consider t he effects of tiioleculat. difliision. ('onsequcntly t he energy argu~ i i ~ t i t
U ~ C L I b! Turticr ( I W S ) crititiiM be vnlid: iit1 iiltcr~litti~e siitisfiictl)r>
expl;ination of the K i ' l;i\t has not lci heen pro\idcd.
The a h w c result5 indiciite that when the Pcclet number is large and
niolccular diffusion is unimportant llie thickness of the interface is indepen(lent o f thc Richardson nunibcr iit about 1.5 cm. This equilibrium thickness
must result, in ii wiry not yet understood, from a balance between the scouring of the i~~terl'iicc: due to the turbulent eddies and the production of intcrmediate dcnsily lluid by niixing across the intcrfacc. A concept often used to
describe this type of balance when the turbulcnee is produced by shear at the
interface is one of' a critical gradient Richardson number. The appropriate
gradient Richardson number for the geometry of these experiments is
Ri' = g A p / T , ' ~ U ~ ,
where h represents the interface thickness. It is clear from
a n exaniinution of tlie data (see Fig. 5) that Ri'does not remain constant for
a high Pcclct number interface. This fact points to one of the major diffcr.ences hetween these experiments described here and those involving ii mean
shear hetween the layers o n either side of the interface (c.g.. Kato and
Phillips, 1969). It is conceivable that tlie results obtained in the absence of
nicii~i Ilows may bc applied to the case where meiin shears produce turhulcncc due to instability of the interfacc provided thitt the energies of the
turbulcnce in both situatioiis is the same. Howevcr. in the latter case tlic
intcrfricc thickness is also affected by the likelihood of shear instability and
this csscntial feature is missing from the experiments described in this paper.
We rcturn now to the geophysical uxamples cited in the introduction. In
the ciiw o f mixing across an atmospheric inversion or the oceanic thermocline. IypiciiIly Pe 2 10'. At these high values of the Peclet number molecuIirr difliision ciin he neglccted. In the case of oceanic niicrostructure reported
by (ircgg i~nd (.'ox (1972) they reported temperature interfaces of thickness
v;rrying bctwecn 0.8 and 4. I cm (see their Table 2). In the latter case it seems
that niolccular diffusion would be an essential determining feature of the
slructitrc and fluxes across that interface.
One aspcct of pollutant disposal discussed recently by Fischer (1971 ) is
the effect of doublc-diffusion convecticm 011 ScWiige deposited in the sea.
Fischer pointed out that in some circumstances vigorous salt-finger convection could occur. enhancing the vertical spreid of the scwagc cloud. Linden
(1971) discussed the effect of turbulent niotions on siilt-fingcrs and it is
appropriate to mention some of the results in relation to the work discussed
in this pitper. In pnrticulur. Linden showed that the Icngth of the fingcrs
rormed ;it it11 ititcrfiice dccreased i i s the intensity of the turbulcncc i~icreii~ctl
(or cquivalently ;is the Pcclet number o f the motions increased). His nieasurements intlic;rtcd v;tltics of the interfircc thickness. its detcrniined from vcrtical tcinl~cratttrc profiles. very similar to those obtained for it simpie
U ~ C L I b! Turticr ( I W S ) crititiiM be vnlid: iit1 iiltcr~litti~e siitisfiictl)r>
expl;ination of the K i ' l;i\t has not lci heen pro\idcd.
The a h w c result5 indiciite that when the Pcclet number is large and
niolccular diffusion is unimportant llie thickness of the interface is indepen(lent o f thc Richardson nunibcr iit about 1.5 cm. This equilibrium thickness
must result, in ii wiry not yet understood, from a balance between the scouring of the i~~terl'iicc: due to the turbulent eddies and the production of intcrmediate dcnsily lluid by niixing across the intcrfacc. A concept often used to
describe this type of balance when the turbulcnee is produced by shear at the
interface is one of' a critical gradient Richardson number. The appropriate
gradient Richardson number for the geometry of these experiments is
Ri' = g A p / T , ' ~ U ~ ,
where h represents the interface thickness. It is clear from
a n exaniinution of tlie data (see Fig. 5) that Ri'does not remain constant for
a high Pcclct number interface. This fact points to one of the major diffcr.ences hetween these experiments described here and those involving ii mean
shear hetween the layers o n either side of the interface (c.g.. Kato and
Phillips, 1969). It is conceivable that tlie results obtained in the absence of
nicii~i Ilows may bc applied to the case where meiin shears produce turhulcncc due to instability of the interfacc provided thitt the energies of the
turbulcnce in both situatioiis is the same. Howevcr. in the latter case tlic
intcrfricc thickness is also affected by the likelihood of shear instability and
this csscntial feature is missing from the experiments described in this paper.
We rcturn now to the geophysical uxamples cited in the introduction. In
the ciiw o f mixing across an atmospheric inversion or the oceanic thermocline. IypiciiIly Pe 2 10'. At these high values of the Peclet number molecuIirr difliision ciin he neglccted. In the case of oceanic niicrostructure reported
by (ircgg i~nd (.'ox (1972) they reported temperature interfaces of thickness
v;rrying bctwecn 0.8 and 4. I cm (see their Table 2). In the latter case it seems
that niolccular diffusion would be an essential determining feature of the
slructitrc and fluxes across that interface.
One aspcct of pollutant disposal discussed recently by Fischer (1971 ) is
the effect of doublc-diffusion convecticm 011 ScWiige deposited in the sea.
Fischer pointed out that in some circumstances vigorous salt-finger convection could occur. enhancing the vertical spreid of the scwagc cloud. Linden
(1971) discussed the effect of turbulent niotions on siilt-fingcrs and it is
appropriate to mention some of the results in relation to the work discussed
in this pitper. In pnrticulur. Linden showed that the Icngth of the fingcrs
rormed ;it it11 ititcrfiice dccreased i i s the intensity of the turbulcncc i~icreii~ctl
(or cquivalently ;is the Pcclet number o f the motions increased). His nieasurements intlic;rtcd v;tltics of the interfircc thickness. its detcrniined from vcrtical tcinl~cratttrc profiles. very similar to those obtained for it simpie