Critical control of zonal jets by bottom topography

The nonlinear influence of isolated topography on an equivalent barotropic, quasigeostrophic jet is considered. The flow depends on several dimensional parameters including the mass flux Q, the mean layer thickness H, the planetary potential vorticity gradient β the inertial boundary layer thickness (u0/β)½ and a parameter a – c measuring the north-south potential vorticity difference across the jet. Eastward jets can achieve one of two steady forms, the first supercritical and the second subcritical with respect to upstream propagation of a long potential vorticity wave. An isolated topographic feature such as a ridge can cause the jet to undergo transition from subcritical to supercritical flow and thereby achieve a steady state analogous to hydraulically controlled open channel flow. In a critically-controlled state the values of Q, a-c, H, and (u0/β)½ cannot be specified independently of the topographic parameters and the topography thereby exerts an \u27upstream influence\u27 which is felt by the general circulation of the ocean as a whole. Critically-controlled states also experience topographic form drag, whereas noncontrolled states experience none. The form drag is determined by the upstream potential vorticity distribution of the flow and the critical jet width, suggesting that this type of drag might be estimated in practice by a combination of hydrographic data and satellite imagery. The Antarctic Circumpolar Current is discussed as a possible example

A characterization of the power of vector machines

A new formal model of register machines is described. Registers contain bit vectorswhich are manipulated using bitwise Boolean operations and shifts. Our main results relate the language recognition power of such vector machines to that of Turing machines. A class of vector machines is exhibited for which time on a vector machine supplies, to within a polynomial, just as much power as space on a Turing machine. Moreover, this is true regardless of whether the machines are deterministic or non-deterministic

On the stability of ocean overflows

Author Posting. © Cambridge University Press, 2008. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 602 (2008): 241-266, doi:10.1017/S0022112008000827.The stability of a hydraulically driven sill flow in a rotating channel with smoothly varying cross-section is considered. The smooth topography forces the thickness of the moving layer to vanish at its two edges. The basic flow is assumed to have zero potential vorticity, as is the case in elementary models of the hydraulic behaviour of deep ocean straits. Such flows are found to always satisfy Ripa's necessary condition for instability. Direct calculation of the linear growth rates and numerical simulation of finite-amplitude behaviour suggests that the flows are, in fact, always unstable. The growth rates and nonlinear evolution depend largely on the dimensionless channel curvature κ=2αg′/f2, where 2α is the dimensional curvature, g′ is the reduced gravity, and f is the Coriolis parameter. Very small positive (or negative) values of κ correspond to dynamically wide channels and are associated with strong instability and the breakup of the basic flow into a train of eddies. For moderate or large values of κ, the instability widens the flow and increases its potential vorticity but does not destroy its character as a coherent stream. Ripa's condition for stability suggests a theory for the final width and potential vorticity that works moderately well. The observed and predicted growth in these quantities are minimal for κ≥1, suggesting that the zero-potential-vorticity approximation holds when the channel is narrower than a Rossby radius based on the initial maximum depth. The instability results from a resonant interaction between two waves trapped on opposite edges of the stream. Interactions can occur between two Kelvin-like frontal waves, between two inertia–gravity waves, or between one wave of each type. The growing disturbance has zero energy and extracts zero energy from the mean. At the same time, there is an overall conversion of kinetic energy to potential energy for κ>0, with the reverse occurring for κ<0. When it acts on a hydraulically controlled basic state, the instability tends to eliminate the band of counterflow that is predicted by hydraulic theory and that confounds hydraulic-based estimates of volume fluxes in the field. Eddy generation downstream of the controlling sill occurs if the downstream value of κ is sufficiently small.This work was supported by the National Science Foundation (Grant OCE- 0525729)

Generalized conditions for hydraulic criticality of oceanic overflows

Author Posting. © American Meteorological Society, 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 35 (2005): 1782–1800, doi:10.1175/JPO2788.1.Two methods for assessing the hydraulic criticality of an observed or modeled overflow are discussed. The methods are valid for single-layer deep flows with arbitrary potential vorticity and cross section. The first method is based on a purely steady view in which the flow at a given section is divided up into a group of “streamtubes.” A hydraulic analysis requires an extension of Gill’s functional formulation to systems with many degrees of freedom. The general form of the critical condition and associated compatibility condition for such a system are derived and applied to the streamtube model. As an aside, it is shown by example that Gill’s original critical condition can fail to capture all possible critical states, but that this problem is fixed when the multivariable approach is used. It is also shown how Gill’s method can be applied to certain dispersive or dissipative systems. The second method of assessing criticality involves direct calculation of linear, long-wave speeds using a time-dependent version of the streamtube model. This approach turns out to be better suited to the analysis of geophysical datasets. The significance of the local Froude number F is discussed. It is argued that F must take on the value unity at some point across a critical section.This work was supported by National Science Foundation Grant OCE-0132903 and the Office of Naval Research under Grant N00014-01-1- 0167

Comparison of measured and modeled ambient hydrogen sulfide concentrations near a 4000 head swine facility

Air dispersion models are currently being used to regulate agriculture facilities and/or assess their environmental impact. As such, it is critical that these models accurately reflect these impacts. Meteorological conditions, hydrogen sulfide emissions, and downwind hydrogen sulfide concentrations at a four barn, 4000-head, swine finishing facility in Northeast Iowa were measured for a three week period in October 2003. Meteorological conditions and hydrogen sulfide emissions from the barns were used as inputs into two air dispersion models, INPUFF-2 and AERMOD. Model results were compared to measured results at eighteen receptor locations. Results indicate the models did not accurately predict spatial and temporal ambient concentrations. However, a rank order comparison of data (not matched in space and time) shows the models may be useful in predicting maximum concentrations over a period of time

