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Laurence Armi and Henry Stommel

Abstract

Data from four cruises to the “β-triangle” centered at 27°N, 32°30′W were smoothed by fitting second-degree polynomials at each of about 30 different density surfaces. The density intervals were Δσp=0.3‰, corresponding to about 50 db intervals in pressure. From the polynomials, determination was made of central values, horizontal derivatives and Laplacians of the fields of pressure, salt, oxygen and dynamic height. In addition, maps of the fits and deviations of each nation from the smoothed fits were produced.

From the steady advective diffusive equation and the smoothed fits to the age oxygen and dynamic height fields, the lateral isopycnal diffusivity as estimated to be K H ∼ 0.5 × 103 m2 s−1. Although the salt field was reasonably stable from cruise to cruise, the variability of the baroclinic velocity shear was found to be as large as the baroclinic shear itself. The maps suggest a wobble of the gyre. The standard deviation of the fluctuations at each nation from the smoothed fits, when normalized by the gradient l′ = s′/|∇S′| gives the mixing length of the horizontal turbulence. This was found to be ∼80 km, presumably due to mesoscale turbulence. These fluctuations were all Found, with one exception, to be normally distributed, suggesting the suitability in the subtropical gyre of a Fickian gradient transport diffusion. The one notable exception to the normal distribution was the discovery at one out of 143 stations of relatively undiluted Mediterranean water. The anomaly of salinity was as large as 0.65‰ or 20 standard deviations. A crude estimate suggests that the flux divergence due to the anomaly is approximately an order of magnitude less than either the advective or diffusive flux divergence.

There is a range of densities over which horizontal gradients of potential vorticity are small or nearly indeterminate. This range of densities intersects the ocean surface where the wind stress curl produces downwelling at the base of the Ekman layer. Deep density surface that intersect farther north at upwelling latitudes have strong potential vorticity gradients.

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Pierre Flament and Laurence Armi

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With the objective of measuring convergence directly to confirm previous observations of frontal subduction, a seaward upwelling jet off central California was studied using satellite infrared images, hydrographic sections, ship drift, and clusters of surface drifters. The cyclonic front of the jet was sharper than 1 km, resulting in a shear several times larger than f. A cross-frontal convergence of 7 cm s−1 over the width of the front (equivalent to 0.8f) was visible as a 20-m-wide accumulation of debris. The sharpness of the front lasted at least for a day. Away from the cyclonic front, the divergence of the flow was small and the shear was less than 0.6f. Thermohaline layers, originating at the front, were interleaving along isopycnals, suggesting water subduction. It is proposed that the asymetry between anticyclonic and cyclonic sides of the jet, and the strong convergence at the cyclonicfront, resulted from a frictionally driven ageostrophic secondary circulation superimposed on the geostrophic flow.

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Laurence Armi and Walter Zenk

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Isolated compact anticyclonic eddies or salt lenses were found in the Canary Basin. Hydrographic surveys of three such lenses show large anomalies of salinity and temperature (∼0.8, 2.5°C). They are centered at ∼1100 m, have a vertical extent of up to 900 m and radii of ∼50 km. Current meter records indicate anticyclonic velocities up to 29 cm s−1. Fine structure with vertical scales of ∼20 m and less, possibly due to intrusive decay, appears at the outer edges of the lenses whereas the centers are free of such structure. The probability of finding a salt lens at any station in the Canary Basin is fairly high (∼0.08).

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Libe Washburn and Laurence Armi

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Frontal instabilities were observed along a density front on the cyclonic boundary of an upwelling filament that formed north of Pt. Arguello, California in October 1983. Observations of the instabilities were conducted using satellite sea surface temperature images and in situ sampling. The instabilities formed on the southern (cyclonic) boundary of the filament at a wavelength of about 20 km and consisted of two lobes, one warm and one cool, each with a width of about 4 km. The time scale for formation of the instabilities is about 1 day. Near-surface distributions of temperature, salinity, and density within the cool lobes of the instabilities are consistent with local upwelling at the rate of about 30 m d−1. A simple model based on conservation of potential vorticity is presented, which accounts for the observed upwelling. Based on isopycnal displacements and the distribution of salinity, the signature of the instabilities appears to be confined to the upper 50 m of the water column.

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Laurence Armi and Dale B. Haidvogel

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The hypothesis that variations in eddy diffusivity may account for some aspects of the observed distributions of oceanic scalars is examined by generating solutions to the diffusion equation with spatially variable and/or anisotropic eddy diffusivity. In particular, the solutions generated here demonstrate how a purely diffusive field, with variable and anisotropic diffusion, can itself generate tongue-like property distributions. Although tongues of various oceanic properties have often been interpreted as due primarily to advective effects, such interpretations must be viewed with caution when the gradients of eddy diffusivity are comparable to, or greater than, the local velocity field.

