The Probability Distribution Function of Column Density in Molecular Clouds

(Abridged) We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). We suggest that a ``decorrelation length'' can be defined as the distance over which the density auto-correlation function has decayed to, for example, 10% of its zero-lag value, so that the density ``events'' along a line of sight can be assumed to be independent over distances larger than this, and the Central Limit Theorem should be applicable. However, using random realizations of lognormal fields, we show that the convergence to a Gaussian is extremely slow in the high- density tail. Thus, the column density PDF is not expected to exhibit a unique functional shape, but to transit instead from a lognormal to a Gaussian form as the ratio $\eta$ of the column length to the decorrelation length increases. Simultaneously, the PDF's variance decreases. For intermediate values of $\eta$, the column density PDF assumes a nearly exponential decay. We then discuss the density power spectrum and the expected value of $\eta$ in actual molecular clouds. Observationally, our results suggest that $\eta$ may be inferred from the shape and width of the column density PDF in optically-thin-line or extinction studies. Our results should also hold for gas with finite-extent power-law underlying density PDFs, which should be characteristic of the diffuse, non-isothermal neutral medium (temperatures ranging from a few hundred to a few thousand degrees). Finally, we note that for $\eta \gtrsim 100$, the dynamic range in column density is small ($\lesssim$ a factor of 10), but this is only an averaging effect, with no implication on the dynamic range of the underlying density distribution.Comment: 13 pages, 7 figures (10 postscript files). Accepted in ApJ. Eliminated implication that ratio of column length to correlation length necessarily increases with resolution, and thus that 3D simulations are unresolved. Added discussion of dependence of autocorrelation function with parameters of the turbulenc

Two-layer rotating exchange flow between two deep basins : theory and application to the Strait of Gibraltar

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): 1568–1592, doi:10.1175/JPO2775.1.Rotating two-layer exchange flow over a sill in a strait separating two relatively deep and wide basins is analyzed. Upstream of the sill in the deep upstream basin, the infinitely deep dense lower layer is assumed to be inactive, while the relatively thin upper layer flowing away from the sill forms a detached boundary current in the upstream basin. This analysis emphasizes the importance of this upstream boundary current, incorporating its width as a key parameter in a formalism for deducing the volume exchange rate and discriminating between maximal and submaximal states. Hence, even for narrow straits in which rotation does not dominate the dynamics within the strait, the importance of rotation in the wide upstream basin can be exploited. It is shown that the maximal allowable exchange transport through straits wider than 1½ Rossby deformation radii increases as rotation increases, unlike for smaller rotations, where the exchange decreases as rotation increases. The theory is applied to the exchange flow through the Strait of Gibraltar. This application illustrates how images of the oceans taken from space showing the width of the upstream flow, in this case a space shuttle photograph, might be used to determine the exchange transport through a strait. Maximal exchange conditions in the Strait of Gibraltar are predicted to apply at the time the space shuttle photograph was taken

Structure and Generation of Turbulence at Interfaces Strained by Internal Solitary Waves Propagating Shoreward over the Continental Shelf

Detailed observations of the structure within internal solitary waves propagating shoreward over Oregon\u27s continental shelf reveal the evolving nature of interfaces as they become unstable and break, creating turbulent flow. A persistent feature is high acoustic backscatter beginning in the vicinity of the wave trough and continuing through its trailing edge and wake. This is demonstrated to be due to enhanced density microstructure. Increased small-scale strain ahead of the wave trough compresses select density interfaces, thereby locally increasing stratification. This is followed by a sequence of overturning, high-density microstructure, and turbulence at the interface, which is coincident with the high acoustic backscatter. The Richardson number estimated from observations is larger than 1/4, indicating that the interface is stable. However, density profiles reveal these preturbulent interfaces to be O(10 cm) thick, much thinner than can be resolved with shipboard velocity measurements. By assuming that streamlines parallel isopycnals ahead of the wave trough, a velocity profile is inferred in which the shear is sufficiently high to create explosively growing, small wavelength shear instabilities. It is argued that this is the generation mechanism for the observed turbulence and hence the persistent structure of high acoustic backscatter in these internal solitary waves

SOFAR float Mediterranean outflow experiment data from the second year, 1985-86

In October, 1984, the Woods Hole Oceanographic Institution SOFAR float group began a three-year-long field program to observe the low frequency currents in the Canary Basin. The principal scientific goal was to learn how advection and diffusion by these currents determine the shape and amplitude of the Mediterranean salt tongue. Fourteen floats were launched at a depth of 1100 min a cluster centered on 32°N, 24°W, and seven other floats were launched incoherently along a north/south line from 24°N to 37°N. At the same time investigators from Scripps Institution of Oceanography and the University of Rhode Island used four other SOFAR floats to tag a Meddy, a submesoscale lens of Mediterranean water. In October, 1985, seven additional floats were launched, four in three different Meddies, one of which was tracked during year 1. This report describes the second year of the floats launched in 1984 and the first year of the ones launched in 1985. Approximately 41 years of float trajectories were produced during the first two years of the experiment. One of the striking accomplishments is the successful tracking of one Meddy over two full years plus the tracking of two other Meddies during the second year.Funding was provided by the National Science Foundation under grant Numbers OCE 82-14066 and OCE 86-00055

