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Xia Liu, Mu Mu, and Qiang Wang

Eq. (3) is called the CNOP. To calculate the CNOP, the nonlinear optimization system is built based on the ROMS and the spectral projected gradient (SPG) algorithm ( Birgin et al. 2000 ). The detailed steps of the algorithm used to compute the CNOP are shown in the appendix . In the following, we describe the major preparations of calculating the CNOP: Selection of the reference state. We focus on the perturbation that triggers the LM from the NLM path in this paper; thus the NLM path is

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R. M. Holmes and L. N. Thomas

(see section 5 ). This suggests that the mixing scheme is not able to provide enough mixing at high in order to restrict the to negative or near-zero daily averaged values. To evaluate the influence of this issue on our results, we constructed an algorithm to enforce marginal stability offline for all regions in the simulations where . The algorithm is similar to the Price et al. (1986) mixing scheme and iteratively applies vertical fluxes of temperature, salinity, and momentum in a Prandtl

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Masoud Jalali, Vamsi K. Chalamalla, and Sutanu Sarkar

following procedure is based on the discussion in Klymak et al. (2008) , and the associated algorithm is given in the appendix (algorithm 1). The density profile containing inversions is resorted into a stable monotonic density profile. Note that if the vertical grid is not constantly spaced, an interpolation of the density profile to an evenly spaced grid is performed to conserve the average density of the profile in the resorting process. The Thorpe-scale displacement is given by the difference in

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Juan A. Saenz, Rémi Tailleux, Edward D. Butler, Graham O. Hughes, and Kevin I. C. Oliver

the two tasks simultaneously. As we justify below, such a divorce is not only feasible but also essential for elucidating the nature of the difficulties associated with the nonlinearity of the equation of state and its binary character through the dependence on temperature and salinity. From a computational viewpoint, such a divorce also proves essential for understanding how to design algorithms that are computationally more efficient and parallelizable than sorting-based approaches. In this

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

North Atlantic Ocean to successive child grids with Δ x ≈ 1.5 km, Δ x ≈ 500 m, and finally Δ x ≈ 150 m. The procedure is offline, one-way nesting from larger to finer scales without feedback from the child grid solution onto the parent grid ( Penven et al. 2006 ). The boundary condition algorithm consists of a modified Flather-type scheme for the barotropic mode ( Mason et al. 2010 ) and Orlanski-type scheme for the baroclinic mode (including T and S ; Marchesiello et al. 2001 ). Bathymetry

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Katherine McCaffrey, Baylor Fox-Kemper, and Gael Forget

created, and the structure function was calculated. A noise floor for the structure function including the error from the climatology was also considered, using the total standard deviation, . This more realistic noise floor of O (10 −4 ) is still below the majority of the structure functions calculated, allowing this analysis of turbulence from Argo data to continue without fear of data measurement errors interfering. APPENDIX D Line-Fitting Algorithm To quantify the differences among structure

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

be resolved in order to simultaneously capture both Langmuir turbulence and submesoscale eddies. To meet this challenge, Malecha et al. (2013) have proposed an asymptotically motivated multiscale numerical algorithm to simulate Langmuir cell dynamics at ocean submesoscales. In the present study, we instead use large-eddy simulation (LES)—where an attempt is made to resolve all dynamically active scales—in order to address the following important questions: To what extent does vertical mixing

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Vamsi K. Chalamalla and Sutanu Sarkar

. Numerical method The simulations use a mixed, spectral–finite difference algorithm. Derivatives in the streamwise and spanwise directions are treated with a pseudospectral method and derivatives in the vertical direction are computed with second-order finite differences. A staggered grid is used in the wall-normal direction. A low-storage, third-order Runge–Kutta–Wray method is used for time stepping, and viscous terms are treated implicitly with the Crank–Nicolson method. The code is parallelized using

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