Abstract

A semiempirical model of midlatitude sea surface height (SSH) variability is formulated and tested against two decades of weekly global fields of merged altimeter data. The model is constrained to match approximately the observed SSH wavenumber power spectrum, but it predicts the spatiotemporal SSH field structure as a propagating, damped, linear response to a stochastic forcing field. An objective, coherent-eddy identification and tracking procedure is applied to the model and altimeter SSH fields, with a focus on eddies with lifetimes L ≥ 16 weeks. The model eddy dataset reproduces the basic global-mean characteristics of the altimeter eddy dataset, including the structure of mean amplitude and scale life cycles, the number distributions versus lifetime, and the distributions of all eddy length scale realizations. The model underpredicts the numbers of eddy realizations with large amplitudes and large scales, overpredicts the growth of mean amplitude and scale with lifetime, and modestly overpredicts the curvature of the mean amplitude life cycle and the number of eddies with intermediate lifetimes. The stochastic forcing evidently represents nonlinear dynamical interactions, implying that eddy splitting and merging events are equally likely, and that mesoscale nonlinearity is weaker than longwave linearity but as strong as shortwave dispersion. The time-reversal symmetry of the life cycles is explained by the time reversibility of the underlying stochastic model. The random SSH increment processes are effectively continuous on the derived 25-week damping time scale, with SSH-increment standard deviation σ _W ≈ 2.5 × 10⁻³ cm s^−1/2.

Abstract

A statistical-equilibrium, geostrophic-turbulence regime of the stochastically forced, one-layer, reduced-gravity, quasigeostrophic model is identified in which the numerical solutions are representative of global mean, midlatitude, open-ocean mesoscale variability. Solutions are forced near the internal deformation wavenumber and damped linearly and by high-wavenumber enstrophy dissipation. The results partially rationalize a recent semiempirical stochastic field model of mesoscale variability motivated by a global eddy identification and tracking analysis of two decades of satellite altimeter sea surface height (SSH) observations. Comparisons of model results with observed SSH variance, autocorrelation, eddy, and spectral statistics place constraints on the model parameters. A nominal best fit is obtained for a dimensional SSH stochastic-forcing variance production rate of 1/4 cm² day⁻¹, an SSH damping rate of 1/62 week⁻¹, and a stochastic forcing autocorrelation time scale near or greater than 1 week. This ocean mesoscale regime is nonlinear and appears to fall near the stochastic limit, at which wave-mean interaction is just strong enough to begin to reduce the local mesoscale variance production, but is still weak relative to the overall nonlinearity. Comparison of linearly inverted wavenumber–frequency spectra shows that a strong effect of nonlinearity, the removal of energy from the resonant linear wave field, is resolved by the gridded altimeter SSH data. These inversions further suggest a possible signature in the merged altimeter SSH dataset of signal propagation characteristics from the objective analysis procedure.

Abstract

Measurements of surface wind stress by the SeaWinds scatterometer on NASA's Quick Scatterometer (QuikSCAT) satellite are analyzed and compared with several different atmospheric model products, from an operational model and two high-resolution nested regional models, during two summer periods, June through September 2000 and 2001, in the coastal region west of Oregon and northern California. The mean summer wind stress had a southward component over the entire region in both years. Orographic intensifications of both the mean and fluctuating wind stress occurred near Cape Blanco, Cape Mendocino, and Point Arena. Substantial differences between the model products are found for the mean, variable, and diurnal wind stress fields. Temporal correlations with the QuikSCAT observations are highest for the operational model, and are not improved by either nested model. The highest-resolution nested model most accurately reproduced the mean observed stress fields, but slightly degrades the temporal correlations due to incoherent high-frequency (0.5–2 cpd) fluctuations. The QuikSCAT data reveal surprisingly strong diurnal fluctuations that extend offshore 150 km or more with magnitudes that are a significant fraction of the mean wind stress. Wind stress curl fields from QuikSCAT and the models show local cyclonic and anticyclonic maxima associated with the orographic wind intensification around the capes. The present results are consistent with the hypothesis of a wind-driven mechanism for coastal jet separation and cold water plume and anticyclonic eddy formation in the California Current System south of Cape Blanco.

