Instability and nonlinear evolution of a density-driven coastal current with a surface front in a two-layer ocean
作者:
Atsushi Kubokawa,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1988)
卷期:
Volume 40,
issue 3-4
页码: 195-223
ISSN:0309-1929
年代: 1988
DOI:10.1080/03091928808208825
出版商: Taylor & Francis Group
关键词: Coastal current;front;nonlinear wave dynamics;stability
数据来源: Taylor
摘要:
Coupled equations describing the nonlinear evolution of a disturbance in a two-layer coastal current with a surface front are derived by assuming that the alongshore scale of the disturbance is much longer than the current width, the lower layer is much thicker than the upper layer and the potential vorticity in the upper layer is zero. Linear stability and the characteristics of the cnoidal wave and soliton solutions governed by these equations are examined analytically, and the nonlinear evolution of disturbance is discussed using numerical methods. The main results are as follows. (1) The current is linearly stable when the current speed is greater than a certain critical value. (2) Even in such a situation, there is no stable nonlinear solution whose amplitude lies between certain critical values,acanda′c, which are functions of the wavelength and the basic flow speed. (3) A solitary disturbance whose amplitude lies betweenacanda′cgrows with an eddy-pair-like structure in the lower layer. After its amplitude exceedsa′c, a soliton with a large amplitude separates from the eddy-pair-like structure and propagates by itself. (4) In the linearly unstable case, a wave-like perturbation with small amplitude grows. However, this unstable mode does not grow indefinitely but reaches a maximum amplitude, having exceeded the critical amplitude,a′c. Its amplitude then oscillates with time. (5) When several unstable waves have been given as the initial condition, the unstable waves interact nonlinearly with each other and solitary disturbances are produced. These solitary disturbances also repeat the growth and decay, and a turbulence-like phenomenon occurs.
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