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Patrick F. Cummins and Laurence Armi

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The time-dependent response of upstream undular bores and internal hydraulic jumps from initial formation to eventual release is documented. Two events, characterized by qualitatively different responses, are discussed. In the first case, an undular bore develops upstream of the sill crest. This disturbance remains upstream through the ebb tidal flow but is transformed to a hydraulic jump as its amplitude increases. Toward the end of ebb tide, it is released and subsequently disperses into a group of solitary-like waves. During the second event, an upstream jump also develops at an early stage of the tide. However, it is subsequently swept downstream by the tidal flow such that the upstream region then appears featureless. Approaching slack tide, as an exchange flow becomes established, a large bore or gravity current is emitted. The different responses seen in these two events are interpreted in terms of the Froude number associated with the near-surface stratification.

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Lawrence J. Pratt and Laurence Armi

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The hydraulics of flow contained in a channel and having nonuniform potential vorticity is considered from a general standpoint. The channel cross section is rectangular and the potential vorticity is assumed to be prescribed in terms of the streamfunction. We show that the general computational problem can be expressed in two traditional forms, the first of which consists of an algebraic relation between the channel geometry and a single dependent flow variable and the second of which consists of a pair of quasi-linear differential equations relating the geometry to two dependent flow variables. From these forms we derive a general “branch condition” indicating a merger of different solutions having the same flow rate and energy and show that this condition implies that the flow is critical with respect to a certain long wave. It is shown that critical flow can occur only at the sill in a channel of constant width (with one exception) at a point of width extremum in a flat bottom channel. We also discuss the situation in which the fluid becomes detached from one of sidewalls.

An example is given in which the potential vorticity is a linear function of the streamfunction and the rotation rate is zero, a case which can be solved analytically. When the potential vorticity gradient points downstream, allowing propagation of potential vorticity waves against the flow, multiple pairs of steady states are possible, each having a unique modal structure. Critical control of the higher-mode solutions is primarily over vorticity, rather than depth. Flow reversals arise in some situations, possible invalidating the prescription of potential vorticity.

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Laurence Armi and Georg J. Mayr

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Cross-barrier density differences and westerly flow established a descending stratified flow across the Sierra Nevada (United States) on 9–10 April 2006. Downslope flow and an internal hydraulic jump occurred only when the potential temperature of the westerly descending flow was at least as cold as the existing upvalley-flowing valley air mass. The onset was observed in sequences of visible satellite images and with weather stations. The University of Wyoming King Air flew through the stratified flow and imaged the structure of the internal hydraulic jump with its cloud radar. Shear-layer instabilities, which first developed near the jump face, grew and paired downstream, mixing the internal hydraulic jump layer. A single wave response to the downslope flow and internal hydraulic jump was observed aloft, but only after the downslope flow had become established.

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Georg J. Mayr and Laurence Armi

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The potential for a stably stratified air mass upstream of the Sierra Nevada (California) to descend as foehn into the nearly 3-km-deep Owens Valley was studied for the 2 March 2006 case with observations from sondes, weather stations, and two aircraft flights. While upstream conditions remained almost unchanged throughout the day, strong diurnal heating on the downstream side warmed the valley air mass sufficiently to permit flow through the passes to descend to the valley floor only in the late afternoon. Potential temperatures of air crossing the crest were too warm to descend past a virtual floor formed by the strong potential temperature step at the top of the valley air mass, the height of which changed throughout the day primarily due to diurnal heating in the valley. The descending stably stratified flow and its rebound with vertical velocities as high as 8 m s−1 were shaped by the underlying topography and the virtual valley floor.

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Laurence Armi and Georg J. Mayr

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A combination of real and virtual topography is shown to be crucial to describe the essentials of stratified flow over mountain ranges and leeside valleys. On 14 March 2006 [Intensive Observation Period 4 of the Terrain-Induced Rotor Experiment (T-REX)], a nearly neutral cloud-filled layer, capped by a strong density step, overflowed the Sierra Nevada and separated from the lee slope upon encountering a cooler valley air mass. The flow in this lowest layer was asymmetric across and hydraulically controlled at the crest with subcritical flow upstream and supercritical flow downstream. The density step at the top of this flowing layer formed a virtual topography, which descended 1.9 km and determined the horizontal scale and shape of the flow response aloft reaching into the stratosphere. A comparison shows that the 11 January 1972 Boulder, Colorado, windstorm case was similar: hydraulically controlled at the crest with the same strength and descent of the virtual topography. In the 18 February 1970 Boulder case, however, the layer beneath the stronger virtual topography was subcritical everywhere with a symmetric dip across the Continental Divide of only 0.5 km. In all three cases, the response and strength of the flow aloft depend on the virtual topography. The layer up to the next strong density step at or near the tropopause was hydraulically supercritical for the 18 February case, subcritical for the T-REX case, and critically controlled for the 11 January case, for which a weak density step and isolating layer aloft made possible the strong response aloft for which it is famous.

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