Walter Munk

Measurement of the Roughness of the Sea Surface from Photographs of the Sun’s Glitter

A method is developed for interpreting the statistics of the sun’s glitter on the sea surface in terms of the statistics of the slope distribution. The method consists of two principal phases: (1) of identifying, from geometric considerations, any point on the surface with the particular slope required for the reflection of the” sun’s rays toward the observer; and (2) of interpreting the average brightness of the sea surface in the vicinity of this point in terms of the frequency with which this particular slope occurs. The computation of the probability of large (and infrequent) slopes is limited by the disappearance of the glitter into a background consisting of (1) the sunlight scattered from particles beneath the sea surface, and (2) the skylight reflected by the sea surface.The method has been applied to aerial photographs taken under carefully chosen conditions in the Hawaiian area. Winds were measured from a vessel at the time and place of the aerial photographs, and cover a range from 1 to 14 m sec−1. The effect of surface slicks, laid by the vessel, are included in the study. A two-dimensional Gram-Charlier series is fitted to the data. As a first approximation the distribution is Gaussian and isotropic with respect to direction. The mean square slope (regardless of direction) increases linearly with the wind speed, reaching a value of (tan16°)2 for a wind speed of 14 m sec−1. The ratio of the up/ downwind to the crosswind component of mean square slope varies from 1.0 to 1.9. There is some up/downwind skewness which increases with increasing wind speed. As a result the most probable slope at high winds is not zero but a few degrees, with the azimuth of ascent pointing downwind. The measured peakedness which is barely above the limit of observational error, is such as to make the probability of very large and very small slopes greater than Gaussian. The effect of oil slicks covering an area of one-quarter square mile is to reduce the mean square slopes by a factor of two or three, to eliminate skewness, but to leave peakedness unchanged.

Abyssal recipes II: energetics of tidal and wind mixing

Without deep mixing, the ocean would turn, within a few thousand years, into a stagnant pool of cold salty water with equilibrium maintained locally by near-surface mixing and with very weak convectively driven surface-intensified circulation. (This result follows from Sandstrom’s theorem for a fluid heated and cooled at the surface.) In this context we revisit the 1966 “Abyssal Recipes”, which called for a diapycnal diffusivity of 10-4m2/s (1 cgs) to maintain the abyssal stratification against global upwelling associated with 25 Sverdrups of deep water formation. Subsequent microstructure measurements gave a pelagic diffusivity (away from topography) of 10-5 m2/s — a low value confirmed by dye release experiments. A new solution (without restriction to constant coefficients) leads to approximately the same values of global upwelling and diffusivity, but we reinterpret the computed diffusivity as a surrogate for a small number of concentrated sources of buoyancy flux (regions of intense mixing) from which the water masses (but not the turbulence) are exported into the ocean interior. Using the Levitus climatology we find that 2.1 TW (terawatts) are required to maintain the global abyssal density distribution against 30 Sverdrups of deep water formation. The winds and tides are the only possible source of mechanical energy to drive the interior mixing. Tidal dissipation is known from astronomy to equal 3.7 TW (2.50±0.05 TW from M2 alone), but nearly all of this has traditionally been allocated to dissipation in the turbulent bottom boundary layers of marginal seas. However, two recent TOPEX/POSEIDON altimetric estimates combined with dynamical models suggest that 0.6–0.9 TW may be available for abyssal mixing. A recent estimate of wind-driving suggests 1 TW of additional mixing power. All values are very uncertain. A surprising conclusion is that the equator-to-pole heat flux of 2000 TW associated with the meridional overturning circulation would not exist without the comparatively minute mechanical mixing sources. Coupled with the findings that mixing occurs at a few dominant sites, there is a host of questions concerning the maintenance of the present climate state, but also that of paleoclimates and their relation to detailed continental configurations, the history of the Earth–Moon system, and a possible great sensitivity to details of the wind system.

ON THE WIND-DRIVEN OCEAN CIRCULATION

Abstract Streamlines of oceanic mass transport are derived from solutions to a vertically integrated vorticity equation which relates planetary vorticity, lateral stress curl, and the curl of the stress exerted by the winds on the sea surface. These solutions account for many of the gross features of the general ocean circulation, and some of its details, on the basis of the observed mean annual winds. The solution for zonal winds (section 3) gives the main gyres of the ocean circulation. The northern and southern boundaries of these gyres are the west wind drift, the equatorial currents, and equatorial counter-current. They are determined by the westerly winds, the trades, and the doldrums, respectively. For each gyre the solution gives the following observed features (from west to east): a concentrated current (e.g., the Gulf Stream), a countercurrent, boundary vortices (the Sargasso Sea), and a steady compensating drift. Using mean Atlantic zonal winds, the solution yields a transport for the Gulf Stre...

Space-Time scales of internal waves

Abstract We have contrived a model E(αω) α μ−1ω−p+1(ω 2−ω i 2)−+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω r-1 (ω 2−ω i 2)½, and frequency ω extending from the inertial frequency ω i to the local Vaisala frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE(α1, α2, ω), with α1, α2 designating components of α. Certain moments of E(α1, α2, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F (u,η,…)(ω) = ∫∫ (U 2, Z 2,…)E(α1, ∞2, ω) dα1 dα2, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F (…)(α1) = ∫∫… dα2 dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is ...

