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- Author or Editor: Walter Munk x

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## 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.

## 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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## Abstract

Seven times in a year's continuous observations, marked oscillations with periods from 5 to 15 minutes were simultaneously recorded on a barograph and a damped anemometer located at La Jolla, California. The oscillations often followed a reversal of the land- and sea-breeze regime, and they were sometimes preceded by a pressure pulse. Perturbations of pressure (*p*) and wind speed (*v*) attain double amplitudes up to several millibars and several meters per second, respectively, with maximum pressure occurring at the time of maximum “orbital” wind. This suggests propagating gravity waves in the atmosphere. Their velocity (*C*) can be inferred from the La Jolla records according to the impedance relationship, *p* = ρ*v*C; the computed arrival time at Point Loma, 11 miles to the south, agrees with the recorded arrival. Phase velocities are of the order of 10 m/s and greatly exceed ambient winds. Wavelengths range from 4 to 10 kilometers. A slight effect on sea level is apparent. Under steady meteorological conditions, there is good coherence for at least four wavelengths in the direction of propagation, but less coherence at right angles to this direction. The wave crests appear to be oriented normal to the wind shear between the upper and lower winds. The observed wave velocity is of the order given by the shallow “water” theory, *i.e.*, (*gh* ∇ ln θ)^{½}, where *h* is the elevation of the inversion layer, and ∇ ln θ is the logarithmic change in potential temperature across this layer. The observed period is not inconsistent with the period 2π/*s* of the fundamental mode of the least dispersive (longest) “trapped” waves, where *s*
^{2} = *g d* (ln θ)/*dz* is a measure of the stability *above *the inversion layer.

## Abstract

Seven times in a year's continuous observations, marked oscillations with periods from 5 to 15 minutes were simultaneously recorded on a barograph and a damped anemometer located at La Jolla, California. The oscillations often followed a reversal of the land- and sea-breeze regime, and they were sometimes preceded by a pressure pulse. Perturbations of pressure (*p*) and wind speed (*v*) attain double amplitudes up to several millibars and several meters per second, respectively, with maximum pressure occurring at the time of maximum “orbital” wind. This suggests propagating gravity waves in the atmosphere. Their velocity (*C*) can be inferred from the La Jolla records according to the impedance relationship, *p* = ρ*v*C; the computed arrival time at Point Loma, 11 miles to the south, agrees with the recorded arrival. Phase velocities are of the order of 10 m/s and greatly exceed ambient winds. Wavelengths range from 4 to 10 kilometers. A slight effect on sea level is apparent. Under steady meteorological conditions, there is good coherence for at least four wavelengths in the direction of propagation, but less coherence at right angles to this direction. The wave crests appear to be oriented normal to the wind shear between the upper and lower winds. The observed wave velocity is of the order given by the shallow “water” theory, *i.e.*, (*gh* ∇ ln θ)^{½}, where *h* is the elevation of the inversion layer, and ∇ ln θ is the logarithmic change in potential temperature across this layer. The observed period is not inconsistent with the period 2π/*s* of the fundamental mode of the least dispersive (longest) “trapped” waves, where *s*
^{2} = *g d* (ln θ)/*dz* is a measure of the stability *above *the inversion layer.

## 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.

## 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.

## Abstract

An elliptical excursion (mean diameter 20 feet), described annually by the pole of instantaneous rotation over the earth's surface, has been deduced from precise astronomic observations of latitude. According to Jeffreys and Rosenhead, most of this excursion can be ascribed to the seasonal variation in the distribution of matter (air, water, snow and vegetable matter). The most important single factor is the gain, in winter, of air mass over the Asiatic continent, and the corresponding loss over the Atlantic and east Pacific oceans.

In this paper, it is shown that the effect of winds may be far from negligible. Here the important factor is the pressure against the Himalayas during the monsoon winds. Ocean currents account for only 1 per cent of the excursion. It is suggested that the latitude observations, together with related astronomic observations concerning an annual change in the length of day, provide a promising method for measuring certain fundamental modes in the annual oscillation of the atmosphere.

## Abstract

An elliptical excursion (mean diameter 20 feet), described annually by the pole of instantaneous rotation over the earth's surface, has been deduced from precise astronomic observations of latitude. According to Jeffreys and Rosenhead, most of this excursion can be ascribed to the seasonal variation in the distribution of matter (air, water, snow and vegetable matter). The most important single factor is the gain, in winter, of air mass over the Asiatic continent, and the corresponding loss over the Atlantic and east Pacific oceans.

In this paper, it is shown that the effect of winds may be far from negligible. Here the important factor is the pressure against the Himalayas during the monsoon winds. Ocean currents account for only 1 per cent of the excursion. It is suggested that the latitude observations, together with related astronomic observations concerning an annual change in the length of day, provide a promising method for measuring certain fundamental modes in the annual oscillation of the atmosphere.

