2.4 Laminar and Thrbulent Flow
33
viscous fluids, the 'layers' of fluid slide smoothly across one another with all
particles moving in an orderly fashion. Such flow when all fluid particles move
very nearly parallel to each other is termed laminar flow.
However, the motion of fluid is seldom orderly. Usually the flow is accompanied by tiny individual particles moving in a highly irregular manner, even
if the fluid, as a whole, appears to travel smoothly in one direction. Intense
small-scale motion in all directions is superimposed on the main large-scale
flow. Wakes extending downstream of islands (Fig. 2.9) or breaking waves
(Fig. 4.17) are examples. These small-scale chaotic motions of fluid are known
as turbulence. The changeover between laminar and turbulent flow is called
the transition to turbulence. Turbulence is essentially a statistical phenomenon.
Descriptions of the overall motion in turbulent flows should not be presumed
to describe the paths of individual particles.
In turbulent flow it is not only momentum that is transferred across the flow
but similarly actual mass moves in directions other than that of the overall flow.
The intensity of the momentum and mass exchange, or intensity of turbulence,
is measured by the 'turbulent viscosity coefficient', which is analogous to the
molecular viscosity, as was mentioned in Sect. 1.2.2. The process of exchange
of momentum and energy in turbulent motion is a cascade from large structures (eddies) through increasingly smaller structures until energy is ultimately
dissipated as heat by the action of viscosity. This pattern has been parodied
in a piece of poetry by meteorologist Richardson (Perry and Walker, 1977):
Big whirls have little whirls
That feed on their velocity;
And little whirls have lesser whirls,
And so on to viscosity.
In the forties, the Russian mathematician Kolmogorov postulated that the
dominant energy balance of the smallest eddies depends on the rate at which
energy cascades down from large-scale motions and the viscosity of the fluid.
The theory of the cascade exchange of turbulence energy and turbulence as
a whole is beyond the scope of this book. The interested reader should consult Monin and Yaglom (1971) or Ozmidov (1986) for an in-depth discussion.
However, some aspects of turbulence, for example, turbulent diffusion and its
significance for life in the ocean, will be discussed in Chap. 8 and 13.
2.4.2 Reynolds Number
We are now back to the fundamental quefltion of how to distinguish between
laminar and turbulent regimes? Since turbulent flow is more prevalent than
laminar flow, turbulence has been observed for centuries, but without any understanding of its nature. However, the abrupt character of the transition
between the two regimes has been recognized for a long time. A basic experiment to understand the nature of the transition phenomenon was conducted by
33
viscous fluids, the 'layers' of fluid slide smoothly across one another with all
particles moving in an orderly fashion. Such flow when all fluid particles move
very nearly parallel to each other is termed laminar flow.
However, the motion of fluid is seldom orderly. Usually the flow is accompanied by tiny individual particles moving in a highly irregular manner, even
if the fluid, as a whole, appears to travel smoothly in one direction. Intense
small-scale motion in all directions is superimposed on the main large-scale
flow. Wakes extending downstream of islands (Fig. 2.9) or breaking waves
(Fig. 4.17) are examples. These small-scale chaotic motions of fluid are known
as turbulence. The changeover between laminar and turbulent flow is called
the transition to turbulence. Turbulence is essentially a statistical phenomenon.
Descriptions of the overall motion in turbulent flows should not be presumed
to describe the paths of individual particles.
In turbulent flow it is not only momentum that is transferred across the flow
but similarly actual mass moves in directions other than that of the overall flow.
The intensity of the momentum and mass exchange, or intensity of turbulence,
is measured by the 'turbulent viscosity coefficient', which is analogous to the
molecular viscosity, as was mentioned in Sect. 1.2.2. The process of exchange
of momentum and energy in turbulent motion is a cascade from large structures (eddies) through increasingly smaller structures until energy is ultimately
dissipated as heat by the action of viscosity. This pattern has been parodied
in a piece of poetry by meteorologist Richardson (Perry and Walker, 1977):
Big whirls have little whirls
That feed on their velocity;
And little whirls have lesser whirls,
And so on to viscosity.
In the forties, the Russian mathematician Kolmogorov postulated that the
dominant energy balance of the smallest eddies depends on the rate at which
energy cascades down from large-scale motions and the viscosity of the fluid.
The theory of the cascade exchange of turbulence energy and turbulence as
a whole is beyond the scope of this book. The interested reader should consult Monin and Yaglom (1971) or Ozmidov (1986) for an in-depth discussion.
However, some aspects of turbulence, for example, turbulent diffusion and its
significance for life in the ocean, will be discussed in Chap. 8 and 13.
2.4.2 Reynolds Number
We are now back to the fundamental quefltion of how to distinguish between
laminar and turbulent regimes? Since turbulent flow is more prevalent than
laminar flow, turbulence has been observed for centuries, but without any understanding of its nature. However, the abrupt character of the transition
between the two regimes has been recognized for a long time. A basic experiment to understand the nature of the transition phenomenon was conducted by