An explanation for salinity- and SPM-induced vertical countergradient buoyancy fluxes

Abstract

Measurements of turbulent fluctuations of velocity, salinity, and suspended particulate matter (SPM) are presented. The data show persistent countergradient buoyancy fluxes. These countergradient fluxes are controlled by the ratio of vertical turbulent kinetic energy (VKE) and available potential energy (APE) terms in the buoyancy flux equation. The onset of countergradient fluxes is found to approximately coincide with larger APE than VKE. It is shown here that the ratio of VKE to APE can be written as the square of a vertical Froude number. This number signifies the onset of the dynamical significance of buoyancy in the transport of mass. That is when motions driven by buoyancy begin to actively determine the vertical turbulent transport of mass. Spectral and quadrant analyses show that the occurrence of countergradient fluxes coincides with a change in the relative importance of turbulent energetic structures and buoyancydriven motions in the transport of mass. Furthermore, these analyses show that with increasing salinity-induced Richardson number (Ri), countergradient contributions expand to the larger scales of motions and the relative importance of outward and inward interactions increases. At the smaller scales, at moderate Ri, the countergradient buoyancy fluxes are physically associated with an asymmetry in transport of fluid parcels by energetic turbulent motions. At the large scales, at large Ri, the countergradient buoyancy fluxes are physically associated with convective motions induced by buoyancy of incompletely dispersed fluid parcels which have been transported by energetic motions in the past. Moreover, these convective motions induce restratification and enhanced settling of SPM. The latter is generally the result of salinity-induced convective motions, but SPM-induced buoyancy is also found to play a role.

On total turbulent energy and the passive and active role of buoyancy in turbulent momentum and mass transfer

“…Based on large eddy simulation (LES) results, Gerz and Schumann ( 1996 ) developed conceptual models for countergradient transport of momentum and heat by intermittent motions in stratified homogeneous shear flows. These principles also hold for nonhomogeneous turbulent conditions, (de Nijs and Pietrzak 2011 ). Based on quadrant and spectral analysis, they determined that at relatively large stratification and shear, the turbulent transports of momentum and mass are governed by energetic turbulent structures produced by velocity shear, while at large stratification and weak shear remnants of transports by energetic turbulent structures in the past induce convective motions.…”

“…The density ( ρ ) is defined as ρ = ρ 0 + γ c ∙ C + γ s ∙ S , with γ an expression to convert salinity ( γ s ≈ 0.72 kg(m) −3 (PSU) −1 ) and SPM concentration ( γ c = ( ρ s − ρ w )( ρ w ) −1 ≈ 0.62, where ρ w and ρ s are the densities of water and sand particles, respectively) to density as indicated by the subscripts s and c , respectively (West and Oduyemi 1989 ). However, C << S and therefore C is not separately treated in the analysis (see de Nijs and Pietrzak 2011 ). In Eqs.…”

“…However, levels 3 and 4 models of Mellor and Yamada ( 1974 ) show countergradient heat fluxes for a stratified atmospheric boundary layer, although they did not elaborate upon this finding. Since then, many studies have appeared on the countergradient buoyancy fluxes (see de Nijs and Pietrzak 2011 and references therein). The second-order closure framework shows the importance of the buoyancy correlation terms in the buoyancy flux and density variance balance equation.…”

“…The second-order closure framework shows the importance of the buoyancy correlation terms in the buoyancy flux and density variance balance equation. This complicates the analysis of the turbulent transport of mass in a density field setup by multiple active scalars, such as salt and SPM (de Nijs and Pietrzak 2011 ). In the case of downgradient transport this precludes the use of similar turbulent diffusivities for salinity and SPM.…”

“…For this condition, the correction of the log profile results in an increase of drag instead of a decrease as for stable conditions. At large stable stratification, countergradient buoyancy fluxes are observed (de Nijs and Pietrzak 2011 ). These buoyancy fluxes indicate a conversion of turbulent potential energy (PE) to TKE.…”