TRANSPORT OF HEAT ACROSS A PLANE
TURBULENT MIXING LAYER'
1. INTRODUCTION
It is a well-known characteristic of turbulent shear flows that the spread of
scalar quantities, i.e., heat or matter, is faster than the spread of momentum.
The turbulent Prandtl number PrT = E,,,/+ conventionally used in describing this phenomenon is therefore 0.5 S Pr, I 1.0, with q,, and being the
diffusivities of momentum and of scalar quantities, rcspectively. The upper
and lower limits of the Prandtl number are matched by Prandtl's mixing
length hypothesis or Taylor's vorticity transport hypothesis, respectively. In
reality, however, the Prandtl number has neither the same value for different
flows nor for different locations within a single flow. This behaviour is not
yet fully understood; it seems, however, to exclude the possibility of identical
transport mechanisms for momentum and scalar quantities.
More recent conceptions, originating from T o d s concepts of bulk
convection transfer and of a double structure of tutbukacx are therefore
based on the ideas of different transfer mechanisms and of a strong
significance of the intermittent structure of the tbw at fme boundaries (see
Townsend, 1956; Yen, 1967; Mayer and Divoky, 1966; Tyldesley, 1969).
The experimental investigation reported here Q aimed at finding a model
for the transport mechanism of a scalar quantity in typical turbulent shear
flows. As a first configuration the twodimensbnai shear layer was chosen
for the following reasons:
(a) Its velocity structure is well known (Wygnanski and Fiedler, 1970).
(b) Self-preservation is attained at an early stage.
(c) Heat-transfer measurements have not been reported previously.
(d) This flow has constant boundary values.
In the present state of the investigation measurements of the temperature
field alone have been obtained. For more detailed and specific information
' This work was supported by Deutschc Forschungsgemsinilhaft.
93
TURBULENT MIXING LAYER'
1. INTRODUCTION
It is a well-known characteristic of turbulent shear flows that the spread of
scalar quantities, i.e., heat or matter, is faster than the spread of momentum.
The turbulent Prandtl number PrT = E,,,/+ conventionally used in describing this phenomenon is therefore 0.5 S Pr, I 1.0, with q,, and being the
diffusivities of momentum and of scalar quantities, rcspectively. The upper
and lower limits of the Prandtl number are matched by Prandtl's mixing
length hypothesis or Taylor's vorticity transport hypothesis, respectively. In
reality, however, the Prandtl number has neither the same value for different
flows nor for different locations within a single flow. This behaviour is not
yet fully understood; it seems, however, to exclude the possibility of identical
transport mechanisms for momentum and scalar quantities.
More recent conceptions, originating from T o d s concepts of bulk
convection transfer and of a double structure of tutbukacx are therefore
based on the ideas of different transfer mechanisms and of a strong
significance of the intermittent structure of the tbw at fme boundaries (see
Townsend, 1956; Yen, 1967; Mayer and Divoky, 1966; Tyldesley, 1969).
The experimental investigation reported here Q aimed at finding a model
for the transport mechanism of a scalar quantity in typical turbulent shear
flows. As a first configuration the twodimensbnai shear layer was chosen
for the following reasons:
(a) Its velocity structure is well known (Wygnanski and Fiedler, 1970).
(b) Self-preservation is attained at an early stage.
(c) Heat-transfer measurements have not been reported previously.
(d) This flow has constant boundary values.
In the present state of the investigation measurements of the temperature
field alone have been obtained. For more detailed and specific information
' This work was supported by Deutschc Forschungsgemsinilhaft.
93