Abstract

The long-term evolution of initially Gaussian eddies is studied in a reduced-gravity shallow-water model using both linear and nonlinear quasigeostrophic theory in an attempt to understand westward-propagating mesoscale eddies observed and tracked by satellite altimetry. By examining both isolated eddies and a large basin seeded with eddies with statistical characteristics consistent with those of observed eddies, it is shown that long-term eddy coherence and the zonal wavenumber–frequency power spectral density are best matched by the nonlinear model. Individual characteristics of the eddies including amplitude decay, horizontal length scale decay, and zonal and meridional propagation speed of a previously unrecognized quasi-stable state are examined. The results show that the meridional deflections from purely westward flow (poleward for cyclones and equatorward for anticyclones) are consistent with satellite observations. Examination of the fluid transport properties of the eddies shows that an inner core of the eddy, defined by the zero relative vorticity contour, contains only fluid from the eddy origin, whereas a surrounding outer ring contains a mixture of ambient fluid from throughout the eddy’s lifetime.

Abstract

The effects of wind-forced upwelling and downwelling on the continental shelf off Duck, North Carolina, are studied through experiments with a two-dimensional numerical primitive equation model. Moored and shipboard measurements obtained during August–November 1994 as part of the Coastal Ocean Processes (CoOP) Inner Shelf Study (ISS) are used for model–data comparisons. The model is initialized with realistic stratification and forced with observed wind and heat flux data. Both strongly stratified and weakly stratified conditions, found during August and October, respectively, are studied. August is characterized by fluctuating alongshelf wind direction, and October is dominated by downwelling-favorable winds. The across-shelf momentum balance is primarily geostrophic on the continental shelf. The alongshelf momentum balance is mainly between the Coriolis force and vertical diffusion with additional contributions from the local acceleration and nonlinear advection terms. The model solutions are utilized to acquire detailed information on the time- and space-dependent variability of the across-shelf circulation and transport and to investigate the dependence of this circulation on the seasonal change in stratification. When the stratification breaks down, as in October, the across-shelf transport is reduced significantly in comparison with the theoretical Ekman transport for large wind stress values. The paths of individual model water parcels are traced using two methods: calculation of Lagrangian trajectories and time evolution of three Lagrangian label fields. The August period produces complex Lagrangian dynamics because of the switching between upwelling and downwelling winds. The October period illustrates a mean downwelling response that advects parcels across and along the shelf and vertically.

Abstract

A two-dimensional, frictionless, nonlinear model of coastal upwelling is reexamined. The model has been solved previously at steady state and as an initial-value problem. The previous solution to the initial-value problem is inconsistent with the steady-state solution. A new solution to the spinup problem is presented that approaches the existing steady-state solution. In the new solution, a surface equatorward jet develops more rapidly than a poleward undercurrent, but the surface jet is of limited strength so that the undercurrent velocity eventually surpasses that of the surface flow. Consideration of dimensional scales implies that the magnitude of the wind stress determines how quickly steady state is approached but does not affect the steady-state fields. Exact solutions found with an arbitrary alongshore pressure gradient imply that there is no poleward flow without a poleward pressure gradient.

Abstract

An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model. In ventilated thermocline theory, the western pool is a region bounded on the east by subsurface streamlines that outcrop at the western edge of the interior, and in which additional dynamical assumptions are necessary to complete the solution. Solutions for the western pool were originally obtained under the assumption that the potential vorticity of the subsurface layer was homogenized. In the present theory, it is instead assumed that all of the water in the pool region is ventilated and, therefore, that all the Sverdrup transport is carried in the uppermost, outcropping layer. The result is the formation of a deep, vertically homogeneous, fluid layer in the northwest corner of the subtropical gyre that extends from the surface to the base of the ventilated thermocline. This ventilated pool is an analog of the observed subtropical mode waters. The pool also has the interesting properties that it determines its own boundaries and affects the global potential vorticity–pressure relationship. When there are multiple outcropping layers, ventilated pool fluid is subducted to form a set of nested annuli in ventilated, subsurface layers, which are the deepest subducted layers in the ventilated thermocline.

