Jerome A. Smith

Observed growth of Langmuir circulation

Surface velocity patterns and upper ocean density profiles are presented from a period following a sudden increase in wind. A prior wind speed of 8 m/s failed to produce visible signs of Langmuir circulation. After the wind speed increased to 13 m/s, Langmuir circulation developed within 15 min. The initial scale observed was about 16 m, streak to streak, and may have been restricted by the depth scale of the measurements. This spacing is about two thirds of the dominant wavelength (4-s-period waves). The streak spacing (two cell widths) increased at roughly 40 m/h for the next hour. The density measurements indicate a depth of mixing which increased over the same period at a rate of 20 m/h; thus the vertical to horizontal aspect ratio was about 1:1. Prior stratification was weak (buoyancy frequency of about 1.5 cph), and probably did not affect the circulation initially. Mixing at the surface of the oceans is important to a wide variety of concerns, including global climate and the health of marine life. Two main causes of this mixing can be identified: (1) when surface water is cooled, it becomes denser and sinks, mixing downward either to the bottom or until limited by the preexisting stratification; and (2) the wind can mechanically stir the surface layer to some depth, usually limited by stratification. The former can result in mixing to considerable depths, but the latter occurs more often, over the majority of the world oceans. Frequently, the two driving forces occur together. What are the details of this mixing? For example, are bubbles dragged deep into the mixed layer, injecting gases at depth? Are there repeatable features which could lead to improved models of surface mixing and its effects? When wind blows over water, lines are often visible on the surface, running roughly parallel to the wind. In an exemplary series of experiments, Langmuir [1938] found these to be lines of convergence along the surface, with downwelling below each line. He found also that maxima in the downwind surface currents occur along these lines. Thus the mixing layer is organized into rolls of alternating sign, aligned with the wind, and water parcels follow helical paths downwind. This form of circulation in surface layers of water has come to be called “Langmuir circulation.” Historically, this term has not implied any particular mechanism of formation, and it generally has not been used in reference to other similar structures (e.g., roll vortices in the atmosphere or in wall-bounded convection). Langmuir [1938, p. 123] expressed his belief that “the helical vortices set up by wind apparently constitute the essential mechanism by which the epilimnion is produced.” Clearly, this form of “helical vortices” is efficient in transporting momentum, energy, and matter throughout the surface layer of water. Three mechanisms are currently considered to drive Langmuir circulation. (1) An interaction between surface waves and winddriven shear gives rise to this form of circulation as a linear instability. A review of this theory, and of observations before 1983, is given by Leibovich [1983]. (2) Even without surface waves, turbulent mixing will occur due to the breakdown of the

Structure and variability of Langmuir circulation during the Surface Waves Processes Program

A cooperative, multiplatform field experiment was conducted in the eastern North Pacific during February and March of 1990 as part of the Surface Waves Processes Program (SWAPP). One of the experimental objectives was to investigate Langmuir circulation so that its role in the evolution of the oceanic surface boundary layer could be better understood. The concurrent use of different observational techniques, ranging from simple surface drifters to complex Doppler sonar systems, resulted in new information about Langmuir circulation structure and variability. Estimates of Langmuir cell spacing indicated that a broad range of scales, from about 2 to 200 m, was excited during periods of strong surface forcing and that the energy containing scales evolved with time. Estimates of cell spacing based on Doppler velocities from a surface-scanning sonar directed crosswind showed this scale evolution, but estimates based on backscattered intensity did not. This was attributed to the fact that the intensity-based estimates were only indirectly related to circulation strength. The near-surface convergent velocities from the sonar were used to form an objective, quantitative measure of the temporal variations in Langmuir circulation strength. As expected, the circulation strength increased dramatically during strong wind events. However, circulation strength and wind stress did not decrease simultaneously, and Langmuir circulation was detectable for up to a day after abrupt reductions in wind stress. Energy from the surface wave field, which decayed more slowly than the wind, was apparently responsible for maintaining the circulation. The variation of circulation strength was found to be better related to (u*Us)½ than to u*, where u* = (τ/ρ)½ is the friction velocity, τ is the wind stress, and Us is the surface wave Stokes drift. This scaling is consistent with wave-current interaction theories of Langmuir cell generation.

Wave-current interactions in finite depth

The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified. The formulation is made in terms of the vertically integrated flow. The various terms are identified with other analyses and interpreted in terms of physical mechanisms, permitting reasonable estimates of the associated depth dependencies. One term is identified with the integrated “CL vortex force” implemented, for example, in simulations of Langmuir circulation. However, as illustrated with a simple example of steady refraction across a shear zone, other terms of the same order can significantly alter the results. The classic example of long waves forced by short-wave groups is also revisited. In this case, an apparent singularity arising in shallow water is countered by finite-amplitude dispersion corrections, these being formally of the same order as the forced long-wave response, and becoming significant or dominant as shallow water is approached.

Observed directional characteristics of the wind, wind stress, and surface waves on the open ocean

Sonic anemometer data were taken during the Surface Waves Processes Program (SWAPP) in March 1990 in the North Pacific. Measurements of the wind stress vector span several strong wind events. Significant angles between the wind stress vector and the mean wind vector are seen. Simultaneous measurements of the directional wave field were made with a surface scanning Doppler sonar. The data suggest that the wind stress direction is influenced by the direction of the surface waves, especially for stronger winds. Overall, the stress vector lies between the mean wind and the mean wave directions. At the higher wind speeds (over 8.6 m/s), there is a nonzero correlation between the variations in wave directions and stress directions as well. Finally, the stress and wave component directions have similar frequency dependence over the frequency band where wave energy is nonnegligible, suggesting a dynamic link.

