44 I
The work described above was essentiitlly motivated by the meisurernents
of the entr;tinnicnt rate ;icross ;I density interface made by Turner (1968)
which showed that fluid was entrained at different rates depending on
whether the density step was produced by heat or salt. The two nondimensional parameters describing the turbulent flow (ignoring molecular viscosity) viz the Peclet number Pe = i d h and the Richardson number
R i = g Ap / / p i t z both depend on the turbulent velocity if in such a way that
higher is Ri associated with lower Pe. Thus the divergence in the entrainment rates found by Turner (1968) at high Ri occurs when the P e c k number
for the salt interface is much larger than the Peclet number for the heat
in terfacc.
The structure of the intcrfacc shows why the observed entrainment rates
should differ at high Ri. At high values of Pe it was found that the thickness
of the interfacc remained constant (and independent of Ri) at about 1.5 cm;
we shall describe this interface as dynamically “ t h i n ” in that eddies in one
layer were observed to penetrate through the interface and interact directly
with Huid in the other Iaycr. At low values of Pe ( 5 200) the interface was
‘.thick ’‘ with the eddies not penetrating to the centre of the interface. In this
latter case wc conclude that the centre of the interface consists of a diffusive
core which prwides a tlux, by molecular diffusion alone, which balances the
entrainment tlux from the edges of the interface into the turbulent layers. On
the other hand. whcn the interface is thin it is not possible to provide a large
enough flux by diffusion and mechanical breakdown with direct mixing of
fluid from each layer must occur.
The conclusion that a thick interfacc contains a diffusive core is supported
by two observations. First. estimates of the flux by diffusion along the gradient in the core showed that this was comparable to the observed fluxes into
the well-mixed layers. Second, the gradient in the centre of the interface
itlwiiys aci.jt~stcd very quickly when the interface changed in thickness implying ;I balance bctwccn the diffusive iind entrainment fluxes; this is in contrast
to thc salt interfitcc where the originnl gradient could be maintained in the
interior o f the intcrfwe for a considerable pcriod of time.
At high 1% when thc interfacc is thin, und mechanical breakdown of the
interface is required to produce the required amount of entrainment. it
would seem reasonable t o attempt to explain the entrainment process in
tcrms of incrlial processes ignoring the effccts of diffusion. A mcchanistic
e~plit1iati011 along these lines has been provi,ded by Linden ( 1973) which
accounts for the observed Ri
mixing rate. At lower values of Pe ( 5 900)
the eddies can no longer penetrate through the interface and it is essential to
,’
The work described above was essentiitlly motivated by the meisurernents
of the entr;tinnicnt rate ;icross ;I density interface made by Turner (1968)
which showed that fluid was entrained at different rates depending on
whether the density step was produced by heat or salt. The two nondimensional parameters describing the turbulent flow (ignoring molecular viscosity) viz the Peclet number Pe = i d h and the Richardson number
R i = g Ap / / p i t z both depend on the turbulent velocity if in such a way that
higher is Ri associated with lower Pe. Thus the divergence in the entrainment rates found by Turner (1968) at high Ri occurs when the P e c k number
for the salt interface is much larger than the Peclet number for the heat
in terfacc.
The structure of the intcrfacc shows why the observed entrainment rates
should differ at high Ri. At high values of Pe it was found that the thickness
of the interfacc remained constant (and independent of Ri) at about 1.5 cm;
we shall describe this interface as dynamically “ t h i n ” in that eddies in one
layer were observed to penetrate through the interface and interact directly
with Huid in the other Iaycr. At low values of Pe ( 5 200) the interface was
‘.thick ’‘ with the eddies not penetrating to the centre of the interface. In this
latter case wc conclude that the centre of the interface consists of a diffusive
core which prwides a tlux, by molecular diffusion alone, which balances the
entrainment tlux from the edges of the interface into the turbulent layers. On
the other hand. whcn the interface is thin it is not possible to provide a large
enough flux by diffusion and mechanical breakdown with direct mixing of
fluid from each layer must occur.
The conclusion that a thick interfacc contains a diffusive core is supported
by two observations. First. estimates of the flux by diffusion along the gradient in the core showed that this was comparable to the observed fluxes into
the well-mixed layers. Second, the gradient in the centre of the interface
itlwiiys aci.jt~stcd very quickly when the interface changed in thickness implying ;I balance bctwccn the diffusive iind entrainment fluxes; this is in contrast
to thc salt interfitcc where the originnl gradient could be maintained in the
interior o f the intcrfwe for a considerable pcriod of time.
At high 1% when thc interfacc is thin, und mechanical breakdown of the
interface is required to produce the required amount of entrainment. it
would seem reasonable t o attempt to explain the entrainment process in
tcrms of incrlial processes ignoring the effccts of diffusion. A mcchanistic
e~plit1iati011 along these lines has been provi,ded by Linden ( 1973) which
accounts for the observed Ri
mixing rate. At lower values of Pe ( 5 900)
the eddies can no longer penetrate through the interface and it is essential to
,’