Low-Frequency Basin Modes in a Two-Layer Quasigeostrophic Model in the Presence of a Mean Gyre Flow* (original) (raw)
Related papers
Journal of Marine Research, 2010
Using a fully-implicit high-resolution two-layer quasi-geostrophic model combined with pseudoarclength continuation methods, we perform a bifurcation analysis of double-gyre ocean flows to study their initial oscillatory instabilities. In this model, both wind-and thermally-forced flows can be represented. We demonstrate that on the branch of anti-symmetric steady-state solutions the ratio, Ω, of the flow advective speed to the long internal Rossby wave speed determines the type of oscillatory modes to first become unstable. This is the same nondimensional parameter that controls the shape of the geostrophic contours in the linear limit of the circulation. For large values of Ω, the first Hopf bifurcations correspond to the classical baroclinic modes with inter-monthly time periods arising from shear instability of the flow. For small values of Ω, the first Hopf bifurcations correspond instead to barotropic Rossby modes with shorter, monthly periods arising from mixed barotropic-baroclinic instability of the flow. By considering both a wind-forced and a thermally-forced ocean, we show that this is a robust feature that does not depend on the type of forcing driving the circulation. 215 216
Basin-Mode Interactions and Selection by the Mean Flow in a Reduced-Gravity Quasigeostrophic Model
Journal of Physical Oceanography, 2003
The selection mechanisms of Rossby basin modes are investigated in the reduced-gravity quasigeostrophic framework. The linear solution of the wind-driven circulation is decomposed in a steady forced-dissipated solution and a time-dependent component. The steady solution consists in a classical Sverdrup flow dissipated in a thin western boundary layer. The time-dependent solution is a sum of Rossby basin modes with arbitrary amplitudes. The effect of the nonlinear term is handled through a weakly nonlinear analysis providing a set of evolution equations for the mode amplitudes. It is shown both analytically (infinite Burger number) and numerically (finite Burger number) that mode stability is related to the gyre configuration. For cyclonic or anticyclonic single gyres, all basin modes are neutral. In the traditional (reversed) double-gyre case, large-scale basin modes are damped (unstable). Pure basin-mode interactions yield triads with cycling energy and subharmonic instabilities. The latter provide a potential mechanism for spectral reddening.
On turbulence and normal modes in a basin
Journal of Marine Research, 2002
The problem of forced, geostrophicturbulence in a basin is revisited. The primary focus is the time dependent eld, which is shown to be approximately isotropic (in contrast to the strongly zonally anisotropic elds seen in periodic domains). It is also approximately homogeneous, away from the boundaries. Phenomenologicalarguments suggest the isotropy occurs because the inverse cascade of energy is arrested by basin normal modes rather than by free Rossby waves. Peaks in the velocity spectra at modal frequencies are consistent with basin modes, as has been noted previously. We discuss which modes would be excited and whether dissipation or the mean ow would be expected to alter the modes and their frequencies. A relatively novel feature is the use of Eulerian velocity statistics to quantify the wave and turbulence characteristics. These measures are more suitable to this environment than measures like wavenumber spectra, given the inhomogeneities associated with the boundaries. With regards to the mean, we observe a linear^q& 2^c& relation in the region of the mean gyres (at the northern and southern boundaries), consistent with previous theories. This is of interest because our numerical advection scheme has implicit rather than explicit small scale dissipation, and requires no boundary conditions on the vorticity. The gyre structure is however somewhat different than in an (inviscid) Fofonoff-type solution, suggesting dissipation cannot be neglected.
Baroclinic Rossby Waves in Irregular Basins*
Journal of Physical Oceanography, 2002
The properties of baroclinic, quasigeostrophic Rossby basin waves are examined. Full analytical solutions are derived to elucidate the response in irregular basins, specifically in a (horizontally) tilted rectangular basin and in a circular one. When the basin is much larger than the (internal) deformation radius, the basin mode properties depend profoundly on whether one allows the streamfunction to oscillate at the boundary or not, as has been shown previously. With boundary oscillations, modes occur that have low frequencies and, with scale-selective dissipation, decay at a rate less than or equal to that of the imposed dissipation. These modes approximately satisfy the long-wave equation in the interior. Using both unforced and forced solutions, the variation of the response with basin geometry and dissipation is documented. The long-wave modes obtain with scale-selective dissipation, but also with damping that acts equally at all scales. One finds evidence of them as well in the forced response, even when the dissipation is weak and the corresponding free modes are apparently absent.
