Forced Rossby Wave Research Articles

Wind-Driven Fluctuating Western Boundary Currents

Abstract In this paper a linear theory for the barotropic large-scale current fluctuations at midlatitudes driven by fluctuating winds is presented. It is based on both numerical and analytical arguments and provides an extention of the steady Munk’s theory of the wind-driven circulation to the case of a time-dependent wind forcing. The numerical resolution of a circulation model forced by an idealized oscillatory wind in a box leads to two distinct ranges for the oceanic fluctuating response. The first one is Rossby wavelike and westward intensified, with a width of the western boundary layer decreasing with increasing eddy viscosity AH. For sufficiently high values of the latter, a second range arises in which the wavelike character disappears and the boundary layer width increases with AH. To explain this behavior an analytical expression is proposed for the first (linear inertial–viscous) range in terms of an appropriate superposition of damped forced Rossby waves. Such expression provides also a leng...

Forced Rossby wave packets in barotropic shear flows with critical layers

In this paper, we investigate the meridional propagation of a forced Rossby wave packet towards a critical layer in a zonal shear flow by solving the linearized barotropic vorticity equation. The forcing is applied north of the critical layer. Two approaches are employed for solving this problem. First, an analytic solution valid for large time is derived, using Fourier and Laplace transform techniques and asymptotic approximations. This solution exhibits the modification due to the wave packet of the solution obtained by Warn and Warn (1976) [Warn, T., Warn H., 1976. On the development of a Rossby wave critical level. J. Atmos. Sci., 33, 2021–2024.] in the monochromatic case. A numerical investigation is then carried out using a finite difference scheme and a time-dependent radiation condition. It is found that the forced wave packet is absorbed at the critical layer and the total momentum transferred to the mean flow as a result of the absorption is observed to be proportional to the length scale of the wave packet. We also consider the case of a north–south mean flow with a longitudinally propagating wave packet forced to the east or west of the critical layer. The monochromatic version of this problem has been used before (Geisler, J.E., Dickinson, R.E., 1975. Critical level absorption of barotropic Rossby waves in a north–south flow. J. Geophys. Res., 80, 3805–3811.) to examine the interaction of western boundary currents and oceanic Rossby waves.

Dynamics of vorticity defects in shear

Matched asymptotic expansions are used to obtain a reduced description of the nonlinear and viscous evolution of small, localized vorticity defects embedded in a Couette flow. This vorticity defect approximation is similar to the Vlasov equation, and to other reduced descriptions used to study forced Rossby wave critical layers and their secondary instabilities. The linear stability theory of the vorticity defect approximation is developed in a concise and complete form. The dispersion relations for the normal modes of both inviscid and viscous defects are obtained explicitly. The Nyquist method is used to obtain necessary and sufficient conditions for instability, and to understand qualitatively how changes in the basic state alter the stability properties. The linear initial value problem is solved explicitly with Laplace transforms; the resulting solutions exhibit the transient growth and eventual decay of the streamfunction associated with the continuous spectrum. The expansion scheme can be generalized to handle vorticity defects in non-Couette, but monotonic, velocity profiles.

Links between Tropical Convection and Variations of the Extratropical Circulation during TOGA COARE

Data from the Intensive Observation Period of the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (November 1992-February 1993) have been used to investigate the links between intraseasonal variations in tropical convection and those in forcing of upper-tropospheric Rossby waves in the extratropics. The primary databases are Geostationary Meteorological Satellite imagery and tropical wind analyses from the Bureau of Meteorology, Australia. A number of 5-day periods showing convection in different locations were chosen. For each period, mean fields of divergence, cloud-top temperature, and upper-tropospheric Rossby wave source are presented. Vorticity budgets are used to demonstrate the processes responsible for the Rossby wave source patterns. The approach follows earlier studies of links between interannual variations of tropical convection associated with the Southern Oscillation and variations of the extratropical circulation. It is shown that the regions of tropical convection correspond to longitudinally localized Hadley cells. In the subtropics, at the higher-latitude end of each cell, there is a Rossby wave source dipole with anticyclonic and cyclonic forcing. The anticyclonic forcing of Rossby waves is associated with advection of vorticity by the divergent outflow, while the cyclonic forcing is due to the region of convergence immediately above the downward branch of the local Hadley cell. Hence, the authors provide a dynamical basis for tropical-midlatitude interactions associated with intraseasonal variations of tropical convection.

Response of the Zonally Asymmetric Flow to Time-Dependent Tropical Heating

Abstract An atmospheric general circulation model is used to study the impact of idealized zonally propagating tropical heating anomalies on the low-frequency variability in the North Pacific region. The propagating heating is designed to mimic the thermal forcing associated with the Madden–Julian oscillation (MJO). Results are examined by separating the forced response from other variability and by comparing with runs employing fixed-phase (stationary) heating anomalies. For both the forced and free circulations, the main modes of variability consist of a zonal expansion and retraction of the East Asian jet. The effective Rossby wave forcing associated with the heating is dominated by the advection term and located in the subtropics in the regions of strong absolute vorticity gradients. Compared with cases using stationary forcing, the response to the propagating forcing is weaker and of different phase, indicating that the 40-day period used for the propagating anomalies is too short to allow the develo...

