Fig. 1.  Density interfaces simulated in the low-latitude pycnocline below well-mixed upper quasi-homogeneous layer.  Initial linear density profile has a gradient dr/dz = 2.5×10^-8 g/cm³,  u_* = 0.9 cm/s and Coriolis parameter f = 10^-5 s^-1.

We have developed a detailed numerical model of a rotating, stratified and sheared turbulent boundary layer.  This model can produce a series of fine-scale quasi-homogeneous layers in a pycnocline of constant buoyancy frequency N_o .  Numerical experiments were run with  small-scale parameterizations written in the following form:

where K_N is the eddy diffusivity, K_M is the eddy viscosity and K_Sh is the shear-dependent eddy viscosity in non-stratified flows.  This parameterization ensures instability of density gradients in a stably-stratified layer with decreasing buoyancy flux F_b, when N² exceeds a critical value, corresponding to a local maximum of F_b(N²).  This type of instability was independently proposed by Phillips [1972] and Posmentier [1977] and later treated by several others.  It was also found, that the development and decay of fine-structure are strongly dependent on inertial oscillations which enhance vertical shear at the density interfaces between homogeneous layers locally.  As a result, the local Richardson numbers decreases, thus generating shear-induced turbulence within interfaces.  This is why some of the interfaces are rapidly destroyed and fine-structure may even vanish at times, as can be seen in the Fig. 2 (left).

Fig. 2 (left).  The generation and decay of the density steps in the upper pycnocline at the end of the 2^nd inertial period, counting from the beginning of computation. A constant friction velocity u_* = 0.9 cm/s, linear initial stratification, N² = 2.5×10^-5 s^-2, and Coriolis parameter f = 10^-4 s^-1 were used in this numerical experiment.  The layering phases alternate between “calm” periods and those during which the steps vanish completely.  The “calm” stages may last up to (0.5 - 0.9)×T_in, where the inertial period T_in is 17.45 h.

Fig. 2 (right).  Formation of a near-bottom pycnocline rich in step-like structure during the development of quasi-homogeneous bottom turbulent layer from the linear density profile set at t = 0.  A constant boundary stress (u_* = 0.8 cm/s) is associated with a geostrophic current of U_g = 25 cm/s.

It was found that a small, but sustained, background shear is required to generate the steps.  This minimal shear Sh_o corresponds to a background bulk Richardson number Ri_o close to 6, and this criterion limits the steps generation in the model.  This may indicate that, only in the regions with pre-existing global Ri < Ri_o, intermittent step-like structure can be generated in stably stratified waters under synoptic variations of wind stress (or tidal-induced bottom stresses).

Fig. 3.  The appearance of a series of fine-scale homogeneous layers and density interfaces in the near-bottom pycnocline influenced by a tidal current with semidiurnal and diurnal constituents.  The initial density profile is the same as for calculations given in Fig. 2.  The calculations are targeted to simulate the near bottom boundary layer at the West Sahara shelf.