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1. Introduction Estuaries can be regarded as mixing zones which dilute saltwater inflowing from the ocean with freshwater from river runoff to produce brackish water flowing back into the ocean ( Fischer 1976 ). To underline this key estuarine function, Wang et al. (2017) used the name mixing machine to characterize estuarine dynamics. Since mixing is such a fundamental property in estuaries, several authors have proposed quantitative measures for it. In an early estuarine model, Hansen
1. Introduction Estuaries can be regarded as mixing zones which dilute saltwater inflowing from the ocean with freshwater from river runoff to produce brackish water flowing back into the ocean ( Fischer 1976 ). To underline this key estuarine function, Wang et al. (2017) used the name mixing machine to characterize estuarine dynamics. Since mixing is such a fundamental property in estuaries, several authors have proposed quantitative measures for it. In an early estuarine model, Hansen
1. Introduction Despite its significance for large-scale geophysical flows ( Wunsch and Ferrari 2004 ), we still lack a precise understanding of how mixing in a stratified environment depends on the environmental conditions that drive it [see, e.g., the review by Ivey et al. (2008) and references therein]. If we view mixing as any mechanism that pumps buoyancy against a gravitational potential gradient, we can think of its efficiency as the fraction of the energy consumed by the system that
1. Introduction Despite its significance for large-scale geophysical flows ( Wunsch and Ferrari 2004 ), we still lack a precise understanding of how mixing in a stratified environment depends on the environmental conditions that drive it [see, e.g., the review by Ivey et al. (2008) and references therein]. If we view mixing as any mechanism that pumps buoyancy against a gravitational potential gradient, we can think of its efficiency as the fraction of the energy consumed by the system that
1. Introduction Mixing can be defined as the destruction of variance. For microstructure variations in momentum, this is written as ϵ , the rate of turbulent kinetic energy dissipation; for tracers it is written as χ , the rate of tracer microstructure variance destruction. In both cases, the destruction of variance is an irreversible process. Currently, not even very high-resolution numerical ocean models that focus on estuarine and coastal ocean domains are able to resolve
1. Introduction Mixing can be defined as the destruction of variance. For microstructure variations in momentum, this is written as ϵ , the rate of turbulent kinetic energy dissipation; for tracers it is written as χ , the rate of tracer microstructure variance destruction. In both cases, the destruction of variance is an irreversible process. Currently, not even very high-resolution numerical ocean models that focus on estuarine and coastal ocean domains are able to resolve
of which may lead to turbulence and mixing. These are the Kelvin–Helmholtz (KH) instability, which consists of a stationary train of billows focused at the central plane, and the Holmboe instability, which consists of a pair of oppositely propagating wave trains, focused above and below the central plane, that interfere to form a standing wave–like structure ( Holmboe 1962 ; Smyth et al. 1988 ). In this paper, we examine mixing processes in direct numerical simulations (DNSs) of Holmboe
of which may lead to turbulence and mixing. These are the Kelvin–Helmholtz (KH) instability, which consists of a stationary train of billows focused at the central plane, and the Holmboe instability, which consists of a pair of oppositely propagating wave trains, focused above and below the central plane, that interfere to form a standing wave–like structure ( Holmboe 1962 ; Smyth et al. 1988 ). In this paper, we examine mixing processes in direct numerical simulations (DNSs) of Holmboe
available, (1) yields K ρ . One can then take advantage of the fact that different scalar concentrations diffuse at similar rates and therefore use K ρ as an approximation for the diffusivity of heat, salt, CO 2 , or any other scalar. Eventually we hope to be able to calculate values of Γ for all the various processes that mix geophysical fluids. In the interim, we use the provisional value Γ = 0.2. This is an oversimplification, but when checked independently as described below, Γ = 0.2 gives
available, (1) yields K ρ . One can then take advantage of the fact that different scalar concentrations diffuse at similar rates and therefore use K ρ as an approximation for the diffusivity of heat, salt, CO 2 , or any other scalar. Eventually we hope to be able to calculate values of Γ for all the various processes that mix geophysical fluids. In the interim, we use the provisional value Γ = 0.2. This is an oversimplification, but when checked independently as described below, Γ = 0.2 gives
