ABSTRACT
In many geophysical and environmental flow situations, motion-fields are strongly affected and determined by buoyancy and Coriolis forces (Turner 1979; Fernando 1991; Riley & LeLong 2000), which can be described by the continuity (1.1), horizontal (1.2) and vertical (1.3) momentum and buoyancy conservation (1.4) equations. They are:
where ui = (uα,w) is the dimensionless velocity field and LH and LV are the horizontal and vertical length scales, respectively, with corresponding velocity scales of uV and uH (e.g., uα = u˜α/uH , w= w˜/uv, xα = x˜/LH , z = z˜/Lv, where tilde represents dimensional quantities);
where p is the dimensionless pressure perturbation from its adiabatic hydrostatic scale and p0 the corresponding scale, f∼= fl∼= (0, 0, f ) the inertial frequency [Coriolis parameter in z direction, anti-parallel to the gravitational acceleration g= (0, 0, −g)], Ro = ( fLH/uH )−1 the Rossby number, TH and TV the time scales of flow evolution in horizontal and vertical directions, Re = uHLH/ν the Reynolds number and v the kinematic viscosity;
where b is the dimensionless buoyancy perturbation with a characteristic scale b0; Rib = b0LV /u2H is the bulk Richardson number,
where Tb is the time scale of buoyancy variations, κ the molecular diffusivity of the stratifying substance (heat, salt, etc.), Sc= v/κ the Schmidt number, N 2 = db¯/dz
the buoyancy frequency (in motionless state) and b¯ the mean buoyancy.
