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Walter H. Munk

Abstract

Spectra of the vertical displacement (potential energy) have been observed to be only slightly enhanced at the buoyancy frequency ω = N, whereas spectra of horizontal velocity u, v (kinetic energy) are greatly enhanced at the inertial frequency ω = f (except at equatorial latitudes). Consequently. the former are ignored in certain model spectra, whereas the latter are allowed for explicitly (e.g., by a term (ω2f 2)−1/2). I have attempted to interpret these observations in terms of the behavior of free wave packets at the turning points. Local resonant generation may also be a factor (Fu, 1980) but is not considered here.

In this tutorial N′ = dN/dz and f′ = df/dy ≡ β are taken as constant in order to make the derivation of the solutions near N and f as simple and as parallel as possible; these turning point solutions (in terms of Airy functions) fail in narrow waveguides, e.g., near a sharp buoyancy peak and at equatorial latitudes. The β-plane approximation fails at polar latitudes. Limit functions are evaluated numerically for a super-position of wave modes with relative energy (j 2 + j * 2)−1, j = 3, assuming horizontal isotropy. The computed cutoffs are smooth functions of frequency, with a peak just below N and just above f, respectively. The N amplification in the vertical displacement spectrum is by less than 2 (but equals 5 for the spectrum of vertical strain rate). The f amplification in the horizontal velocity spectrum is by a factor of 8 at latitude θ = 30°, and diminishes With latitude as (sinθ tanθ)1/3. In general, the amplification varies with the width of the waveguide (vertical and latitudinal) expressed in units of a characteristic wavelength. Thus the inertial peak is a consequence of linear wave theory and should not be independently imposed on model spectra.

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Walter H. Munk

Abstract

The horizontal angular deflection of a ray path through a circular eddy is roughly 2v, where v is the fractional variation in sound speed at the eddy center; v may reach 0.03 for intense Gulf Stream rings but is typically < 0.01 for mesoscale eddies. A critical parameter is the ratio σ=vR/r of acoustic range R to the “eddy focal length” r/v, where r is the eddy radius. Rays are split into horizontal multipaths for σ > 1. However, even for very intense rings at extreme ranges, we have σ < 1, and generally σ ≪ 1. Simple formulas are given for the horizontal deflection and for the perturbations in intensity and in travel time due to an eddy passing between source and receiver. Signatures of cold and warm core rings differ markedly because of differences in eddy dynamics, as well as differences in acoustic propagation properties. Fine-structure associated with internal waves induces a slight spread in the acoustic beam; the horizontal spread is of the same order as the horizontal deflection from mesoscale eddies.

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Walter H. Munk

Abstract

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Walter H. Munk

Abstract

Long, low waves preceding the arrival of the visible swell from a storm have been recorded off Pendeen, England, and Woods Hole, Massachusetts, by means of new instruments for the measurement and analysis of ocean waves. These forerunners provide storm warnings of practical value. Expressions giving the fore-runner's distance from the storm system and its travel time as functions of recorded period and rate of change of period are derived from very general assumptions. The expressions are suitable for simple graphical representation. The application of the method to tracking storms across the ocean is illustrated by means of a few actual examples, and the computed storm tracks are shown to be in good agreement with the information contained on weather maps. Certain features of the wave records may eventually make it possible to compute not only the location but also the size, intensity, and general character of the storm.

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Walter H. Munk

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 Stream of 36 million metric tons per second, compared to 74 million as derived from oceanographic observations. The discrepancy can probably be ascribed, at least in part, to an underestimate of the wind stress at low wind speeds (Beaufort 4 and less) as derived from the relationship now generally accepted.

The solution for meridional winds (section 5) accounts for the main features of the current system off California. For a circular wind system (section 8) the solution gives a wind-spun vortex which is displaced westward in relation to the wind system, in agreement with observations in the Northeast Pacific high-pressure area.

Based on these three solutions, a general nomenclature of ocean currents is introduced (section 9), applicable to all oceans regardless of hemisphere, and suggestive of the meteorologic features to which the currents are so closely related. In the light of this general system, the circulations of the northern and southern hemispheres, and of the North Atlantic and North Pacific are compared (section 10). Rossby's jet-stream theory of the Gulf Stream, and Maury's theory of thermohaline circulation are discussed, and it is concluded that the circulation in the upper layers of the oceans are the result chiefly of the stresses exerted by the winds.

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