sample a broad size spectrum of oceanic animals from microzooplankton to micronekton. The systems differ in mouth opening dimensions (ranging from 1/4 to 20 m2), the number of nets carried (from 5 to 20), and the mesh size of the netting (from 64 μm to 3.0 mm). A new electronics package enables an operator to send commands down a single conductor, armored cable to open/close the nets and provides 12-bit resolution for the environmental (temperature, depth, conductivity) and net operation data (flow, net-frame angle, net-bar release), which are transmitted up the cable to the deck unit at 2-s intervals. A microcomputer system, interfaced to the deck unit, calculates salinity, volume filtered by a net, net trajectory velocity, and vertical velocity. The data are printed out and stored on disc, and profiles of temperature and salinity versus depth are plotted during the course of the tow. Analysis of the relationship between the geometry of the MOCNESS under tow and the past and present methods used to estimate the water filtered by a net revealed that significant bias is introduced when the ascent or descent angle of a net is disregarded. The bias is a function of the ratio of vertical velocity to net trajectory velocity and results in an underestimate of volume filtered while shooting a net and an overestimate while hauling.

On the Evolution of Isolated, Nonlinear Vortices

Abstract The evolution of an isolated, axially symmetric vortex is calculated with a quasi-geostrophic, adiabatic, hydrostatic. β-plane, two vertical mode model. The circumstances of greatest interest are those of weak friction and large vortex amplitude (strong nonlinearity). Systematic studies are made of the consequences of varying the frictional coefficient, the vortex amplitude, the vortex radius (relative to the deformation radius), the degree of nonlinear coupling between the two vertical modes and the initial vertical structure of the vortex. Results of note include the following. Within the approximation of a single vertical mode model (i.e., in the absence of modal coupling), a baroclinic vortex has an increased westward and a finite meridional propagation speed when its amplitude is greater than infinitesimal. Both of these speeds, however, are limited by the wave speeds (as determined from infinitesimal amplitude theory) of the weak dispersion field outside the vortex. The vortex amplitude dec...

THE DYNAMICS OF BAROCLINIC AND BAROTROPIC SOLITARY EDDIES

Abstract We derive exact nonlinear solutions to the inviscid quasigeostrophic two-layer equations. The solutions represent isolated eddies with an amplitude that decays rapidly away from the eddy. They translate steadily either to the east (if there is a barotropic component in the fringes of the eddy) or either to the east or rapidly to the west (if the exterior field has only a baroclinic mode structure). They are strong in the sense that all of the fluid within a finite radius from the center is carried along with the eddy as it translates. The solutions have a characteristic north-south antisymmetry with the nonlinear vortex pair interactions being an essential feature of the dynamics. However, we also show that radially symmetric perturbations of a special form but arbitrary amplitude can be superimposed on the basic solutions; thus the antisymmetric structure may to some extent be masked. We show nondimensional dispersion relationships: atmospheric and oceanic planetary wave phenomena do fall in the range of parameters where theory predicts solitary eddy solutions can exist.

Behavior of a simple plankton model with food-level acclimation by herbivores

The acclimation of herbivores to variation in their phytoplankton food source was expressed mathematically and its effect on phytoplankton, herbivore and nutrient cycles explored with a plankton model. The grazing formulation is a modified version of the function experimentally determined by Mayzaud and Poulet. Their function differs from the traditional Ivlev expression for herbivore grazing in that there is no asymptotic limit to the grazing rate. The steady-state solutions of the phytoplankton-herbivorenutrient model were similar with the two grazing formulations, but the time-dependent behaviour of the two models differed markedly. The model with Ivlev grazing showed oscillations when the grazing pressure was high. The model with acclimated herbivore grazing showed only small, highly damped oscillations as it approached steady state. The latter is more similar to the evolution of plankton trophic levels observed in controlled ecosystem experiments.

Particle motions in large-amplitude wave fields

Abstract We calculate the trajectories of particles in two-dimensional model flows typifying atmospheric or oceanic eddy motions. Rather than restricting the flows to be weak (but solutions to the relevant dynamics), we have considered motions where the streamfunction is only a kinematic model resembling the actual flows but the amplitude can be large so that flow speeds can greatly exceed the phase speed. For steadily propagating disturbances, there is an equivalent one-dimensional Lagrangian motion problem and we have applied results from analyses of such to periodic channel waves and isolated circular eddies. We show that the mean Lagrangian drift rate in periodic channel waves is very sensitive to the initial position and may be either prograde or retrograde. Large volumes of the fluid may be “trapped” to translate along with the wave. The wave drift depends on the phase velocity relative to the Eulerian mean flow and peaks at about 1/3 of the transient Eulerian speed at geophysically relevant amplitu...

