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• W2772503882 abstract "Mixing efficiency in stratified turbulence Andrea Maffioli, Geert Brethouwer and Erik Lindborg Linn´e Flow Centre, KTH Royal Institute of Technology, 10044 Stockholm, Sweden maffioli@mech.kth.se Abstract We investigate how the mixing efficiency in stratified turbulence is affected by the strength of the stratification. We show that the mixing coefficient Γ ∼ F r −2 for weakly stratified turbulence, where Γ = ǫ p /ǫ k and F r = ǫ k /(N u 2 h ) is the turbulent Froude number, taken as F r ≫ 1 in our scaling analysis. A series of direct numerical simulations of forced turbulence with uniform stratification N confirm that Γ ∝ F r −2 for F r > 1. In the simulations the Froude number is then decreased below F r = 1 and we find Γ max = 0.51 at F r ≈ 0.3 suggesting efficient mixing despite a stronger vertical stability. At even lower F r, there is an approach towards a constant Γ of order unity in accordance with the strongly stratified turbulence theory. We briefly discuss the implications our results may have on mixing efficiency parametrizations based on the buoyancy Reynolds number. Introduction Turbulent mixing in the atmosphere and oceans is a key factor to consider when estimating global energetics. In oceanographic applications, the density perturbation ρ away from the background density profile ρ 0 , and hence defined as ρ = ρ tot − ρ 0 , acts as the scalar field. The corresponding eddy diffusivity is defined as K ρ = B/N 2 ; this is actually the eddy diffusivity for the buoyancy field b = −ρg/ρ ref since it is the ratio of the buoyancy flux B = −hbu z i to the mean background buoyancy gradient N 2 = db 0 /dz. The buoyancy flux can be modelled as B = −hbu z i = K ρ db 0 /dz, analogously to how the Reynolds stresses are typically calculated. We denote volume averaging over the physical domain by h. . .i while time averaging over the statistically steady period of a quantity is denoted by the overbar (. . .). Note that we mostly consider stratified turbulence in the absence of a mean flow so we do not use primes for turbulence quantities and simply write them as u = (u x , u y , u z ), ρ and b. Starting from the eddy diffusivity framework, Osborn (1980) introduced the flux Richard- son number Ri f = B/(B+ǫ k ), which is the ratio of buoyancy flux to turbulence production and can be thought of as a mixing efficiency. The mixing coefficient is similarly defined as Γ = B/ǫ k related to the eddy diffusivity as K ρ = Γǫ k /N 2 . The kinetic energy dis- sipation rate is defined as ǫ k = 2νhS ij S ij i where S ij is the velocity gradient tensor. A constant mixing efficiency Ri f = 0.17 was assumed by Osborn (1980) leading to a mix- ing coefficient Γ = Ri f /(1 − Ri f ) = 0.2, a value which has been used in oceanographic applications ever since. More recently, Salehipour and Peltier (2015) have suggested to use the potential energy dissipation rate ǫ p instead of the buoyancy flux when calculating Γ because in steady-state stratified turbulence B = ǫ p and the irreversible conversion of available potential energy into background potential energy due to mixing is given by ǫ p . The potential energy dissipation rate is defined as ǫ p = (D/N 2 )h∇b · ∇bi since the VIII th Int. Symp. on Stratified Flows, San Diego, USA, Aug. 29 - Sept. 1, 2016" @default.
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• W2772503882 date "2016-08-30" @default.
• W2772503882 modified "2023-09-25" @default.
• W2772503882 title "Mixing efficiency in stratified turbulence" @default.
• W2772503882 hasPublicationYear "2016" @default.
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