Repeat-Sequence Coding for Improved Precision of Doppler Sonar and Sodar

Abstract Repeat-sequence coding is a robust method for improving the precision of velocity estimates from incoherent Doppler sounders. The method involves transmitting a number of repeats of a broadband “subcode.” The Doppler shift is estimated from the complex autocovariance of the return, evaluated at a time lag, equal to the subcode duration. The repeat-sequence code is an extension of the simple pulse-train concept developed in the early days of radar. By transmitting codes, rather than discrete pulses, the average transmitted power is increased. A model is developed here to predict performance enhancement for specified codes. The model is based on the sample error of the covariance estimates. It explicitly accounts for the lag used. Root-mean-square precision is enhanced roughly in proportion to the square root of the time-bandwidth product of the subcode. Coded pulse technology has been implemented on a variety of Doppler sonar systems at Scripps Institution of Oceanography and used in both open-oce...

Velocity Structure in the Mixed Layer during MILDEX

Abstract During October–November 1983, a MIxed Layer Dynamics EXperiment (MILDEX) took place off the coast of California. As a part of MILDEX, a number of sensors were deployed from the Research Platform FLIP in an effort to monitor the flow structure in the near-surface mixed layer. Profiling current meters (VMCMs) measured velocities down to 150 m on an hourly basis. Other VMVMs were set at fixed depths. Depths of interest were examined using a package which measured three-component velocities and displayed them in FLIPs laboratory in real time. The current meters often observed sequences of downwind-directed jets, with maximum velocities exceeding 25 cm s−1. Downwelling velocities of equal magnitude were also observed. The strongest currents were found 10 to 35 m below the surface, at mid-depth in the mixed layer. Surface convergences associated with these jets were visualized by scattering tracers (computer cards) on the sea surface. These features suggest Langmuir circulation. Six Doppler sonars wer...

Doppler Sonar and Surface Waves: Range and Resolution

Abstract The performance limitations of an acoustic Doppler sonar system are explored and compared with anticipated requirements for the measurement of surface wave directional/frequency spectra. To obtain measurements to a range D requires a delay Δt between pings long enough for sound to propagate out to D and back: Δt(c/2) ≥ D. This defines a Nyquist frequency, ωN (radiances s−1). Linear dispersion relates this to a “matched wavenumber,” kN = ωN2/ g. Waves travelling obliquely and harmonics of longer waves appearing at ωN all have smaller wavenumbers, k ≤ kN; thus, kN; defines a maximum wavenumber requirement, or (equivalently) a matched range resolution, ΔR. From idealized surface wave spectra, the velocity resolution ΔV required to measure spectra out to (ωN, kN) can be estimated. For a given sonar “tone,” the error-product E = ΔRΔV is a constant, so velocity resolution and range resolution must be traded off. The error product decreases with increasing acoustic frequency f0 and number of tones. High...

On the Interaction Between Long and Short Surface Waves

Abstract Short, dissipative, surface waves superposed on longer waves cause a growth of the long wave momentum Ml at a ratewhere kl, al are the amplitude and wavenumber of the long waves, so that klal is their steepness; Sa is the radiation stress of the short waves and τs, the rate of transfer of momentum to the short waves by the wind; and the angle braces denote an average over the long-wave phase θ = klx−ωlt. The first term in the above equation is the radiation stress interaction (Phillips, 1963; Hasselmann, 1971) and is generally negligible compared with the second term, neglected by Hasselmann (1971), which shows that long waves can grow if short wave generation (rather than dissipation) is correlated with the long wave orbital velocity. Even if the modulation of τs is only O(klal) times 〈τs〉, this mechanism can contribute a significant fraction of long wave momentum. However, even a substantially greater modulation of τs, perhaps due to varying exposure of short waves to the wind, is unlikely to a...

The Wirewalker: A Vertically Profiling Instrument Carrier Powered by Ocean Waves

Abstract Ocean wave energy is used to drive a buoyant instrument platform down a wire suspended from a surface float. At the lower terminus of the profiling range, the cam that rectifies wave vertical motion is released and the package, termed the Wirewalker, free ascends. No electronic components are used in the profiler, and only a few moving parts are involved. The Wirewalker is tolerant of a broad range of payloads: the ballast is adjusted by adding discrete foam blocks. The Wirewalker profiles 1000–3000 km month−1, vertically, with typical missions lasting from days to months. A description of the profiler is presented along with a discussion of basic profiling dynamics.

Observed Variability of Ocean Wave Stokes Drift, and the Eulerian Response to Passing Groups

Waves and currents interact via exchanges of mass and momentum. The mass and momentum fluxes associated with surface waves are closely linked to their Stokes drift. Both the variability of the Stokes drift and the corresponding response of the underlying flow are important in a wide range of contexts. Three methods are developed and implemented to evaluate Stokes drift from a recently gathered oceanic dataset, involving surface velocities measured continually over an area 1.5 km in radius by 45°. The estimated Stokes drift varies significantly, in line with the occurrence of compact wave groups, resulting in highly intermittent maxima. One method also provides currents at a fixed level (Eulerian velocities). It is found that Eulerian counterflows occur that completely cancel the Stokes drift variations at the surface. Thus, the estimated Lagrangian surface flow has no discernable mean response to wave group passage. This response is larger than anticipated and is hard to reconcile with current theory.