Turbulent transport of heat and momentum from an infinite rough plane

Abstract

In the first part of the paper the dimensional laws governing the processes of heat and momentum transport from an infinite rough plane are assembled and their consequences set out. In the second part, the detailed equations for the turbulent energy, the mean square temperature fluctuation and the covariance of temperature and vertical velocity are used, together with some speculative assumptions concerning the dissipative action of the turbulence, to derive a series of relations between the turbulent intensities and the Austausch coefficients. One of these relations indicates that the flux form of the Richardson number cannot exceed a critical value which is about 0·15. It follows that in highly stable conditions the buoyancy forces have little direct effect on the turbulent energy balance, their action being primarily to cause a reduction in the scale of the motion and some change in its structure.

Turbulent energy production and entrainment at a highly stratified estuarine front

“…Although the exact value of this ratio may be a function of the evolution of the turbulence field [e.g., Wijesekera and Dillon, 1997;Gibson, 1998] or the gradient Richardson number [Baumert and Peters, 2000], the overturn Froude number is generally of order 1 for all three passes. with Figure 6 also suggests that Ri f % Ri g , indicating that vertical eddy diffusivities for mass and momentum are equal [Ellison, 1957], consistent with a comparison of the vertical profiles of K z r and K z u in Figures 8 and 11. [30] In Figure 14, values of Ri f for the three passes are plotted against the overturn Froude number, and compared with the DNS results of Ivey et al [1998].…”

A conjecture relating oceanic internal waves and small‐scale processes

“…Expressing q in terms of the flux Richardson number (Osborn, 1980) as q = /?//(l -Rf), we appear to need an /Rvalue small compared with i A value as large as Ellison's (1957) R f = 0.15 might be acceptable, whereas Weinstock's (1978b) R f = 0.44 could not be accepted. The present discussion obliges us to reconsider a familiar practice of estimating effective thermal diffusivity by direct observation of temperature variance dissipation rate.…”

Comparison of deep-ocean finescale shear at two sites along the Mid-Atlantic Ridge

“…The factor E = R f c /(1 − R f c ) is a maximum mixing efficiency, with R f c being the critical flux Richardson number (Ellison, 1957). Equality is generally assumed when this expression is used to estimate diffusivity, and this is done here, with a constant mixing efficiency Γ = 0.2 substituted in place of E. Arguments for Γ being in this vicinity are given in Osborn (1980).…”