Mathematical Study of Degenerate Boundary
                    Layers: A Large Scale Ocean Circulation
                    Problem

Abstract A new basin-wide oscillation of the Mediterranean Sea is identified and analyzed using sea level observations from the Ocean Topography Experiment (TOPEX)/Poseidon satellite altimeter and a numerical ocean circulation model. More than 50% of the large-scale, nontidal, and non-pressure-driven variance of sea level can be attributed to this oscillation, which is nearly uniform in phase and amplitude across the entire basin. The oscillation has periods ranging from 10 days to several years and has a magnitude as large as 10 cm. The model suggests that the fluctuations are driven by winds at the Strait of Gibraltar and its neighboring region, including the Alboran Sea and a part of the Atlantic Ocean immediately to the west of the strait. Winds in this region force a net mass flux through the Strait of Gibraltar to which the Mediterranean Sea adjusts almost uniformly across its entire basin with depth-independent pressure perturbations. The wind-driven response can be explained in part by wind setup; a near-stationary balance is established between the along-strait wind in this forcing region and the sea level difference between the Mediterranean Sea and the Atlantic Ocean. The amplitude of this basin-wide wind-driven sea level fluctuation is inversely proportional to the setup region’s depth but is insensitive to its width including that of Gibraltar Strait. The wind-driven fluctuation is coherent with atmospheric pressure over the basin and contributes to the apparent deviation of the Mediterranean Sea from an inverse barometer response.

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Pressure gradient effects on the large-scale structure of turbulent boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.531 ◽

2013 ◽

Vol 715 ◽

pp. 477-498 ◽

Cited By ~ 86

Author(s):

Zambri Harun ◽

Jason P. Monty ◽

Romain Mathis ◽

Ivan Marusic

Keyword(s):

Boundary Layer ◽

Reynolds Number ◽

Pressure Gradient ◽

Boundary Layers ◽

Amplitude Modulation ◽

Large Scale ◽

Outer Region ◽

Adverse Pressure Gradient ◽

Turbulent Boundary Layers ◽

Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

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Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.711 ◽

2018 ◽

Vol 856 ◽

pp. 135-168 ◽

Cited By ~ 19

Author(s):

S. T. Salesky ◽

W. Anderson

Keyword(s):

Boundary Layer ◽

Velocity Field ◽

Boundary Layers ◽

Vertical Velocity ◽

Amplitude Modulation ◽

Large Scale ◽

Streamwise Velocity ◽

Small Scale ◽

Convective Conditions ◽

Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

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How ocean ridges affect large-scale ocean circulation

Eos ◽

10.1029/2011eo420009 ◽

2011 ◽

Vol 92 (42) ◽

pp. 372-372

Author(s):

Colin Schultz

Keyword(s):

Ocean Circulation ◽

Large Scale ◽

Ocean Ridges

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A Diagnostic Model of the Nordic Seas and Arctic Ocean Circulation: Quantifying the Effects of a Variable Bottom Density along a Sloping Topography

Journal of Physical Oceanography ◽

10.1175/2008jpo3862.1 ◽

2008 ◽

Vol 38 (12) ◽

pp. 2685-2703 ◽

Cited By ~ 14

Author(s):

Signe Aaboe ◽

Ole Anders Nøst

Keyword(s):

Arctic Ocean ◽

Ocean Circulation ◽

Large Scale ◽

The Arctic ◽

Diagnostic Model ◽

Large Scale Circulation ◽

Nordic Seas ◽

Variable Bottom ◽

Canadian Basin ◽

Baroclinic Transport

Abstract A linear diagnostic model, solving for the time-mean large-scale circulation in the Nordic seas and Arctic Ocean, is presented. Solutions on depth contours that close within the Nordic seas and Arctic Ocean are found from vorticity balances integrated over the areas enclosed by the contours. Climatological data for wind stress and hydrography are used as input to the model, and the bottom geostrophic flow is assumed to follow depth contours. Comparison against velocity observations shows that the simplified dynamics in the model capture many aspects of the large-scale circulation. Special attention is given to the dynamical effects of an along-isobath varying bottom density, which leads to a transformation between barotropic and baroclinic transport. Along the continental slope, enclosing both the Nordic seas and Arctic Ocean, the along-slope barotropic transport has a maximum in the Nordic seas and a minimum in the Canadian Basin with a difference of 9 Sv (1 Sv ≡ 106 m3 s−1) between the two. This is caused by the relatively lower bottom densities in the Canadian Basin compared to the Nordic seas and suggests that most of the barotropic transport entering the Arctic Ocean through the Fram Strait is transformed to baroclinic transport. A conversion from barotropic to baroclinic flow may be highly important for the slope–basin exchange in the Nordic seas and Arctic Ocean. The model has obvious shortcomings due to its simplicity. However, the simplified physics and the agreement with observations make this model an excellent framework for understanding the large-scale circulation in the Nordic seas and Arctic Ocean.