Tidal Spectroscopy and Prediction

Nineteen years of hourly tide readings at Honolulu, Hawaii, and Newlyn, England, are analysed without astronomical prejudice as to what frequencies are present, and what are not, thus allowing for background noise. The method consists of generating various complex input functions ci, (t) for the same time interval as the recorded tide £(t), and of determining the associated lag weights w in the convolutions ζ^(t)=∑i∑S⁡wisci(t−τs)+∑ij∑ss′⁡wijss′ci(t−τs)cj(t−τs′)+... by the condition ((£—£)2) = minimum. The two expansions represent linear and bilinear processes; the Fourier transforms of w for any chosen i (or ij) are the linear (or bilinear) admittances. Input functions are the (time variable) spherical harmonics of the gravitational potential and of radiant flux on the Earth’s surface; these functions are numerically generated hour by hour, directly from the Kepler-Newton laws and the known orbital constants of Moon and Sun, without time-harmonic expansions (unlike the harmonic method of Kelvin-Darwin-Doodson). The radiative input is required to predict non-gravitational tides, and it allows for the essential distinction that the Earth is opaque to radiation and transparent to gravitation.

Ocean acoustic tomography: a scheme for large scale monitoring

Abstract We consider the problem of monitoring ocean basins for mesoscale fluctuations, using acoustic inverse techniques. The procedure, which has much in common with conventional seismology, consists of measuring perturbations in travel time between acoustic sources and receivers. Because the number of pieces of information is the product of the number of sources, receivers, and resolvable multipath arrivals, the economics of the system is enhanced over usual spot measurements. The temporal resolution required to distinguish multipath arrivals is estimated at 50 ms; the precision required to measure mesosclae perturbations is estimated at 25 ms. The required resolution and precision can be achieved by existing low-frequency (100- to 200-Hz) broadband (> 20-Hz) sources, but we are ultimately limited to 1000-km ranges by the variable ocean finestructure and associated micropaths. There appear to be no practical range limits imposed by micropaths if such broadband sources could be centered at 30 Hz. Given the travel time measurements and their noise estimates, we show how actually to invert the system for the interior changes in sound speed and, by inference, for density. The method is analogous to the medical procedure called tomography (from the Greek ‘slice’). Measures of the spatial resolution and of formal error bars are obtained. We conclude that such a system is achievable now and has potential for development in a number of directions.

The rotation of the earth : a geophysical discussion

This book gives an account of certain observed irregularities on the rotation of the Earth, both in its rate of rotation (giving a variable length of day) and in the position of its axis. These irregularities are caused by events on and within the Earth and provide a means of studying a number of geophysical problems. Seasonal shifts in air masses and variable winds are causes of short-period fluctuations in the rotation. Climatic changes and their attendant sea levels are in part responsible for long-term fluctuations. Modern observations of the Moon and descriptions of ancient elipses both establish a secular increase in the length of day. The interpretation involves atmospheric, oceanic and bodily tides. The book provides a unified treatment of the rotation of the Earth, making this method of studying geophysical phenomena more readily accessible to geophysicists and others.

Propagation of ocean swell across the Pacific

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THE SOLITARY WAVE THEORY AND ITS APPLICATION TO SURF PROBLEMS

The purposes of this paper are: (a) to give a summary of useful relationships derived by means of the solitary wave theory, and to plot these relations using dimensionless parameters for the purpose of making the theory accessible to numerical examples;? (b) to review various studies a t the Scripps Institution dealing with the application of this theory to surf problems; and (c) to discuss the problem of sand transport in or near the surf zone, in the light of the solitary wave theory. This investigation represents part of a general project undertaken during the war for the purpose of providing useful wave forecasts for the amphibious forces. By 1943, methods for forecasting sea and swell had been dwelopedlJ and a study of the transformation of waves in shallow water was initiated for the purpose of extending the wave forecasts right into the surf zone. It should be noted that the outer edge of the surf zone (the greatest depth where waves break) is usually the most critical from the point of view of bringing landing craft ashore. The problem was attacked in-three ways: (a) by field observations along the East Coast by the Woods Hole Oceanographic Institution and along the West Coast by the Scripps Institution of Oceanography; (b) by laboratory observations at the Beach Erosion Board wave tank, in Washington, D. C., and later at the Department of Engineering of the University of California in Berkeley, California; (c) by theoretical studies. A theoretical investigation by Burnside: based on the assumptions of constancy of wave periods, conservation of energy, and the linear shallow water (4iry) wave theory, reveals that the waves decrease somewhat in height after entering shallow water, reach a minimum height and then increase!, The initial decrease in wave height had been noticed by O’Brien in laboratory investigations. A comparison between the subsequent increase in heigh& as derived from Burnside’s equations with that obtained from field and laboratory observations mentioned above, showed the computed increase to be considerably smaller than the observed increase. This discrepancy became increasingly large the nearer one came to the breaking zone, the zone most important for practical forecasts. One reason for this discrepancy is contained in an assumption underlying the linear Airy theory, namely that the wave height be small compared to

Tides off‐shore: Transition from California coastal to deep‐sea waters‡

Abstract Tidal pressures and currents were measured with self‐contained capsules dropped to the sea floor for one month at distances of 175, 190, and 500 nautical miles from San Diego. These observations, together with a one‐week bottom pressure record by Filloux at 750 n miles, and three half‐week bottom current records by Isaacs et al, at intermediary distances, were analyzed for tidal components by cross‐correlation with a noise‐free reference time series. (For short records this method has some merit over classical tide analysis.) It was found that the tide decays seaward to e‐1 times the coastal amplitude over a distance of order 1000 km for the semidiurnal species, slower for the diurnal species. Tidal currents turn counterclockwise, and are polarized with maximum flow parrallel to shore in the direction of tidal propagation (320°T) at local high tide. The current amplitude is roughly 2 cm/sec for the semidiurnal component, 1 cm/sec for the diurnal component. Superimposed baroclinic tidal currents l...