The Instability of Rossby Basin Modes and the Oceanic Eddy Field*
Journal of Physical Oceanography, 2004
have isolated a new class of basin modes particularly resistant to dissipation mechanisms that preferentially damp small scales, such as the type employed by Qiu (1997). While basin modes typically require the synthesis of long Rossby waves with westward propagating group velocity and short Rossby waves with eastward group velocity, these new modes closely resemble free, long Rossby waves with zonal wavelengths that are integral multiples of the basin width. Such
On the dynamics of quasi-geostrophic intergyre gyres
Nuovo Cimento C, 2003
An important aspect of the present climatic change concerns the wind-stress anomalies over the ocean. It is possible to associate to them a special current field, which appears between the subtropical and the subpolar gyres and is known as intergyre gyre. In the present paper we investigate its dynamics by including recent models of stochastic wind field into the classical model of ocean circulation at the basin scale of Rhines and Young. In the framework of an analytical approach, developed at the geostrophic level of approximation, we explore the circulation patterns of this recently discovered characteristic of double gyres. PACS 92.10.Fj -Dynamics of the upper ocean. ( * ) Presently at
On Quasigeostrophic Normal Modes in Ocean Models: Weakly Nonseparable Situation
Journal of Physical Oceanography, 2004
This study examines quasigeostrophic Rossby eigenmodes of homogeneous as well as stratified oceans. Analytical studies of Rossby basin modes are usually done by using simple basin geometries. Simple means that solutions are available by applying a separation ansatz in looking for basin modes. Here the focus is on halftrapezoidal geometry, in particular on a stratified ocean with a half-trapezoidal (zonal) cross section. In this case, separation is not possible. However, approximate solutions can be found. Different approximations are discussed: one related to linearization of the boundary conditions, one related to a sight change in boundary geometry, and one that uses an asymptotic expansion. It is shown that the widely used ''linearized boundary conditions'' give wrong results for low-frequency modes. The reason is that weak asymmetries of the basin are neglected and wave energy is therefore distributed too homogeneously in the basin. Although the basin's geometry used deviates only slightly from a square and the eigenvalue spectrum corresponds well with that of a square basin, eigenmodes can still differ greatly.
Dynamics of Atmospheres and Oceans, 1992
The exchange of fluid mass between quasi-geostrophie and ageostrophic motions during the reflection of Rossby waves from a coast. I. The case of an infinite rectilinear coast. Dyn. Atmos. Oceans, 16: 305-329. When the problem of the reflection of spatially localized Rossby waves from a coast is treated using the quasigeostrophic (QG) approximation, the total fluid mass and the along-shore circulation calculated from the geostrophic height field are not conserved. To understand the correct mass balance and the degree to which the QG equations and boundary conditions may be in error, we analyze an initial-value problem for the Laplace tidal equations on a t-plane in the asymptotic fimit c ~ 1, where ~ is the ratio of the spatial scale of the motion to the Earth's radius. It is shown that there is a coupling between QG and O(c) fields. Physically, the coupfing occurs by a peculiar adjustment process in the O(c) approximation in which' fast gravity waves are permanently generated to build up a quasi-stationary edge Kelvin wave. Different temporal scales (large for O(1) Rossby waves and small for the 0(c) gravity waves make comparable the contributions of the waves to the mass and circulation balance equations. However, QG analysis itself describes the reflection of Rossby waves correctly, but is incomplete, and for satisfactory balances one has to take into account the fields of both orders of the approximation. Applications of the results to closed basins, baroclinicity, and variable bottom topography are discussed. It is conjectured that an interaction of strong oceanic eddies with a coast (continental slope) may give rise to noticeable along-shore jet currents.
Baroclinic and barotropic aspects of the wind-driven ocean circulation
Physica D: Nonlinear Phenomena, 2002
The double-gyre circulation induced by a symmetric wind-stress pattern in a quasi-geostrophic model of the mid-latitude ocean is studied analytically and numerically. The model is discretized vertically by projection onto normal modes of the mean stratification. Within its horizontally rectangular domain, the numerical model captures the wind-driven circulation's three dynamic regimes: (1) a basin-scale double-gyre circulation, cyclonic in the basin's northern part and anticyclonic in the south, which is dominated by Sverdrup balance; (2) a swift western boundary current in either gyre, with dissipation most important near the coast and inertial balance further out; and (3) a strong recirculating dipole near the intersection of the western boundary with the symmetry line of zero wind-stress curl. The flow inside this stationary dipole is highly nonlinear, and equivalent-barotropic. An analytical solution to the potential vorticity equation with variable stratification describes the dipole, and fits well the full numerical model's steady-state solutions. Changes in the numerical model's solutions are investigated systematically as a function of changes in the strength of the wind stress τ and the Rossby radius of deformation L R. The main changes occur in the recirculation region, while the basin-scale gyres and the western boundary currents are affected but little. A unique symmetric dipole is observed for small τ , and agrees in its properties with the analytical solution. As τ increases, multiple asymmetric equilibria arise due to pitchfork bifurcation and are stable for large enough L R. The numerically obtained asymmetric equilibria also agree in their main properties with the analytical ones, as well as with the corresponding solutions of a shallow-water model. Increasing τ further results in two successive Hopf bifurcations, that lead to limit cycles with periods near 10 and 1 years, respectively. Both oscillatory instabilities have a strong baroclinic component. Above a certain threshold in τ the solutions become chaotic. Flow pattern evolution in this chaotic regime resembles qualitatively the circulation found in the Gulf Stream and Kuroshio current systems after their separation from the continent.