422 research outputs found
Isentropic averaging
The equations of motion, thermodynamics and scalar concentration are averaged separately over infra-grid scales (comprising roughly ocean microstructure scales) and sub-grid scales (encompassing 10–100 km scales), the latter average being carried out on constant potential temperature surfaces. (Since variation of salinity has been neglected, potential temperature is synonymous with entropy.) These methods of averaging are used to lend precision to statements about oceanic turbulent diffusion: that infra-grid scales are primarily responsible for dientropic diffusion; and that sub-grid scales are responsible for along-isentropic diffusion of passive scalars. Equivalent sets of averaged equations expressed either in isentropic coordinates or quasi-Cartesian coordinates can be obtained. Diffusion tensors for potential temperature express only infra-grid effects. For other passive tracers, diffusion caused by sub-grid scales of motion is also felt, whose effects are shown by scale analysis to be oriented principally along infra-grid averaged isentropes
Wind-driven mid-ocean baroclinic gyres over topography: A circulation equation extending the Sverdrup relation
What is the circulation driven by wind stress in a stratified ocean above topography? This question was answered by Sverdrup (1947) for vertically integrated transport over flat topography only. By applying the ideas and methods of Rhines and Young (1982a,b), a modified form of the Sverdrup transport relation can be derived for the case of stratification and topography in certain circumstances. This circulation equation is, in quasigeostrophic form,J(Ψ, βy + χf0h′T/H) = − χf0−1gAH J(βy, h′T) + z · ∇xτ/&rho0,where most symbols have their usual meanings, while χ is a parameter no larger than 1 that depends on stratification, bottom friction and horizontal diffusivity. The effect of topography is attenuated (χ is reduced) by strong stratification, strong bottom friction, or weak horizontal diffusivity. The circulation equation applies strictly to uniform bottom slope or other topographies obeying ∇2h′T = 0, though it approximately holds for ∇2h′T ≃ 0, a criterion for which is that the scale of bottom topography greatly exceeds the baroclinic Rossby radius of deformation. It holds only above deep closed circulations. It is remarkable for the form of the characteristic lines for transport, βy + χf0h′T/H = constant, and the extra forcing term on the right, which depends on topography.Examples are given of two-layer flows driven by wind-stress curl over east-west and north-south sloping topography. The determination of the boundary of the deep gyre is an implicit nonlinear problem. The solution for the case of east-west slope illustrates the general method for solving such a problem
Some effects of bottom topography on baroclinic stability
The effects of Fourier components of cross-stream topographic slope are included in the classical linear theory of quasigeostrophic baroclinic instability. The effect of uniformly sloping topography is reviewed, emphasis being placed on the possibility of destabilization through interaction between long topographic baroclinic Rossby waves and short thermal baroclinic Rossby waves with the same downstream wave number and phase speed...
Asymptotic regimes in mixed-layer deepening
The model equation for the mixed layer proposed by Niiler (1975) combines the Kraus-Turner turbulent erosion prescription with the Pollard-Rhines-Thompson treatment of induced shear-flow deepening and limiting by Coriolis forces. We show here that both are special cases which emerge asymptotically from the model equation. Numerical solutions show the dynamics to pass through four distinct regimes, in the case of wind-mixing of an initially resting fluid
The all-Atlantic temperature-salinity-pressure relation and patched potential density
The relation between temperature, salinity, and pressure in the Atlantic Ocean is examined. Most of the Atlantic resolves itself into three two-dimensional manifolds of three-dimensional thermodynamic space: a northern, more saline, branch, and a southern, fresher, branch, each quite independent of pressure, and between them a bridge, on which density is uniform at constant pressure. The properties of the branches are crucial to the construction of joint potential density surfaces, patched together at 1000 db intervals. By resolving more finely in pressure (illustrated with 200 db spacing), a finer system of patched potential density surfaces can be obtained, and indeed the continuous limit can be taken. This limit gives a form of orthobaric density, regionally differentiated because it is based on the duplicate regional branches. A mapping can be devised, using the properties of the bridge waters, that links the southern and northern forms of orthobaric density across the boundary between their respective regions of validity. The parallel of patched potential density surfaces to orthobaric density surfaces permits the use of measures developed for the latter to estimate quantitative measures of the material nature (or otherwise) of the former. Simply put, within the waters of the respective branches the patched isopycnals, or orthobaric isopycnals, are very nearly material, limited only by inherent irreversible mixing processes. However, where these isopycnals cross the bridge waters, significant, reversible, material exchange across them may occur.A difficulty may be encountered with coarsely resolved, regionally differentiated, patched potential density. This is that there exist ranges of density which cannot be consistently linked across the regional boundary. A solution for the difficulty, suggested by the continuousform (regionally differentiated orthobaric density), is proposed
Meridional heat transport across the Antarctic Circumpolar Current by the Antarctic Bottom Water overturning cell
