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Paola Cessi and Christopher L. Wolfe

(and, less importantly, no-slip boundary), and there must be no flux of buoyancy into the wall. In general, these conditions are fulfilled in thin boundary layers where geostrophy is broken. In our numerical simulations we find that in these thin boundary layers, Reynolds stresses become large in the alongshore momentum balance, while the across-shore balance remains geostrophic. In this way, the velocity along the boundary is geostrophic but the component normal to the boundary is not. This is the

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Michael A. Spall

with a uniform heat flux of 500 W m −2 ( Fig. 1 ). The Coriolis parameter is f 0 = 10 −4 s −1 and uniform. The inflowing velocity has a maximum value of 30 cm s −1 at the surface on the southern boundary and decreases linearly to zero at 500-m depth and at the northern side of the domain. 1 The model is initialized with this velocity field and a geostrophically balanced density field and sea surface height. The inflow conditions are steady in time, and the outflow boundary conditions for

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Baylor Fox-Kemper and Raffaele Ferrari

eddy-parameterizing model can the shear be quantified. e. Boundary conditions and global constraints The treatment of eddies here is more realistic than in previous models. However, it should be noted that inertial terms are neglected by assuming that eddy and mean scales exceed the deformation radius. Relaxing this constraint defies eddy parameterization, because the neglected terms (e.g., ∇ K i ) are unlikely to be downgradient or local ( Holland and Rhines 1980 ; Berloff 2005 ). Global

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R. M. Samelson

the horizontal transport so that Then where the natural no-normal-flow conditions imply ∇Φ · n = 0 and Ψ = const on the contiguous rigid boundaries, and J( a , b ) = a x b y − a y b x . Suppose that the contiguous boundaries are broken at southern latitudes by a circumpolar channel with periodic boundary conditions at x = { x W , x E } over the latitude interval y 1 < y < y 2 and the depth range 0 < z < − h s , where the sill depth h s is a given constant ( Fig. 1 ). An

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Onno Bokhove and Vijaya Ambati

evolution of this potential vorticity weighted by the depth H follows by scaling with (4) and rewriting the nondimensionalized form of the system (1) into with transport velocity U , two-dimensional curl operator ∇ ⊥ = (−∂ y , ∂ x ) T , and parameter A cylindrical domain Ω is considered with Ψ = 0 at the boundary ∂Ω: r = R and initial conditions ξ = ξ ( x , y , 0); we also used ξ ≈ 1/ H to simplify forcing and damping terms. The numerical (dis)continuous Galerkin finite

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J. A. Whitehead

top and another at the bottom allowed circulation between the two test tanks. One storage tank containing hot salty water along with its test tank represented the tropical ocean. The other storage–test tank pair with cold and freshwater represented a polar region. The model illustrated the properties of convection with combined heat flux and freshwater flux boundary conditions. As the governing parameters (temperature and salinity differences between the two storage tanks) were slowly changed

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K. Shafer Smith and John Marshall

well known, writing = − κ q ∇ Q with κ q a constant violates the kinematic requirement (3.3) : if β is not negligible, then ∫ ∇ Q dz ≠ 0 (the stretching part of the mean PV gradient itself does integrate to zero, if the mean flow satisfies the same boundary conditions as the eddies). Therefore, κ q must be a function of depth. Indeed, this constraint was used by Marshall (1981) to help guide the choice of vertical variation of the diffusivity in a zonal-average model of the ACC

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Yafang Zhong and Zhengyu Liu

their valuable comments and thoughtful suggestions. This work is supported by DOE and NOAA. REFERENCES Arzel , O. , T. Huck , and A. Colin De Verdière , 2006 : The different nature of the interdecadal variability of the thermohaline circulation under mixed and flux boundary conditions. J. Phys. Oceanogr. , 36 , 1703 – 1718 . Auad , G. , 2003 : Interdecadal dynamics of the North Pacific Ocean. J. Phys. Oceanogr. , 33 , 2483 – 2503 . Barsugli , J. J. , and D. S. Battisti

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Carl Wunsch and Patrick Heimbach

) to earlier near-optimized solutions (v2.216 and v3.22) display nearly indistinguishable results, supporting the inference of a now stable estimate. Readers unfamiliar with the details of the ECCO–GODAE methods need only be aware that the estimates used here are computed from a freely running forward model, whose initial–boundary conditions have been adjusted by least squares so that the model comes as close as practical to the data within estimated error estimates: unlike some other approaches

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