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Large Scale Motion in Turbulent Boundary Layers

Turbulent Mixing in Nonreactive and Reactive Flows ◽

10.1007/978-1-4615-8738-5_13 ◽

1975 ◽

pp. 277-284

Author(s):

Leslie S. G. Kovasznay

Keyword(s):

Boundary Layers ◽

Large Scale ◽

Turbulent Boundary Layers ◽

Large Scale Motion ◽

Scale Motion

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Structure of ocean circulation between the Galápagos Islands and Ecuador

Advances in Geosciences ◽

10.5194/adgeo-33-3-2013 ◽

2013 ◽

Vol 33 ◽

pp. 3-12 ◽

Cited By ~ 6

Author(s):

C. Collins ◽

A. Mascarenhas ◽

R. Martinez

Keyword(s):

Sea Level ◽

Ocean Circulation ◽

Large Scale ◽

Southern Oscillation ◽

Galapagos Islands ◽

Surface Flow ◽

Climate Indices ◽

Late Winter ◽

Coastal Current ◽

Galápagos Islands

Abstract. From 27 March to 5 April 2009, upper ocean velocities between the Galápagos Islands and Ecuador were measured using a vessel mounted ADCP. A region of possible strong cross-hemisphere exchange was observed immediately to the east of the Galápagos, where a shallow (200 m) 300 km wide northeastward surface flow transported 7–11 Sv. Underlying this strong northeastward surface current, a southward flowing undercurrent was observed which was at least 600 m thick, 100 km wide, and had an observed transport of 7–8 Sv. Next to the Ecuador coast, the shallow (< 200 m) Ecuador Coastal Current was observed to extend offshore 100 km with strongest flow, 0.33 m s−1, near the surface. Immediately to the west of the Ecuador Coastal Current, flow was directed eastward and southward into the beginnings of the Peru-Chile Countercurrent. The integral of the surface currents between the Galápagos and Ecuador agreed well with observed sea level differences. Although the correlation of the sea level differences with large scale climate indices (Niño3 and the Southern Oscillation Index) was significant, more than half of the sea level variability was not explained. Seasonal variability of the sea level difference indicated that sea level was 2 cm higher at the Galápagos during late winter and early spring, which could be associated with the pattern of northward surface flows observed by R/V Knorr.

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Upper-Bound General Circulation of the Ocean: a Theoretical Exposition

10.20944/preprints202109.0239.v1 ◽

2021 ◽

Author(s):

Hsien-Wang Ou

Keyword(s):

Ocean Circulation ◽

Upper Bound ◽

First Principles ◽

General Circulation ◽

Large Scale ◽

Companion Paper ◽

Jet Stream ◽

Equatorial Undercurrent ◽

Macroscopic Motion ◽

Dynamical Principle

This paper considers the general ocean circulation within the thermodynamical closure of our climate theory, which aims to deduce the generic climate state from first principles. The preceding papers of the theory have reduced planetary fluids to warm/cold masses and determined their bulk thermal properties, which provide prior constraints for the derivation of the upper-bound circulation when the potential vorticity is homogenized in moving masses. In a companion paper on the atmosphere, this upper bound is seen to reproduce the prevailing wind, forsaking therefore previous discordant explanations of the easterly trade and the polar jet stream. In this paper on the ocean, we again show that this upper bound may replicate broad features of the observed circulation, including a western-intensified subtropical gyre and a counter-rotating tropical gyre feeding the equatorial undercurrent. Together, we posit that PV homogenization may provide a unifying dynamical principle of the large-scale planetary circulation, which may be interpreted as the maximum macroscopic motion extractable by microscopic stirring --- within the confine of the thermal differentiation.

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