The heat transported by the lower limb of the Southern Ocean meridional overturning circulation is commonly held to be negligible in comparison with that transported by eddies higher in the water column. We use output from one of the first global high resolution models to have a reasonably realistic export of Antarctic Bottom Water, the OCCAM one twelfth degree model. The heat fluxed southward by the deep overturning cell using the annual mean field for 1994 at 56S is 0.033 PW, but the 5-day mean fields give a larger heat flux (0.048 and 0.061 PW depending on calculation method). This is more than 30% of previous estimates of the total heat flux. Eddies and other transients add considerably to the heat flux. These results imply that this component of meridional heat flux may not be negligible as has been supposed
Thermodynamic and Aerosol Controls in Southeast Pacific Stratocumulus
This is the publisher's version, also available electronically from http://journals.ametsoc.org/doi/abs/10.1175/JAS-D-11-0165.1.A near-large-eddy simulation approach with size-revolving (bin) microphysics is employed to evaluate the relative sensitivity of southeast Pacific marine boundary layer cloud properties to thermodynamic and aerosol parameters. Simulations are based on a heavily drizzling cloud system observed by the NOAA ship Ronald H. Brown during the Variability of the American Monsoon Systems (VAMOS) Ocean–Cloud–Atmosphere–Land Study—Regional Experiment (VOCALS-Rex) field campaign. A suite of numerical experiments examines the sensitivity of drizzle to variations in boundary layer depth and cloud condensation nuclei (CCN) concentration in a manner consistent with the variability of those parameters observed during VOCALS-Rex. All four simulations produce cellular structures and turbulence characteristics of a circulation driven predominantly in a bottom-up fashion. The cloud and subcloud layers are coupled by strong convective updrafts that provide moisture to the cloud layer. Distributions of reflectivity calculated from model droplet spectra agree well with reflectivity distributions from the 5-cm-wavelength scanning radar aboard the ship, and the statistical behavior of cells over the course of the simulation is similar to that documented in previous studies of southeast Pacific stratocumulus. The simulations suggest that increased aerosol concentration delays the onset of drizzle, whereas changes in the boundary layer height are more important in modulating drizzle intensity
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An Effect of the Thermobaric Nonlinearity of the Equation of State: A Mechanism for Sustaining Solitary Rossby Waves
The thermobaric nonlinearity in the equation of state for seawater density—namely, the dependence of thermal expansibility on pressure—coupled with spatial variation of the oceanic temperature–salinity (θ–s) relation generates a nonlinear behavior in the buoyant force that can counter the linear dispersion of baroclinic Rossby waves and produce solitary waves. A Korteweg–deVries equation is derived in which the coefficient of the nonlinear term depends on the thermobaric parameter and the spatial gradient of the anomaly of the θ–s relation. Quantitative estimates can be made of the magnitude of the effect in terms of these parameters. For example, given first-baroclinic-mode spatial variations of order 0.1 psu (1000 km)⁻¹ or 0.7°C (1000 km)⁻¹, from a θ–s relation with a density ratio of 2, a solitary Rossby wave of maximum vertical displacement of approximately 100 m and horizontal scale of approximately 30 baroclinic Rossby radii of deformation can be generated
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An Improved Bound for the Complex Phase Speed of Baroclinic Instability
An improved bound is obtained for the radius of the semicircle in the complex plane containing the complex phase speed of baroclinically unstable plane wave disturbances. In the limit of long waves, this bound contains a term increasing with β and decreasing with the mean stratification (i.e., decreasing with the baroclinic Rossby radius of deformation). An extension of the bound, valid for finite wavelengths longer than order (δu/β)[superscript]1/2, where δu is half the range of velocities in the mean shear flow, is also obtained
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The Dissipation of Fluctuating Tracer Variances
The evolution of the covariance of two tracers involves a quantity called codissipation, proportional to the covariance of the gradients of the two tracers, and analogous to the dissipation of tracer variance. The evolution of the variance of a composite tracer—a linear combination of two simple, primary tracers—depends on the“composite dissipation,” a combination of the individual simple tracer dissipations and the codissipation. The composite dissipation can be negative (implying growth of the variance of the composite tracer) for structures in which the correlation of the simple tracer gradients are large enough (i.e., large codissipation). This situation occurs in the phenomena of double diffusion and salt fingering. A particular composite tracer called watermass variation, a measure of water-type scatter about the mean tracer versus tracer relationship, lacks production terms of the conventional form—tracer flux multiplying tracer gradient—in its variance evolution balance. Only codissipation can produce variance of watermass variation. The requirements that watermass variance production and dissipation be in equilibrium, and that no other composite tracer variance be tending to grow due to codissipation, lead to a particular relation among codissipation and the simple dissipations and between the simple dissipations themselves. The latter are proportional to one another, the proportionality factor being the square of the slope of the mean tracer versus tracer relation. The same results can be obtained by modifying Batchelor’s argument to give the equilibrium cospectrum of two tracer gradients at high wavenumbers in a well-developed field of isotropic turbulence. As a consequence of these arguments, the turbulent eddy tracer fluxes are also proportional, with the mean tracer–tracer slope as proportionality factor. Further, the ratio of turbulent diffusivities of two tracers is unity. The dissipation of buoyancy, a composite tracer constructed from temperature and salinity, is proportional at equilibrium to thermal dissipation multiplied by a factor that depends on the stability ratio. This previously established result is obtained here under less restrictive conditions
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