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Ricardo P. Matano and Elbio D. Palma

presented numerical simulations of BTP showing no upstream spreading. They argued that a “realistic” model setup including a long estuary, a canyon at the mouth of the estuary, and the use of periodic (cyclic) boundary conditions prevents this phenomenon. In this article, we show that the lack of upstream spreading in the P11 simulations is an artifact created by the model’s boundary conditions—specifically, that simulations in periodic or closed domains develop a spurious cyclonic current that

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E. M. Lane, J. M. Restrepo, and J. C. McWilliams

alternative scalings and other averaging frameworks. In section 7 we summarize our view of the important elements in wave–current interaction. 2. Preliminaries a. Basic equations In the absence of body forces and dissipation, the equations of motion are with tracer equation The surface boundary conditions are and the bottom boundary condition is The physics and well-posedness considerations determine the lateral boundary conditions. The Eulerian velocity vector is U = ( Q , W ). The density is

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W. D. Smyth

frictionless, ∂ u /∂ z = ∂ υ /∂ z = 0. Conditions of constant temperature and salinity, b i = 0, are imposed. It will be seen that the boundaries have little effect on interleaving modes but they destabilize two additional classes of modes that must be carefully distinguished as their oceanic significance is uncertain. b. Flow decomposition Motions are assumed to take place in a frontal zone of scale sufficiently large that it can be represented locally by uniform property gradients. The fields are

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David W. Pierce

1552 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 26Reducing Phase and Amplitude Errors in Restoring Boundary Conditions DAVID W. I>IERCEClimate Research Division, Scripps Institution of Oceanography. La Jolla, California(Manuscript received 11 August 1995, in final form 21 February 1996)ABSTRACT Restoring boundary conditions are often used to drive ocean general circulation models

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I. Shulman and James K. Lewis

1006 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME25Optimization Approach to the Treatment of Open Boundary Conditions I. SHULMANCenter for Ocean and.4tmospheric Modeling, University of Southern Misst~sippL Stennis Space Center, Mississippi JAMES K. LEW~SOcean Physics Research and Development, Long Beach, Mississippi15 February 1994 and 26 August 1994 A solution to an

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Nirnimesh Kumar, Douglas L. Cahl, Sean C. Crosby, and George Voulgaris

observations is not sufficient to provide adequate wave boundary conditions for relatively large-scale (10 2 –10 3 km), regional, coupled ocean circulation and wave model simulations or to estimate Stokes drift with sufficient spatial resolution. On the other hand, large-scale, near-surface Lagrangian (i.e., Eulerian mean + Stokes drift) current estimates are routinely obtained through the use of high-frequency (HF) radars ( Harlan et al. 2010 ). These current estimates can be assimilated into numerical

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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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Jae-Yul Yun, James M. Price, and Lorenz Magaard

crossflow structure function Φ n = A n e ry , ϕ n was substituted into the potential vorticity equation in the rotated Cartesian coordinate system. Then the amplitude ratio A 2 / A 1 was obtained for each layer, and the two amplitude ratios from the upper and lower layer equations were combined to yield a relation for the crossflow wavenumber. Assuming an infinitely wide ocean, the boundary conditions for a crossflow structure function Φ n were: Φ n → 0 as y = H → ∞ (or y = − H → −∞) and d

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Peter D. Killworth

requires boundary conditions at rigid surfaces. The horizontal component of u + is related to the horizontal components of u ′ and u , and so vanishes on vertical sidewalls. The value of w + , the vertical component of u + , at surface or floor is less obvious. (Unlike the horizontal component of the quasi-Stokes velocity, there is no kinematic reason for w + to vanish, since w + exists to satisfy continuity.) The problems are best seen by considering recent direct eddy

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Paola Cessi, Christopher L. Wolfe, and Bonnie C. Ludka

flow allows a meaningful distinction between the MOC and the ROC. We find that the advection by the barotropic flow opposes the poleward transport by the MOC in the subtropical gyre and reinforces it in the subpolar gyre. The net result is a shift of the maximum of the ROC poleward relative to the MOC. This shift is also found in the eddy-resolving computations reported in Wolfe and Cessi (2010) . 2. The model equations and boundary conditions We employ the planetary geostrophic equations

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