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Michael A. Spall

-layer analytic model was developed to aid in the understanding of what controls the basic characteristics of the numerical model results. The assumption that the halocline is maintained by lateral eddy fluxes from the boundary current and vertical diffusion in the interior provides the necessary conditions to obtain analytic solutions for the halocline depth, surface salinity, and freshwater content. A single nondimensional number controls most aspects of the analytic solution. Making use of an empirical

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Catherine A. Vreugdenhil, Andrew McC. Hogg, Ross W. Griffiths, and Graham O. Hughes

-term equilibrium states and consider the time scales of adjustment using complementary insights from conceptually simple laboratory experiments and a complex numerical ocean model. Our focus on the long-term adjustment time scales follows previous results in a thermally driven circulation that shows different scaling of equilibration times for boundary conditions of imposed flux and of imposed surface buoyancy such that the two time scales can be substantially different (Griffiths et al. 2013) . The results

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Nicolas Grisouard and Leif N. Thomas

to retain is n = 1, which corresponds to the incident wave for our configuration (e.g., Fig. 3 ). All signals created by the reflection have to decrease with depth; thus, the three other depth-increasing solutions ( n = 6, 7, 8) can be discarded. The other solutions we retain are therefore the viscosity-modified reflected wave ( n = 2) as well as the solutions n = 3, 4, 5. Constraining the coefficients in Eq. (17) requires knowledge of the boundary conditions. In this section, we

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Vamsi K. Chalamalla and Sutanu Sarkar

(slope-parallel plane); expressions for calculating these coefficients are described by Gayen et al. (2010) . For the DNS, τ and λ are zero. b. Boundary conditions No slip boundary conditions are imposed at the bottom boundary for u s , υ s , and w s . The total density can be written as the sum of the background density and the density deviation: The zero mass flux boundary condition is imposed at the sloping bottom, resulting in the density deviation at the sloping boundary given by c

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Jonathan Gula, M. Jeroen Molemaker, and James C. McWilliams

flow is decomposed into a divergent and a nondivergent part. This decomposition is done by solving a Poisson equation for the divergence of the flow using a multigrid solver with Dirichlet boundary conditions. We get the corresponding nondivergent part of the flow by taking the difference between the total and the divergent part. The nondivergent part of the flow is not formally equal to the geostrophic part but can be considered as a proxy at such scales ( Molemaker et al. 2010 ). The nondivergent

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Peter E. Hamlington, Luke P. Van Roekel, Baylor Fox-Kemper, Keith Julien, and Gregory P. Chini

in McWilliams et al. (1997) and Sullivan et al. (2007) . Spatial derivatives are calculated spectrally in the horizontal ( x and y ) directions and using either second-order (for u ) or third-order (for tracers such as θ or b ) finite differences in the vertical ( z ) direction. Periodic boundary conditions are used for u and θ in the horizontal directions. The vertical velocity is zero at both the top and bottom boundaries, and horizontal velocities are determined by wind stress and

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Masoud Jalali, Vamsi K. Chalamalla, and Sutanu Sarkar

, and derivatives in the streamwise and vertical directions are computed with a second-order, central, finite-difference scheme. A third-order Runge–Kutta–Wray time advancement is used within a fractional step method, and a multigrid solver is employed to solve the Poisson equation for pressure. A sponge layer or Rayleigh damping is added at the left and right boundaries to minimize spurious reflections. Boundary conditions, sponge layer, and numerical methods are designed and implemented along the

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Roy Barkan, Kraig B. Winters, and Stefan G. Llewellyn Smith

wave interactions in the interior, instability of geostrophic motions, and direct interactions with side and bottom boundaries ( Müller et al. 2005 ; Ferrari and Wunsch 2010 ). About 90% of the E k in the oceans is stored in the geostrophic eddy field ( Ferrari and Wunsch 2009 ) and, given this large fraction, we focus here on the “instability” pathway to dissipation. Geostrophic eddies are formed, primarily, via baroclinic instability of large-scale ocean currents that are in approximate

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R. M. Holmes and L. N. Thomas

a set of 3D nested simulations of the equatorial Pacific performed with the Regional Ocean Modeling System (ROMS) ( Shchepetkin and McWilliams 2005 ). The outer nest is a Pacific basinwide simulation over the region 30°S to 30°N, −240° to −70°E with 0.25° horizontal resolution, 50 vertical levels, and a time step of 10 min. It was spun up for 5 yr, initialized from a previous 10-yr spinup run ( Holmes et al. 2014 ). Daily climatological surface forcing, initial conditions, and boundary

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Ryan Abernathey and Paola Cessi

maintains a meridional sea surface temperature gradient. For simplicity, we make the gradient linear, with magnitude Δ θ / L y . A quasi-adiabatic interior, with negligibly weak diapycnal mixing. For the case with topography, a large topographic obstruction in the abyss. Given these conditions, the system will equilibrate with sloping isopycnals of the thermocline overlying a weakly stratified abyss. The slope of the isopycnals determines the depth of the thermocline at the northern boundary, which we

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