On the role of dissipation in the finite amplitude interactions between forced and free baroclinic waves

1989 ◽  
Vol 45 (1-2) ◽  
pp. 113-130 ◽  
Author(s):  
Terrence R. Nathan
2010 ◽  
Vol 67 (2) ◽  
pp. 434-451 ◽  
Author(s):  
Sukyoung Lee

Abstract A two-layer quasigeostrophic model is used to study the equilibration of baroclinic waves. In this model, if the background flow is relaxed toward a jetlike profile, a finite-amplitude baroclinic wave solution can be realized in both supercritical and subcritical regions of the model’s parameter space. Analyses of the model equations and numerical model calculations indicate that the finite-amplitude wave equilibration hinges on the breaking of Rossby waves before they reach their critical latitude. This “jetward” wave breaking results in an increase in the upper-layer wave generation and a reduction in the vertical phase tilt. This change in the phase tilt has a substantial impact on the Ekman pumping, as it weakens the damping on the lower-layer wave for some parameter settings and enables the Ekman pumping to serve as a source of wave growth at other settings. Together, these processes can account for the O(1)-amplitude wave equilibration. From a potential vorticity (PV) perspective, the wave breaking reduces the meridional scale of the upper-layer eddy PV flux, which destabilizes the mean flow. This is followed by a strengthening of the lower-layer eddy PV flux, which weakens the lower-layer PV gradient and constrains the growth of the lower-layer eddy PV. The same jetward wave breaking focuses the upper-layer PV flux toward the jet center where the upper-layer PV gradient is greatest. This results in an intensification of the upper-layer eddy PV relative to lower-layer eddy PV. Because of this large ratio, the upper-layer eddy PV plays the primary role in inducing the upper- and lower-layer eddy streamfunction fields, decreasing the vertical phase tilt. As a result, the Ekman pumping on the eddies is weakened, and for some parameter settings the Ekman pumping can even act as a wave source, contributing toward O(1)-amplitude wave equilibration. By reducing the horizontal shear of the zonal wind, the same wave breaking process weakens the barotropic decay, which also contributes to the wave amplification.


2014 ◽  
Vol 2 (1) ◽  
pp. 309-321 ◽  
Author(s):  
T. D. Price ◽  
B. G. Ruessink ◽  
B. Castelle

Abstract. Subtidal sandbars often exhibit alongshore variable patterns, such as crescentic plan shapes and rip channels. While the initial formation of these patterns is reasonably well understood, the morphodynamic mechanisms underlying their subsequent finite-amplitude behaviour have been examined far less extensively. This behaviour concerns, among other aspects, the coupling of alongshore variable patterns in an inner bar to similar patterns in a more seaward bar, and the destruction of crescentic patterns. This review aims to present the current state of knowledge on the finite-amplitude behaviour of crescentic sandbars, with a focus on morphological coupling in double sandbar systems. In this context we include results from our recent study, based on a combination of remote-sensing observations, numerical modelling and data–model integration. Morphological coupling is an inherent property of double sandbar systems, where the inner bar may attain a type of morphology not found in single bar systems. Coupling is governed by water depth variability along the outer-bar crest and by various wave characteristics, including the offshore wave height and angle of incidence. In recent research, the role of the angle of wave incidence for sandbar morphodynamics has received more attention. Numerical modelling results have demonstrated that the angle of wave incidence is crucial to the flow pattern, sediment transport, and thus the emerging morphology of the coupled inner bar. Moreover, crescentic patterns predominantly vanish under high-angle wave conditions, highlighting the role of alongshore currents in straightening sandbars and challenging the traditional conception that crescentic patterns vanish under high-energy, erosive wave conditions only.


2014 ◽  
Vol 24 (02) ◽  
pp. 1450019 ◽  
Author(s):  
Ricardo Chacón

The extent of chaos and the suppressory role of Coulomb repulsion in the chaotic dynamics associated with nonsteady finite-amplitude electroconvection is revisited in the context of dynamical systems. Specifically, it is theoretically demonstrated that the threshold value of the charge density taming the heteroclinic chaos associated with laminar chaotic mixing depends on the sinusoidal perturbation's frequency of the fluid velocity field, which is at variance with the fixed threshold value previously reported [Chacón et al., 1994]. Additionally, the consideration of time-periodic multiharmonic perturbations reveals the great complexity of the chaotic mixing scenario.


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