Abstract

A mesoscale atmospheric model is used to address the characteristics of stratified flow bounded by a side wall along a varying coastline. Initial Froude number values are varied through alteration of marine inversion strength, permitting examination of supercritical, subcritical, and transcritical flow regimes encountering several coastal configurations. Consistent with shallow water models, sharp drops in boundary layer depth and flow acceleration occur in flow rounding convex bends; however, significant flow response occurs in the stratified layer aloft, which is unexplained by conventional shallow water theory. The strongest flow acceleration occurs in the transcritical case while, regardless of inversion strength, the deformation of the isentropes aloft shows general structural similarity.

Advection of horizontal momentum is an important component of the horizontal force balance. A simulation having several coastline bends exhibits a detached, oblique hydraulic jump upwind of a concave bend that strongly blocks the flow. For the single-bend case, a shallow water similarity theory for stratified flow provides qualitative, and partial quantitative, agreement with the mesoscale model, in the boundary layer and aloft. Horizontal structure functions for these similarity solutions satisfy a set of equivalent shallow water equations. This comparison provides a new perspective on previous shallow water models of supercritical flow around coastal bends and suggests that the existence of the supercritical flow response may depend more on the presence of a low-level jet than on a sharp boundary layer inversion.

Abstract

The linear stability of a nearly time-periodic, nonlinear, coastal upwelling–downwelling circulation, over alongshore-uniform topography, driven by a time-periodic wind stress is investigated using numerical methods. The near-periodic alongshore-uniform basic flow is obtained by forcing a primitive equation numerical model of coastal ocean circulation with periodic wind stress. Disturbance growth on this near-periodic flow is explored in linear and nonlinear model simulations. Numerous growing normal modes are found in the linear analyses at alongshore scales between 4 and 24 km. These modes vary in cross-shore structure and timing of maximum disturbance growth rate. One group of modes, in the 6.5–8.5-km alongshore-scale range, bears strong resemblance to the ensemble average disturbance structures observed in perturbed nonlinear model simulations. These modes are of a mixed type, exhibiting both strong baroclinic and barotropic energy exchange mechanisms, with maximum disturbance growth occurring during the transition from upwelling favorable to downwelling favorable winds. Nonlinear disturbance growth is characterized by similar structures at these same scales, but with significant exchange of energy between disturbances at different alongshore scales, such that overall disturbance energy accumulates at the longest (domain) scales, and gradually propagates offshore mainly in the pycnocline over numerous forcing cycles.

Abstract

Nonlinear model simulations of a coastal upwelling system show frontal instabilities that initiate at short alongshore scales but rapidly evolve to longer wavelengths. Several factors associated with the nonstationarity of this basic state contribute to the progression in scale. A portion of the system evolution is associated with the external forcing. Another portion is associated with the alteration of the alongshore mean flow resulting from wave growth. Direct interactions between the finite-amplitude disturbances also promote emergence of new scales. The relative role of each of these mechanisms is isolated through tangent linear simulations about basic states that approximate the nonlinear system to differing degrees. The basic states include an alongshore uniform time-evolving upwelling solution, the alongshore average of a three-dimensionally evolving upwelling solution, and the full three-dimensional nonlinear solution. Disturbance growth about a frozen-field upwelling state is also examined. Perturbation experiments are performed for persistent and relaxed wind forcing. Although the frontal disturbances in the nonlinear model exhibit a progression to larger scale over the full range of forcing scenarios considered, the mechanisms most responsible for the process differ between wind-forced and unforced cases. Under relaxed wind conditions, the perturbation growth experiments indicate that the scale evolution over the first four days is reflected in the way linear disturbances respond to the adjustment of an alongshore uniform upwelling front to wind cessation. The continued increase in scale between days 4 and 7 is related to the linear disturbance evolution on the alongshore average of a flow state that has been altered by wave–mean flow interaction. Past day 7, the observed scale change is not captured in the linear growth experiments and evidently results largely from nonlinear wave–wave interaction processes. Under sustained upwelling winds, the linear growth experiments fail to describe even the earliest scale change in the nonlinear solutions, indicating that nonlinear wave–wave effects are significant from very near the start of the simulations.