Chapter 5
SPATIALLY-VARYING AND COHERENT
STRUCTURES
The upper ocean boundary layer is turbulent but not completely
random…
5. SPATIALLY-VARYING AND COHERENT
STRUCTURES
5.1 Introduction
The upper ocean is turbulent, in other words chaotic, because the
Reynolds number is large. This chaos may include organized, so-called
coherent structures.
In the presence of stochastic fluctuations and nonlinear interactions,
quasi-stationary and stable states having an ordered structure can be formed
naturally (Nicolas and Prigogine, 1977). Self–organization occurs in a
variety of nonlinear dissipative systems; the formation of life may be
regarded as one example of such a process.
Kraichnan (1967), Rhines (1975), Hasegawa (1985) and others
developed the self-organization conjecture for hydrodynamic systems.
Important common features of these systems are as follows: The system
should contain more than one quadratic or higher-order conserved quantity
in the absence of dissipation; when the dissipation is introduced, there exists
a selective dissipation process among the conserved quantities, that is one
conserved quantity decays faster than the other(s); and finally, the nature of
the mode coupling through the nonlinear term(s) in the equation is such that
SPATIALLY-VARYING AND COHERENT
STRUCTURES
The upper ocean boundary layer is turbulent but not completely
random…
5. SPATIALLY-VARYING AND COHERENT
STRUCTURES
5.1 Introduction
The upper ocean is turbulent, in other words chaotic, because the
Reynolds number is large. This chaos may include organized, so-called
coherent structures.
In the presence of stochastic fluctuations and nonlinear interactions,
quasi-stationary and stable states having an ordered structure can be formed
naturally (Nicolas and Prigogine, 1977). Self–organization occurs in a
variety of nonlinear dissipative systems; the formation of life may be
regarded as one example of such a process.
Kraichnan (1967), Rhines (1975), Hasegawa (1985) and others
developed the self-organization conjecture for hydrodynamic systems.
Important common features of these systems are as follows: The system
should contain more than one quadratic or higher-order conserved quantity
in the absence of dissipation; when the dissipation is introduced, there exists
a selective dissipation process among the conserved quantities, that is one
conserved quantity decays faster than the other(s); and finally, the nature of
the mode coupling through the nonlinear term(s) in the equation is such that