# Search Results

< z < −120 m, Ri B increases linearly again from 1.5 to 5, and Ri B = 5 for z < −120 m. Note that since the mean vertical component of the relative vorticity is zero in the simulations due to the periodic boundary conditions, a portion of the upper layer is unstable to symmetric instability with Ri B < 1. However, the LES does not capture a number of other physical processes that are likely to be important at the observational site. The alongfront domain size is too small to permit

< z < −120 m, Ri B increases linearly again from 1.5 to 5, and Ri B = 5 for z < −120 m. Note that since the mean vertical component of the relative vorticity is zero in the simulations due to the periodic boundary conditions, a portion of the upper layer is unstable to symmetric instability with Ri B < 1. However, the LES does not capture a number of other physical processes that are likely to be important at the observational site. The alongfront domain size is too small to permit

meridional buoyancy gradient − f Λ ( Taylor and Ferrari 2010 ). The perturbations satisfy periodic boundary conditions in the horizontal coordinates x and y in a domain of zonal extent L x and meridional extent L y . The dynamics are given by the perturbation equations: where u = ( u , υ , w ) is the velocity vector, p is the density-normalized pressure, b is buoyancy, ν is viscosity, κ is diffusivity, and t is time. At the boundaries at z = − H and z = 0, we prescribe the

meridional buoyancy gradient − f Λ ( Taylor and Ferrari 2010 ). The perturbations satisfy periodic boundary conditions in the horizontal coordinates x and y in a domain of zonal extent L x and meridional extent L y . The dynamics are given by the perturbation equations: where u = ( u , υ , w ) is the velocity vector, p is the density-normalized pressure, b is buoyancy, ν is viscosity, κ is diffusivity, and t is time. At the boundaries at z = − H and z = 0, we prescribe the

1. Introduction Midlatitude storms efficiently inject energy into boundary layer inertial oscillations (e.g., Pollard 1970 ; Pollard and Millard 1970 ; D’Asaro 1985 ; D’Asaro et al. 1995 ; Alford 2003b ), and therefore boundary layer near-inertial energy density exhibits spatial and temporal patterns similar to atmospheric storm tracks (e.g., Chaigneau et al. 2008 ; Elipot et al. 2010 ). As storm tracks overlie western boundary current regions, which contain energetic geostrophic flows

1. Introduction Midlatitude storms efficiently inject energy into boundary layer inertial oscillations (e.g., Pollard 1970 ; Pollard and Millard 1970 ; D’Asaro 1985 ; D’Asaro et al. 1995 ; Alford 2003b ), and therefore boundary layer near-inertial energy density exhibits spatial and temporal patterns similar to atmospheric storm tracks (e.g., Chaigneau et al. 2008 ; Elipot et al. 2010 ). As storm tracks overlie western boundary current regions, which contain energetic geostrophic flows

configuration as in Boccaletti et al. (2007) is adopted. The domain spans 192 km both in the zonal and meridional directions and is 300 m deep. The zonal and meridional resolutions are both set at 500 m. The vertical resolution is uniformly set as 5 m. The channel is reentrant with periodic boundary conditions along the zonal direction. The meridional walls of the channel are rigid and impermeable, with free-slip boundary conditions. The bottom of the channel is set with no topography and with free

configuration as in Boccaletti et al. (2007) is adopted. The domain spans 192 km both in the zonal and meridional directions and is 300 m deep. The zonal and meridional resolutions are both set at 500 m. The vertical resolution is uniformly set as 5 m. The channel is reentrant with periodic boundary conditions along the zonal direction. The meridional walls of the channel are rigid and impermeable, with free-slip boundary conditions. The bottom of the channel is set with no topography and with free

) , and (6d) form a linear system. We now form an equation for the perturbation density by combining (6a) , (6c) , and (6d) to eliminate υ ′ and ψ , yielding with T ′ defined by (7) . While an analytic solution to (8) is possible, the high (fourth) order of the equation makes such a solution complex to write down, and we prefer to solve (8) numerically. The horizontal far-field boundary conditions are The vertical boundary conditions are that the vertical velocity vanishes ( w ′ = 0) at

