284
8 Transport in the Oceans and Coastal Zone
where u', w' and T' are fluctuating components of horizontal and vertical velocity, and temperature, respectively; (3 is the volume expansion coefficient. For
gases obeying the perfect gas law, the value of (3 is equal to l/T. Overbars
in Eq. (8.89) denote averaging in the stochastic sense. The denominator is
always negative. Thus, the value of Ri is negative for upward heat flux, when
buoyant forces 'produce' energy, and it is positive when they 'absorb' energy.
Therefore, at some large positive value of Ri, turbulence intensity becomes
zero. This critical value of Ri is about 0.21.
Fluxes through isopycnals are mostly driven by small scale turbulence and
double diffusion. The double diffusion phenomenon will be described in detail
in the next section. Here we will concentrate on turbulence only. Ruddick and
Walsh (1997) reported the results of field observations of diffusion of a tracer
(sulfur hexafluoride) and turbulent microstructure in the North Atlantic. The
turbulent diffusivity has been inferred from the temperature microstructure using the Osborn-Cox (1972) model. This model is based on the assumption that
turbulent overturns against a well-defined mean gradient produce temperature
fluctuations (for detailed description of the model see Osborn and Cox (1972).
The coefficient of vertical diffusion Kyl for the depth range 240-340 m was
found to be 1.0 x 10- 5 m 2 /s in autumn and 2.2 x 10- 5 m 2 /s in spring. In the
experimental area, a mixed layer occupied the upper 60 m of the water column
during autumn, whereas during the following spring, the surface mixed layer
thickness increased to about 90 m.
8.4.4 Double Diffusion and Salt Fingers
In turbulent motion, heat and dissolved substance, such as salt, are exchanged
at the same rate of mixing. However, this is not the case at the level of
molecular diffusion. Molecular diffusion of salt is about two orders of magnitude
smaller than the molecular diffusion of heat. Thus, more energy is needed to
exchange salt on the molecular scale than it is to exchange heat. This difference
between diffusivity can cause specific instabilities in stratification (Tomczak
and Godfrey, 1994).
Let us consider a typical ocean thermocline. Temperature and salinity decrease with depth. Thus, the vertical salinity gradient itself would result in
an unstable density stratification. However, this potential instability is more
than compensated by the stabilizing vertical temperature gradient, because
this gradient is reduced much faster than the salinity gradient. If the temperature gradient is reduced, then it is no longer sufficient to compensate for
the salinity-induced instability. As a result, convection appears in the form
of narrow vertical tubes of rising low salinity water between narrow tubes of
sinking salty water, known as salt fingers (see Fig. 8.11), and the process is
known as double diffusion.
Evidence of the double diffusion mechanism first came from laboratory experiments (Turner, 1967; Taylor and Bucens, 1989). In such experiments, cool
8 Transport in the Oceans and Coastal Zone
where u', w' and T' are fluctuating components of horizontal and vertical velocity, and temperature, respectively; (3 is the volume expansion coefficient. For
gases obeying the perfect gas law, the value of (3 is equal to l/T. Overbars
in Eq. (8.89) denote averaging in the stochastic sense. The denominator is
always negative. Thus, the value of Ri is negative for upward heat flux, when
buoyant forces 'produce' energy, and it is positive when they 'absorb' energy.
Therefore, at some large positive value of Ri, turbulence intensity becomes
zero. This critical value of Ri is about 0.21.
Fluxes through isopycnals are mostly driven by small scale turbulence and
double diffusion. The double diffusion phenomenon will be described in detail
in the next section. Here we will concentrate on turbulence only. Ruddick and
Walsh (1997) reported the results of field observations of diffusion of a tracer
(sulfur hexafluoride) and turbulent microstructure in the North Atlantic. The
turbulent diffusivity has been inferred from the temperature microstructure using the Osborn-Cox (1972) model. This model is based on the assumption that
turbulent overturns against a well-defined mean gradient produce temperature
fluctuations (for detailed description of the model see Osborn and Cox (1972).
The coefficient of vertical diffusion Kyl for the depth range 240-340 m was
found to be 1.0 x 10- 5 m 2 /s in autumn and 2.2 x 10- 5 m 2 /s in spring. In the
experimental area, a mixed layer occupied the upper 60 m of the water column
during autumn, whereas during the following spring, the surface mixed layer
thickness increased to about 90 m.
8.4.4 Double Diffusion and Salt Fingers
In turbulent motion, heat and dissolved substance, such as salt, are exchanged
at the same rate of mixing. However, this is not the case at the level of
molecular diffusion. Molecular diffusion of salt is about two orders of magnitude
smaller than the molecular diffusion of heat. Thus, more energy is needed to
exchange salt on the molecular scale than it is to exchange heat. This difference
between diffusivity can cause specific instabilities in stratification (Tomczak
and Godfrey, 1994).
Let us consider a typical ocean thermocline. Temperature and salinity decrease with depth. Thus, the vertical salinity gradient itself would result in
an unstable density stratification. However, this potential instability is more
than compensated by the stabilizing vertical temperature gradient, because
this gradient is reduced much faster than the salinity gradient. If the temperature gradient is reduced, then it is no longer sufficient to compensate for
the salinity-induced instability. As a result, convection appears in the form
of narrow vertical tubes of rising low salinity water between narrow tubes of
sinking salty water, known as salt fingers (see Fig. 8.11), and the process is
known as double diffusion.
Evidence of the double diffusion mechanism first came from laboratory experiments (Turner, 1967; Taylor and Bucens, 1989). In such experiments, cool