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect. The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode ...

An Observational and Numerical Study of Blocking Episodes near South America

Abstract European Centre for Medium-range Weather Forecasts analyses during June 1985 are used to characterize the flow in the South America sector during a typical blocking episode. Numerical experiments are performed using a hemispheric shallow-water model to test whether such blocking episodes can be a result of local resonance between forced Rossby waves generated by the Andes Mountains and by an upstream forcing. It appears that while blocks generated in the Atlantic Ocean may respond to this mechanism from the beginning, the more frequency ones that develop from a ridge that advances from the Pacific Ocean may also benefit from it in the intensification and maintenance stages.

順圧大気における強制ロスビー波の非線型的な振舞い第1部強制ロスビー波の安定性

A barotropic quasi-geostrophic inviscid β-plane channel model with simple surface topography is constructed to investigate the nonlinear temporal behavior of forced Rossby waves. In particular, an emphasis is placed on the consequent evolution of forced Rossby waves due to growing unstable perturbations, in connection with the wave amplification observed during the blocking and the sudden warming.This paper consists of two parts: In Part I, we investigate linear stability properties of forced Rossby waves. The presence of surface topography is found to have a significant effect to destabilize the basic flow. When the forced Rossby wave has the largest horizontal scale, the flow becomes unstable and produces two kinds of instabilities: One is the topographic instability for the superresonant flow and the other is for the subresonant flow. The former, which can be represented in a loworder model of Charney and DeVore (1979), produces a standing type perturbation characterized by the form-drag through topography, while the latter, which cannot be represented in the low-order model, is characterized by the interaction between wave components of the perturbation and the basic forced Rossby wave. With the decrease of the zonal flow speed, the horizontal scale of the perturbation becomes smaller, as is expected from the necessary condition for instability.It is also found that the topographic instability does not appear when the meridional wavenumber of the forced Rossby wave is even.

On the Three-Dimensional Propagation of Stationary Waves

Abstract A locally applicable (nonzonally-averaged) conservation relation is derived for quasi-geostrophic stationary waves on a zonal flow, a generalization of the Eliassen-Palm relation. The flux which appears in this relation constitutes, it is argued, a useful diagnostic of the three-dimensional propagation of stationary wave activity. This is illustrated by application to a simple theoretical model of a forced Rossby wave train and to a Northern Hemisphere winter climatology. Results of the latter procedure suggest that the major forcing of the stationary wave field derives from the orographic effects of the Tibetan plateau and from nonorographic effects (diabatic heating and/or interaction with transient eddies) in the western North Atlantic and North Pacific Oceans and Siberia. No evidence is found in the data for wave trains of tropical origin; forcing by the orographic effects of the Rocky mountains seems to be of secondary importance.

Critical levels for forced Rossby and continental shelf waves

The generation of waves on a geostrophic shear flow by a travelling forcing pattern is considered. The model describes both atmospheric Rossby waves on a zonal shear flow and continental shelf waves on a boundary current. By means of the Laplace transform technique, the development of the solution in time is studied, starting from some initial instant when the forcing starts. The asymptotic form of the forced solution is shown to depend crucially upon whether the speed of the travelling forcing lies inside the range of the current or not. The possible application of the results to the Florida current is discussed.

Numerical Study of an Interacting Rossby Wave and Barotropic Zonal Flow Near a Critical Level

This paper treats the initial value problem of a forced Rossby wave encountering a critical level in a barotropic zonal shear flow which can change in response to the wave momentum flux divergence. The main result of the calculation is that the shape of the zonal flow profile changes with time in such a way as to reduce the potential vorticity gradient (β−Uyy) to zero at the critical level. For this configuration the wave is totally reflected at the critical level and in the absence of dissipation no longer interacts with the zonal flow. Details of the evolution toward the steady state depend on the ratio of two time scales, one a measure of the wave amplitude and the other representing the time it takes for the wave momentum flux to be concentrated in a well-defined critical layer. The steady-state balance between wave and mean flow probably never occurs in the atmosphere because the time required to set it up is long compared to the expected time scale of natural variability of the zonal flow. More relevant to atmospheric flows is the fact that excursions of (β−Uyy) to negative values during the approach to a steady state are attended by over reflection of the incident wave and a temporary reversal of the wave momentum flux. After the first of these excursions, occurring on a time scale comparable to that required to set up a critical layer, the zonal flow is never far from the final equilibrium profile.