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density sorting method to estimate the vertical length scale of density overturns in a stably stratified fluid. This scale has since been called the Thorpe scale L T . It is theorized that there is a linear relationship (at least statistically) between L T and the Ozmidov length scale L O = . Knowledge of ε through L O then leads to the eddy diffusivity through K ρ = Γ ε / N 2 , where Γ is the mixing efficiency. The Thorpe scale L T is a kinematic measure of the length scale of an
density sorting method to estimate the vertical length scale of density overturns in a stably stratified fluid. This scale has since been called the Thorpe scale L T . It is theorized that there is a linear relationship (at least statistically) between L T and the Ozmidov length scale L O = . Knowledge of ε through L O then leads to the eddy diffusivity through K ρ = Γ ε / N 2 , where Γ is the mixing efficiency. The Thorpe scale L T is a kinematic measure of the length scale of an
fronts appear that seem to show dynamic similarity to the jets in the ACC. “Classic” annulus experiments (with no β effect) provided us with the basic regime diagram that guides thinking to this day, with a flow governed by two dimensionless parameters ( Hide 1958 ), the Taylor number, and the thermal Rossby number, where Ω is the rotation rate of the table, L is the annulus gap width, ν is the kinematic viscosity, d is the fluid depth, g is the acceleration of gravity, α is the linear
fronts appear that seem to show dynamic similarity to the jets in the ACC. “Classic” annulus experiments (with no β effect) provided us with the basic regime diagram that guides thinking to this day, with a flow governed by two dimensionless parameters ( Hide 1958 ), the Taylor number, and the thermal Rossby number, where Ω is the rotation rate of the table, L is the annulus gap width, ν is the kinematic viscosity, d is the fluid depth, g is the acceleration of gravity, α is the linear
. J. Geophys. Res. , 81 , 3725 – 3735 , doi: 10.1029/JC081i021p03725 . Price , J. , R. Weller , and R. Pinkel , 1986 : Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing . J. Geophys. Res. , 91 , 8411 – 8427 , doi: 10.1029/JC091iC07p08411 . Qiao , L. , and R. Weisberg , 1995 : Tropical instability wave kinematics: Observations from the tropical instability wave experiment . J. Geophys. Res. , 100 , 8677 – 8693
. J. Geophys. Res. , 81 , 3725 – 3735 , doi: 10.1029/JC081i021p03725 . Price , J. , R. Weller , and R. Pinkel , 1986 : Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing . J. Geophys. Res. , 91 , 8411 – 8427 , doi: 10.1029/JC091iC07p08411 . Qiao , L. , and R. Weisberg , 1995 : Tropical instability wave kinematics: Observations from the tropical instability wave experiment . J. Geophys. Res. , 100 , 8677 – 8693
. Parameters of the simulated cases. Each case has background stratification N ∞ = 1.6 × 10 −3 rad s −1 , frequency Ω = 1.407 × 10 −4 rad s −1 , and slope angle β = 5°. The Reynolds number is based on the amplitude of the bottom velocity U b and the Stokes boundary layer thickness. The bulk Richardson number, defined as , is 0.59 for both the cases. The kinematic viscosity ν is taken as 10 −6 m 2 s −1 and Prandtl number Pr = 7. Reference density ρ 0 is taken as 1000 kg m −3 for all the
. Parameters of the simulated cases. Each case has background stratification N ∞ = 1.6 × 10 −3 rad s −1 , frequency Ω = 1.407 × 10 −4 rad s −1 , and slope angle β = 5°. The Reynolds number is based on the amplitude of the bottom velocity U b and the Stokes boundary layer thickness. The bulk Richardson number, defined as , is 0.59 for both the cases. The kinematic viscosity ν is taken as 10 −6 m 2 s −1 and Prandtl number Pr = 7. Reference density ρ 0 is taken as 1000 kg m −3 for all the
-dimensional, Eulerian velocity, u S is the Stokes drift, u L ≡ u + u S is the Lagrangian velocity, f is the Coriolis parameter, p is the pressure divided by a reference density, b is the buoyancy, ν is the kinematic viscosity, and κ is the thermal diffusivity. The term u L , j refers to the j th component of the Lagrangian velocity, and, as usual with Einstein notation, the repeated j index implies a summation over the three spatial components. The Stokes shear force u L , j ∇ u S , j form
-dimensional, Eulerian velocity, u S is the Stokes drift, u L ≡ u + u S is the Lagrangian velocity, f is the Coriolis parameter, p is the pressure divided by a reference density, b is the buoyancy, ν is the kinematic viscosity, and κ is the thermal diffusivity. The term u L , j refers to the j th component of the Lagrangian velocity, and, as usual with Einstein notation, the repeated j index implies a summation over the three spatial components. The Stokes shear force u L , j ∇ u S , j form
), where b is the buoyancy. The corresponding Cartesian and Boussinesq equations are The pressure is ρ 0 p , f > 0 is the Coriolis frequency, κ is the diffusivity, ν is the kinematic viscosity, r (s −1 ) is the coefficient of bottom drag, f bot ( z ) is a near-bottom localization function discussed in the appendix , and are the unit vectors in the zonal ( x ), meridional ( y ), and vertical ( z ) directions. No penetration conditions are imposed on the top, bottom, and meridional sides
), where b is the buoyancy. The corresponding Cartesian and Boussinesq equations are The pressure is ρ 0 p , f > 0 is the Coriolis frequency, κ is the diffusivity, ν is the kinematic viscosity, r (s −1 ) is the coefficient of bottom drag, f bot ( z ) is a near-bottom localization function discussed in the appendix , and are the unit vectors in the zonal ( x ), meridional ( y ), and vertical ( z ) directions. No penetration conditions are imposed on the top, bottom, and meridional sides
quantities fix the flux Rayleigh number Ra F = = 5.23 × 10 18 , where B = g ′ Q s is the imposed specific buoyancy flux, g ′ = g Δ ρ / ρ 0 is the reduced gravity, Δ ρ = ρ s − ρ 0 is the imposed density difference, g is the gravitational acceleration, κ m (=1.39 × 10 −9 m 2 s −1 ) is the molecular diffusivity of salt in dilute aqueous solution, and ν m (=1.15 × 10 −6 m 2 s −1 ) is the kinematic viscosity of the solution. Mechanical stirring is introduced by two parallel 8-mm
quantities fix the flux Rayleigh number Ra F = = 5.23 × 10 18 , where B = g ′ Q s is the imposed specific buoyancy flux, g ′ = g Δ ρ / ρ 0 is the reduced gravity, Δ ρ = ρ s − ρ 0 is the imposed density difference, g is the gravitational acceleration, κ m (=1.39 × 10 −9 m 2 s −1 ) is the molecular diffusivity of salt in dilute aqueous solution, and ν m (=1.15 × 10 −6 m 2 s −1 ) is the kinematic viscosity of the solution. Mechanical stirring is introduced by two parallel 8-mm