Transport and dynamics of the Panay Sill overflow in the Philippine Seas

Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 2679–2695, doi:10.1175/2010JPO4395.1.Observations of stratification and currents between June 2007 and March 2009 reveal a strong overflow between 400- and 570-m depth from the Panay Strait into the Sulu Sea. The overflow water is derived from approximately 400 m deep in the South China Sea. Temporal mean velocity is greater than 0.75 m s−1 at 50 m above the 570-m Panay Sill. Empirical orthogonal function analysis of a mooring time series shows that the flow is dominated by the bottom overflow current with little seasonal variance. The overflow does not descend below 1250 m in the Sulu Sea but rather settles above high-salinity deep water derived from the Sulawesi Sea. The mean observed overflow transport at the sill is 0.32 × 106 m3 s−1. The observed transport was used to calculate a bulk diapycnal diffusivity of 4.4 × 10−4 m2 s−1 within the Sulu Sea slab (575–1250 m) ventilated from Panay Strait. Analysis of Froude number variation across the sill shows that the flow is hydraulically controlled. A suitable hydraulic control model shows overflow transport equivalent to the observed overflow. Thorpe-scale estimates show turbulent dissipation rates up to 5 × 10−7 W kg−1 just downstream of the supercritical to subcritical flow transition, suggesting a hydraulic jump downstream of the sill.This work was supported by the Office of Naval Research Grant N00014-09-1-0582 to Lamont-Doherty Earth Observatory of Columbia University; Grants ONR-13759000 and N00014-09-1-0582 to the Woods Hole Oceanographic Institution; Grant ONR-N00014-06-1-0690 to Scripps Institute of Oceanography; and a National Defense Science and Engineering Graduate Fellowship

Analysis of tidal flows through the Strait of Gibraltar using Dynamic Mode Decomposition

The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid motion. In this study, we aim to uncover the underlying physics of these phenomena within 3D MIT general circulation model simulations, including waves, eddies, and gyres. To achieve this, we employ Dynamic Mode Decomposition (DMD) to break down simulation snapshots into Koopman modes, with distinct exponential growth/decay rates and oscillation frequencies. Our objectives encompass evaluating DMD's efficacy in capturing known features, unveiling new elements, ranking modes, and exploring order reduction. We also introduce modifications to enhance DMD's robustness, numerical accuracy, and robustness of eigenvalues. DMD analysis yields a comprehensive understanding of flow patterns, internal wave formation, and the dynamics of the Strait of Gibraltar, its meandering behaviors, and the formation of a secondary gyre, notably the Western Alboran Gyre, as well as the propagation of Kelvin and coastal-trapped waves along the African coast. In doing so, it significantly advances our comprehension of intricate oceanographic phenomena and underscores the immense utility of DMD as an analytical tool for such complex datasets, suggesting that DMD could serve as a valuable addition to the toolkit of oceanographers

Circulation and exchange in choked marginal seas

Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 2639-2661, doi:10.1175/2008JPO3946.1.A theory for the exchange between a rotating, buoyancy-forced marginal sea and an ocean is developed and tested numerically. Cooling over the marginal sea leads to sinking and sets up a two-layer exchange flow, with a warm surface layer entering from the ocean and a cool layer exiting at depth. The connecting strait is sufficiently narrow and shallow to cause the exchange flow to be hydraulically controlled. The incoming surface layer forms a baroclinically unstable boundary current that circles the marginal sea in a cyclonic sense and feeds heat to the interior by way of eddies. Consistent with the overall heat and volume balances for the marginal sea, there is a continuous family of hydraulically controlled states with critical flow at the most constricted section of the strait. Included in this family is a limiting “maximal-exchange” solution with two sections of hydraulic control in the strait and with fixed layer depths at the most constricted section. The state of exchange for a given forcing is predicted using a theory that assumes energy conservation over a certain path connecting the strait to the marginal sea or, in some cases, the ocean. Depending on the configuration of the exchange, long-wave information may be blocked from entering the strait from the marginal sea, from the open ocean, or both. The scenario that holds determines what is predicted and what needs to be input. Numerical tests of the prediction for the temperature difference and the state of exchange are carried out for straits with a pure contraction in width and for a constant width strait with a topographic sill. The comparison is reasonable in most cases, though the numerical model is not able to reproduce cases of multiple states predicted by the theory for certain forcing values. The analytical model is an alternative to the Price and Yang and Siddall et al. models of a marginal sea outflow.This work was supported by the National Science Foundation under Grants OCE-0525729 and OCE-0423975

Organic Carbon, Hydrogen, and Nitrogen Concentrations in Surficial Sediments from Western Long Island Sound, Connecticut and New York

Total organic carbon, hydrogen, and nitrogen (CHN) analyses were performed on 147 surficial sediment samples from study areas off the Norwalk Islands and Milford, Connecticut, in western Long Island Sound. The CHN data and gross lithologic descriptions of the sediments are reported herein. The concentrations of total organic carbon (TOC), hydrogen, and nitrogen in these samples average 1.54, 1.40, and 0.17 weight percent, respectively. The individual CHN concentrations vary inversely with grain size, with CHN values increasing with the percent fines. Increasing nutrient inputs and decreasing circulation cause TOC and nitrogen values to generally increase westward within the Sound. C/N molar elemental ratios suggest that, except for the shoreward northwestern corner of the Norwalk Islands survey site, marine phytoplankton are probably the primary source of sedimentary organic matter in the study areas. Concentrations of the sedimentary organic matter are significantly higher in the spring than in the late summer, suggesting that these concentrations vary seasonally