On the instability of geostrophic vortices

The instabilities of barotropic and baroclinic, quasi-geostrophic, f -plane, circular vortices are found using a linearized contour dynamics model. We model the vortex using a circular region of horizontally uniform potential vorticity surrounded by an annulus of uniform, but different, potential vorticity. We concentrate mostly upon isolated vortices with no circulation in the basic state outside the outer radius b . In addition to linear analyses, we also consider weakly nonlinear waves. The amplitude equation has a cubic nonlinearity and, depending upon the sign of the coefficient of the cubic term, may give nonlinear stabilization or nonlinear enhancement of the growth. Barotropic isolated eddies are unstable when the outer annulus is narrow enough; on the other hand, if the scale of the whole vortex is sufficiently small compared to the radius of deformation of a baroclinic mode, the break up may be preferentially to a depth-varying disturbance corresponding to a twisting and tilting of the vortex. As the vortex becomes more baroclinic, we find that large-scale vortices show an elliptical mode baroclinic instability as well which is relatively insensitive to the scale of the outer annulus. When the baroclinic currents in the basic state dominate, the twisting mode disappears, and we see only the instabilities associated with either strong enough shear in the annular region or sufficiently large vortices compared with the deformation radius. The finite amplitude results show that the baroclinic instability mode for large enough vortices is nonlinearly stabilized while in most cases, the other two kinds of instability are nonlinearly destabilized.

The physical significance of modons: Laboratory experiments and general integral constraints

A barotropic jet emerging from a point source in a rotating fluid is deflected to the right (northern hemisphere) and starts to accumulate in an anticyclonic vortex. This gives rise to a cyclonic neighbor, and the dipole (modon) then propagates away from the source in a circular path. A modification of Batchelors (1967) solution, which takes into account the different strenghts of the anticyclonic-cyclonic pair, is able to account for the path curvature. The experiment shows that highly organized modons can be realized in the laboratory with rather nondescript forcing. The s-effect (not noticeably present in the experiment) should enhance the realizability of these structures in geophysical flows. Therefore, it is suggested that the modon model captures certain essential features of geophysical eddies. This is based on a derived theorem which shows that any slowly varying (not necessarily uniformly propagating) and isolated disturbance on the beta plane must have zero net relative angular momentum, so that the dipole is the simplest dynamically consistent representation of such a disturbance. Some interesting aspects of two-dimensional turbulence in a rotating fluid are also indicated by the laboratory esperiments and by the general integral theorems presented.

Models of vertical structure and the calibration of two-layer models

Methods of calibration layer models (choosing the adjustable parameters defifining the layer depths and density steps) are presented. The radii of deformation, the surface and bottom amplitudes of the vertical normal modes and the depth-averaged triple products of the modes are the important functionals of the stratification which determine the behavior of the system. We show how these can be matched to the equivalent two-layer model functions of the density step e and upper-layer depth H 1 in three different physical situations: time-dependent wind forcing, bottom slope or friction influences, and nonlinear interactions. In each physical situation we illustrate two different choices of which characteristics of the behavior to match and make quantitative comparisons with a continuously stratified model with the stratification derived from oceanic data. These examples show that the optimal calibrations are very different in the three physical situations; i.e., any single choice of e and H 1 will inevitably lead to serious errors in predicting the behavior in at least two of the three physical situations. This inaccuracy may lead to serious qualitative misbehavior of a two-layer model in a situation where two or more physical processes are competing (e.g., bottom topography and nonlinearity). We propose a two-mode model (of the same computational simplicity) which does not suffer from this problem, but is optimally calibrated in all three physical situations without changes in the parameters. In addition, it offers the advantages of being automatically calibrated by the specification of the mean continuous density profile and being readily applied to oceanic data of all kinds.

Rossby Wave Radiation from a Strongly Nonlinear Warm Eddy

Abstract One of the serious flaws in the standard quasi-geostrophic equations, commonly used for understanding the evolution of mesoscale eddies, is the requirement that the change in thickness between density surfaces must be small compared to the mean thickness. In the case of warm core rings, the thickness of the thermostadt layer may range from 500 m at the center to zero at the edge. Yet the prediction of the evolution of such features should be vastly simplified by noting that there is a dominant equilibrium balance of forces in the fluid, with the beta effect and the time derivatives being relatively small. In this paper, the author presents the nonquasi-geostrophic model for the evolution of a warm core ring using a two-layer fluid in which the upper layer has a finite volume so that the interface surfaces on a basically circular boundary. The lowest order flow in the warm pool is much faster than the Rossby wave speeds βL2 and is not geostrophic but rather is assumed to be in a state of cyclostro...

NUMERICAL STUDIES OF BAROTROPIC MODONS

Abstract Numerical solutions of barotropic modons are examined to assess the accuracy with which they can be calculated, their behavior under the influence of dissipation, and their resistance to perturbations.