1. Introduction The return of Antarctic Bottom Water from the abyss back to the surface requires water mass transformation by diapycnal mixing (e.g., Lumpkin and Speer 2007 ; Talley 2013 ). While small-scale turbulence in the bulk of the abyssal ocean is relatively weak, turbulence levels are elevated where tidal or geostrophic flows pass over a rugged seafloor (e.g., Polzin et al. 1997 ; Ledwell et al. 2000 ; St. Laurent et al. 2012 ; Waterhouse et al. 2014 ). Internal waves are excited
1. Introduction The return of Antarctic Bottom Water from the abyss back to the surface requires water mass transformation by diapycnal mixing (e.g., Lumpkin and Speer 2007 ; Talley 2013 ). While small-scale turbulence in the bulk of the abyssal ocean is relatively weak, turbulence levels are elevated where tidal or geostrophic flows pass over a rugged seafloor (e.g., Polzin et al. 1997 ; Ledwell et al. 2000 ; St. Laurent et al. 2012 ; Waterhouse et al. 2014 ). Internal waves are excited
1. Introduction The ocean’s meridional overturning circulation (MOC) regulates Earth’s climate on centennial to millennial time scales through the transport of vast amounts of carbon, heat, and nutrients ( Wunsch 2017 ). While the upper branch of the MOC is thought to be primarily controlled by wind and buoyancy forcing at the ocean surface ( Marshall and Radko 2003 ; Marshall and Speer 2012 ), the lower branch requires interior mixing with overlying waters to balance the surface buoyancy loss
1. Introduction The ocean’s meridional overturning circulation (MOC) regulates Earth’s climate on centennial to millennial time scales through the transport of vast amounts of carbon, heat, and nutrients ( Wunsch 2017 ). While the upper branch of the MOC is thought to be primarily controlled by wind and buoyancy forcing at the ocean surface ( Marshall and Radko 2003 ; Marshall and Speer 2012 ), the lower branch requires interior mixing with overlying waters to balance the surface buoyancy loss
1. Introduction Surface winds induce turbulent mixing in the surface layer, while the mixing is moderated by Earth’s rotation. Stabilizing buoyancy fluxes at the ocean surface further weaken wind-induced mixing and shoal the surface mixing layer. The surface mixed layer, through which surface fluxes have been mixed, is a remnant of this surface mixing layer through which surface fluxes are being actively mixed (e.g., Brainerd and Gregg 1995 ; de Boyer Montegut et al. 2004 ). Both the surface
1. Introduction Surface winds induce turbulent mixing in the surface layer, while the mixing is moderated by Earth’s rotation. Stabilizing buoyancy fluxes at the ocean surface further weaken wind-induced mixing and shoal the surface mixing layer. The surface mixed layer, through which surface fluxes have been mixed, is a remnant of this surface mixing layer through which surface fluxes are being actively mixed (e.g., Brainerd and Gregg 1995 ; de Boyer Montegut et al. 2004 ). Both the surface
1. Introduction In what we will term the “traditional” view, the meridional overturning circulation (MOC) of the ocean is assumed to close through diabatic processes in the ocean interior. In this case, turbulent mixing in the ocean interior acts to transfer heat from the temperate waters of the upper ocean to the colder waters of the abyss. This heat transfer acts to modify the deep and bottom water masses of the abyss: North Atlantic Deep Water (NADW) and Antarctic Bottom Water (AABW). The
1. Introduction In what we will term the “traditional” view, the meridional overturning circulation (MOC) of the ocean is assumed to close through diabatic processes in the ocean interior. In this case, turbulent mixing in the ocean interior acts to transfer heat from the temperate waters of the upper ocean to the colder waters of the abyss. This heat transfer acts to modify the deep and bottom water masses of the abyss: North Atlantic Deep Water (NADW) and Antarctic Bottom Water (AABW). The
1. Introduction Fluid flow in the upper thermocline occurs largely along isopycnal surfaces, while the rate of cross-isopycnal mixing tends to be small. However, understanding the structure of the thermocline (e.g., Samelson and Vallis 1997 ), the overturning circulation ( Scott and Marotzke 2002 ), the efficiency of potential carbon sequestration experiments ( Mignone et al. 2004 ), and the degree of high-latitude control on the atmospheric p CO 2 concentration ( Archer et al. 2000 ) all
1. Introduction Fluid flow in the upper thermocline occurs largely along isopycnal surfaces, while the rate of cross-isopycnal mixing tends to be small. However, understanding the structure of the thermocline (e.g., Samelson and Vallis 1997 ), the overturning circulation ( Scott and Marotzke 2002 ), the efficiency of potential carbon sequestration experiments ( Mignone et al. 2004 ), and the degree of high-latitude control on the atmospheric p CO 2 concentration ( Archer et al. 2000 ) all
