iniposed o i i ;I density interfiicc. ‘1 h i s method o f production of turbulcncc is
c o i i i c i i i c i i ~ I ) c u t i w I I ;illoiis tlie properties 01 itic ~urhulciicl: i111rl tlic intcrhcc to I>c set iirclcpl:iidciit iil’one iitit)thcr. Thcrc .ire, o i i the other hand, LWO
d r ; i \ t I w L lir\t tlic prcqx,rtics of rlic rurbulcncc i i i ; ~ ) lw rclatcd t u tlic
4pcci;il gc*onictr>~ of the tank aild grids ;tiid second. t he experiments iire not
coniplcIclq stciiclj. I l o ~ c \ . c I .
wo will see Ihiit these drawbacks do not appear
to he ni;iJor iind are certainly inconseqiizntial whcn compared with tlic
cciiivenicncc o f tlic cxpcritiiental arrangement.
The ~ ~ t c
ilt which h i d is entrained iicross the intcrfacc has been mei+surcd
hy Turner (196H). (We Iiave uscd the 5iiiiic expcritncntal arrangement a s
Turner s o that our rcsults may be compared with his.) He found that the rate
of entrainment is reduced as the stithility of the interface increased. A nieasure of this stability can be given in terms of a Richardson number
Ri = (1 A p / ; ~ I I ‘ . whcrc II and I arc the velocity and lcngth scale of‘ the
turbulent motions ncar tho interface, and Ap/p is the fractional density step
hctwceii the two layers. Turner consicicred two cast‘s in detiiil: first when ttic
density step was produced by ; I temperature step iind second when it was
produced by salinity difference hetween the layers. He expressed his results
in thc lorni
u, I I I R i . ’ ’ (salt).
whcrc II,. is I he rate of cntrainmcnt (defined as the amount of fluid entrained,
unit :ircaiunit time). Turncr further noted that ( I ) is equivalent to assuming
I11iit rhc rate of change of potential energy due to the mixing is proportional
10 tlic riitc o f kinetic energy production by the grid, and then discussed the
possiihlc rcils(btis for Ills reduced s i i h tritnsporl at Iiirge Ri.
(‘Iciirly the main ditlcrcnce between the two situations described hy ( I )
aiid ( 2 ) is that tlie coefficient of 111olcculitr diffusion of heat is much larger
I hi111 the corresponding coefficient for salt. The appropriate nondimcnsionul
piir;imctcr which dcscrihcs the cflect of molecular diffusion is the Peclet
numhcr Pc = I I / / K . I n terms of this parameter ( 1 ) is the entrainment riltc for
Pc L- O( 10‘) while (2) is for the case Pe = O( lo4).
In this paper we l o o k at the detailed structure of a density interface for ;I
range of Ri and Pc covcring essentially the same values as those itppropri;itc
to ‘Turner’s (196%) experiments. We tind that for the lower values (if Pc
molecular diffusion plays an essential role in determining tlic structurc of tlic
interface and that the energy iirgument given by Turner (196%). which ncglccts all diffusive effects. is not correct. The consequences of thc results ToI
1 Iic gcophysicill situations mentioned above are then discusscd.
c o i i i c i i i c i i ~ I ) c u t i w I I ;illoiis tlie properties 01 itic ~urhulciicl: i111rl tlic intcrhcc to I>c set iirclcpl:iidciit iil’one iitit)thcr. Thcrc .ire, o i i the other hand, LWO
d r ; i \ t I w L lir\t tlic prcqx,rtics of rlic rurbulcncc i i i ; ~ ) lw rclatcd t u tlic
4pcci;il gc*onictr>~ of the tank aild grids ;tiid second. t he experiments iire not
coniplcIclq stciiclj. I l o ~ c \ . c I .
wo will see Ihiit these drawbacks do not appear
to he ni;iJor iind are certainly inconseqiizntial whcn compared with tlic
cciiivenicncc o f tlic cxpcritiiental arrangement.
The ~ ~ t c
ilt which h i d is entrained iicross the intcrfacc has been mei+surcd
hy Turner (196H). (We Iiave uscd the 5iiiiic expcritncntal arrangement a s
Turner s o that our rcsults may be compared with his.) He found that the rate
of entrainment is reduced as the stithility of the interface increased. A nieasure of this stability can be given in terms of a Richardson number
Ri = (1 A p / ; ~ I I ‘ . whcrc II and I arc the velocity and lcngth scale of‘ the
turbulent motions ncar tho interface, and Ap/p is the fractional density step
hctwceii the two layers. Turner consicicred two cast‘s in detiiil: first when ttic
density step was produced by ; I temperature step iind second when it was
produced by salinity difference hetween the layers. He expressed his results
in thc lorni
u, I I I R i . ’ ’ (salt).
whcrc II,. is I he rate of cntrainmcnt (defined as the amount of fluid entrained,
unit :ircaiunit time). Turncr further noted that ( I ) is equivalent to assuming
I11iit rhc rate of change of potential energy due to the mixing is proportional
10 tlic riitc o f kinetic energy production by the grid, and then discussed the
possiihlc rcils(btis for Ills reduced s i i h tritnsporl at Iiirge Ri.
(‘Iciirly the main ditlcrcnce between the two situations described hy ( I )
aiid ( 2 ) is that tlie coefficient of 111olcculitr diffusion of heat is much larger
I hi111 the corresponding coefficient for salt. The appropriate nondimcnsionul
piir;imctcr which dcscrihcs the cflect of molecular diffusion is the Peclet
numhcr Pc = I I / / K . I n terms of this parameter ( 1 ) is the entrainment riltc for
Pc L- O( 10‘) while (2) is for the case Pe = O( lo4).
In this paper we l o o k at the detailed structure of a density interface for ;I
range of Ri and Pc covcring essentially the same values as those itppropri;itc
to ‘Turner’s (196%) experiments. We tind that for the lower values (if Pc
molecular diffusion plays an essential role in determining tlic structurc of tlic
interface and that the energy iirgument given by Turner (196%). which ncglccts all diffusive effects. is not correct. The consequences of thc results ToI
1 Iic gcophysicill situations mentioned above are then discusscd.