) , and (6d) form a linear system. We now form an equation for the perturbation density by combining (6a) , (6c) , and (6d) to eliminate υ ′ and ψ , yielding with T ′ defined by (7) . While an analytic solution to (8) is possible, the high (fourth) order of the equation makes such a solution complex to write down, and we prefer to solve (8) numerically. The horizontal far-field boundary conditions are The vertical boundary conditions are that the vertical velocity vanishes ( w ′ = 0) at

where defines the friction/diffusion operator (different horizontal and vertical Ekman numbers are allowed; the Prandtl number is set to one), and is Stone’s (1971) nonhydrostatic parameter. All perturbations are assumed to be doubly periodic in the horizontal in a square domain of zonal and meridional extent , where L is the dimensional domain width. The vertical boundary conditions are no normal flow ( ), no stress on the perturbations ( ), and no buoyancy flux ( ) at and . For

where defines the friction/diffusion operator (different horizontal and vertical Ekman numbers are allowed; the Prandtl number is set to one), and is Stone’s (1971) nonhydrostatic parameter. All perturbations are assumed to be doubly periodic in the horizontal in a square domain of zonal and meridional extent , where L is the dimensional domain width. The vertical boundary conditions are no normal flow ( ), no stress on the perturbations ( ), and no buoyancy flux ( ) at and . For

periodic channel with impermeable vertical walls at the meridional boundaries and at the bottom. The horizontal dimensions are L y = 192 km in the meridional direction, L x = 96 km in the zonal direction, and H tot = 500-m depth. The horizontal resolution is 1 km. In the vertical the model has 32 layers, but the vertical resolution is variable with depth, with enhanced resolution of 2 m near the sea surface, decreasing to the resolution of 36 m at depth. Lateral free-slip boundary conditions are

periodic channel with impermeable vertical walls at the meridional boundaries and at the bottom. The horizontal dimensions are L y = 192 km in the meridional direction, L x = 96 km in the zonal direction, and H tot = 500-m depth. The horizontal resolution is 1 km. In the vertical the model has 32 layers, but the vertical resolution is variable with depth, with enhanced resolution of 2 m near the sea surface, decreasing to the resolution of 36 m at depth. Lateral free-slip boundary conditions are

splines for the N data points such that the interpolated function x ( t ) crosses all N observations ( t i , x i ). The path x ( t ) is the canonical interpolating spline of order K . Examples are shown in Fig. 1 . The knot placements in (7) and (8) are equivalent to the not-a-knot boundary conditions described in De Boor (1978) and used in the cubic spline implementation in MATLAB. In the usual formulation of the not-a-knot boundary condition, the knot positions do not change as a

splines for the N data points such that the interpolated function x ( t ) crosses all N observations ( t i , x i ). The path x ( t ) is the canonical interpolating spline of order K . Examples are shown in Fig. 1 . The knot placements in (7) and (8) are equivalent to the not-a-knot boundary conditions described in De Boor (1978) and used in the cubic spline implementation in MATLAB. In the usual formulation of the not-a-knot boundary condition, the knot positions do not change as a

temperature variation with depth; the difference | T N ( z ) − T S ( z )| is maximum near/at the surface and decays to zero at depth. For our reference configuration, we set where h = 150 m. Given the temperature and density fields defined by (2) and (3) , the salinity field is determined from the equation of state [ (1) ]. Zero salt, heat, and momentum flux boundary conditions are applied on the northern and southern walls of the domain. Periodic boundary conditions are applied to all fields in the

temperature variation with depth; the difference | T N ( z ) − T S ( z )| is maximum near/at the surface and decays to zero at depth. For our reference configuration, we set where h = 150 m. Given the temperature and density fields defined by (2) and (3) , the salinity field is determined from the equation of state [ (1) ]. Zero salt, heat, and momentum flux boundary conditions are applied on the northern and southern walls of the domain. Periodic boundary conditions are applied to all fields in the

= 2 π / L y . Boundary conditions were changed to free slip in the vertical but kept periodic in the horizontal. This created two opposing surface bound jets with a constant vertical shear in the x – z plane. The jet’s shear was matched to the rms vertical shear of the internal waves in the primary simulations. Two simulations with (i) a s = 0.002 m s −1 and (ii) a s = 0.02 m s −1 resulted in vertical jet shears of −1.3 × 10 −4 s −1 and −1.3 × 10 −3 s −1 , respectively, where (ii) was

= 2 π / L y . Boundary conditions were changed to free slip in the vertical but kept periodic in the horizontal. This created two opposing surface bound jets with a constant vertical shear in the x – z plane. The jet’s shear was matched to the rms vertical shear of the internal waves in the primary simulations. Two simulations with (i) a s = 0.002 m s −1 and (ii) a s = 0.02 m s −1 resulted in vertical jet shears of −1.3 × 10 −4 s −1 and −1.3 × 10 −3 s −1 , respectively, where (ii) was