## Abstract

The horizontal angular deflection of a ray path through a circular eddy is roughly 2*v*, 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.

## Abstract

The horizontal angular deflection of a ray path through a circular eddy is roughly 2*v*, 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.

## Abstract

Phillips has shown that an undulating motion of a layered medium relative to a measuring instrument will result in a σ^{−2} spectrum (frequency or wavenumber) over a bandwidth determined by the thickness of the layers and of the sheets separating them. We show, for *any* (temperature) fine-structure statisteally stationary in depth with covariance *r*
_{θ}(*y*
_{1}−*y*
_{2})=<θ(*y*
_{1})θ(*y*
_{2})>, that the covariance of the observed time ceries can be expressed in terms of *r*
_{θ} and the covariance in the vertical displacement ζ, assuming ζ to he josintly normal. An explicit expression for the spectrum is given for the case that the rms value of ζ is large compared to the vertical coherence scale of the fine-structure. We tentatively conclude that the fine-structure dominates in the upper few octaves of the internal wave spectra, and then extends the spectra beyond the cutoff frequency (wavenumber). The loss of vertical coherence due to fine-structure occurs over a distance inversely proportional to frequency, in general agreement with an empirical rule proposed by Webster.

## Abstract

Phillips has shown that an undulating motion of a layered medium relative to a measuring instrument will result in a σ^{−2} spectrum (frequency or wavenumber) over a bandwidth determined by the thickness of the layers and of the sheets separating them. We show, for *any* (temperature) fine-structure statisteally stationary in depth with covariance *r*
_{θ}(*y*
_{1}−*y*
_{2})=<θ(*y*
_{1})θ(*y*
_{2})>, that the covariance of the observed time ceries can be expressed in terms of *r*
_{θ} and the covariance in the vertical displacement ζ, assuming ζ to he josintly normal. An explicit expression for the spectrum is given for the case that the rms value of ζ is large compared to the vertical coherence scale of the fine-structure. We tentatively conclude that the fine-structure dominates in the upper few octaves of the internal wave spectra, and then extends the spectra beyond the cutoff frequency (wavenumber). The loss of vertical coherence due to fine-structure occurs over a distance inversely proportional to frequency, in general agreement with an empirical rule proposed by Webster.

## 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 (ω^{2} − *f*
^{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.

## 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 (ω^{2} − *f*
^{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.

## Abstract

The important role of tides in the mixing of the pelagic oceans has been established by recent experiments and analyses. The tide potential is modulated by long-period orbital modulations. Previously, Loder and Garrett found evidence for the 18.6-yr lunar nodal cycle in the sea surface temperatures of shallow seas. In this paper, the possible role of the 41 000-yr variation of the obliquity of the ecliptic is considered. The obliquity modulation of tidal mixing by a few percent and the associated modulation in the meridional overturning circulation (MOC) may play a role comparable to the obliquity modulation of the incoming solar radiation (insolation), a cornerstone of the Milanković theory of ice ages. This speculation involves even more than the usual number of uncertainties found in climate speculations.

## Abstract

The important role of tides in the mixing of the pelagic oceans has been established by recent experiments and analyses. The tide potential is modulated by long-period orbital modulations. Previously, Loder and Garrett found evidence for the 18.6-yr lunar nodal cycle in the sea surface temperatures of shallow seas. In this paper, the possible role of the 41 000-yr variation of the obliquity of the ecliptic is considered. The obliquity modulation of tidal mixing by a few percent and the associated modulation in the meridional overturning circulation (MOC) may play a role comparable to the obliquity modulation of the incoming solar radiation (insolation), a cornerstone of the Milanković theory of ice ages. This speculation involves even more than the usual number of uncertainties found in climate speculations.

## Abstract

We have recorded time series of ship GPS (global positioning system) positions at about 10-s intervals under favorable satellite conditions. Errors are less than 10 m rms, as demonstrated by comparing the GPS acoustic-source positions with Doppler-inferred positions from a receiver site 9200 km away. Offsets from a steady course held for 20 miles are of the order of 100 m, and could be the result of orbital surface velocities associated with internal waves. We suggest that such GPS measurements, taken routinely while under way, might produce useful data concerning small-scale oceanographic processes.

## Abstract

We have recorded time series of ship GPS (global positioning system) positions at about 10-s intervals under favorable satellite conditions. Errors are less than 10 m rms, as demonstrated by comparing the GPS acoustic-source positions with Doppler-inferred positions from a receiver site 9200 km away. Offsets from a steady course held for 20 miles are of the order of 100 m, and could be the result of orbital surface velocities associated with internal waves. We suggest that such GPS measurements, taken routinely while under way, might produce useful data concerning small-scale oceanographic processes.