The Statistics of Supersonic Isothermal Turbulence

We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We discuss numerical resolution issues and demonstrate convergence, in a statistical sense, of the inertial range dynamics in simulations on grids larger than 512^3 points. The simulations allowed us to measure the absolute velocity scaling exponents for the first time. The inertial range velocity scaling in this strongly compressible regime deviates substantially from the incompressible Kolmogorov laws. The slope of the velocity power spectrum, for instance, is -1.95 compared to -5/3 in the incompressible case. The exponent of the third-order velocity structure function is 1.28, while in incompressible turbulence it is known to be unity. We propose a natural extension of Kolmogorov's phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the Kolmogorov scaling of the power spectrum and structure functions of the density-weighted velocity v=\rho^{1/3}u. The low-order statistics of v appear to be invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of v is -1.69, and the exponent of the third-order structure function of v is unity. We also directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m = 2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 15 pages, 19 figures, ApJ v665, n2, 200

Sea surface mixed layer during the 10-11 June 1994 California coastally trapped event

A midlevel, coastally trapped atmospheric event occurred along the California coast 10-11 June 1994. This feature reversed the surface wind field along the coast in a northerly phase progression. Along the central California coast, the winds at the coastal stations reverse before the corresponding coastal buoy offshore, then followed hours later by passage of the leading edge of an overcast stratus cloud. The sea surface temperature was much colder in the narrow strip along the coast. The cloud characteristics may be accounted for by a sea surface mixed layer (SSML) model beginning with the wind reversal and growing with the square root of time. Heat is lost from the SSML to the sea surface. A cloud forms when the air temperature at the top of the SSML is equal to the dewpoint. It is suggested that a bore develops on the top of the SSML, increasing the thickness of the SSML and the progression speed of the cloud to 8 m s-1. There is evidence that an undular bore with a leading cloud develops in the thinner inshore SSML. Advancing beyond Monterey Bay, horizontal density contrast is believed to have caused the bore to change character to a gravity current with a narrower cloud that passed a point inshore before the winds reversed at the buoys. The last trace of a disturbed boundary layer ended at Point Arena where strong northerly winds prevented any further northerly progression and contributed to a cyclonic eddy that was formed in the lee of the point. Caution is suggested in the interpretation of stratus cloud phase progression without coastal wind measurements

A quasi-synoptic survey of the thermocline circulation and water mass distribution within the Canary Basin

Shipboard hydrographic measurements and moored current meters are used to infer both the large-scale and mesoscale water mass distribution and features of the general circulation in the Canary Basin. We found a convoluted current system dominated by the time-dependent meandering of the eastward flowing Azores Current and the formation of mesoscale eddies. At middepths, several distinctly different water masses are identified: Subpolar Mode and Labrador Sea Water are centered in the northwest, Subantarctic Intermediate Water is centered in the southeast, and the saltier, warmer Mediterranean tongue lies between them. Mesoscale structures of these water masses suggest the presence of middepth meanders and detached eddies which may be caused by fluctuations of the Azores Current

Flow and hydraulics near the sill of Hood Canal, a strongly sheared, continuously stratified fjord

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): 1087-1105, doi:10.1175/2010JPO4312.1.Hood Canal, a long fjord in Washington State, has strong tides but limited deep-water renewal landward of a complex constriction. Tide-resolving hydrographic and velocity observations at the constriction, with a depth-cycling towed body, varied markedly during three consecutive years, partly because of stratification variations. To determine whether hydraulic control is generally important and to interpret observations of lee waves, blocking, and other features, hydraulic criticality is estimated over full tidal cycles for channel wide internal wave modes 1, 2, and 3, at five cross-channel sections, using mode speeds from the extended Taylor–Goldstein equation. These modes were strongly supercritical during most of ebb and flood on the gentle seaward sill face and for part of flood at the base of the steep landward side. Examining local criticality along the thalweg found repeated changes between mode 1 being critical and supercritical approaching the sill crest during flood, unsurprising given local minima and maxima in the cross-sectional area, with the sill crest near a maximum. Density crossing the sill sometimes resembled an overflow with an internal hydraulic control at the sill, followed by a hydraulic jump or lee wave. Long-wave speeds, however, suggest cross waves, particularly along the shallower gentler side, where flow downstream of a large-amplitude wave was uniformly supercritical. Supercritical approaching the sill, peak ebb was critical to mode 1 and supercritical to modes 2 and 3 at the base while forming a sluggish dome of dense water over the sill. Full interpretation exceeds observations and existing theory.Washington State Sea Grant funded collection of these observations and the Office of Naval Research their publication. Pratt’s efforts were supported by the National Science Foundation under Grant OCE-0525729