Showing papers on "Wavelength published in 1979"

Plasma resonance enhancement of Raman scattering by pyridine adsorbed on silver or gold sol particles of size comparable to the excitation wavelength

Abstract: Intense Raman scattering by pyridine molecules adsorbed on silver or gold aqueous sol particles of dimensions comparable to the wavelength is reported. The degree of intensity enhancement is strongly dependent on the excitation wavelength, with a sharp resonance Raman maximum for excitation at the wavelength of the Mie extinction maximum of the metal particles, and for the silver sols the Raman maximum is shown to follow the extinction maximum to longer wavelengths with increase in particle size. A new resonance Raman phenomenon is thus proposed which is the Raman component of resonant Mie scattering, and in which the polarizability of the metal particles is modulated by the vibrations of the adsorbed molecules. These observations confirm that surface plasma oscillations are involved in the intense Raman scattering already reported for molecules adsorbed at roughened silver surfaces. The metal dielectric function requirements for resonant Mie scattering enable the optimum excitation wavelength for plasma resonance-enhanced Raman studies at the surface of other metals to be estimated.

Constant Q-wave propagation and attenuation

Abstract: A linear model for attenuation of waves is presented, with Q, or the portion of energy lost during each cycle or wavelength, exactly independent of frequency. The wave propagation is completely specified by two parameters, e.g., Q and c0, a phase velocity at an arbitrary reference frequency ω0. A simple exact derivation leads to an expression for the phase velocity c as a function of frequency: c/c0 = (ω/ω0)γ, where γ = (1/π) tan−1 (1/Q). Scaling relationships for pulse propagation are derived and it is shown that for a material with a given value of Q, the risetime or the width of the pulse is exactly proportional to travel time. The travel time for a pulse resulting from a delta function source at x = 0 is proportional to xβ, where β = 1/(1 - γ). On the basis of this relation it is suggested that the velocity dispersion associated with anelasticity may be less ambiguously observed in the time domain than in the frequency domain. A steepest descent approximation derived by Strick gives a good time domain representation for the impulse response. The scaling relations are applied to field observations from the Pierre shale formation in Colorado, published by Ricker, who interpreted his data in terms of a Voigt solid with Q inversely proportional to frequency, and McDonal et al., who interpreted their data in terms of nonlinear friction. The constant Q theory fits both sets of data.

Spectral Sensitivity and Color Vision in Invertebrates

Abstract: The visual world offers a variety of information that enables animals to orient themselves to their surroundings. One specific feature of the visual information is the wavelength difference of light emittedfrom light sources or reflectedfrom objects. Under natural conditions, a general difference in the spectral composition of light is based upon the fact that light coming directly from light sources, e.g., the sun, sky, and moon, is characterized by its relatively high content of short wavelength ( 450nm) (Figs. 1). The physical basis of these differences is the preferential absorption by pigment molecules, which—in contrast to atoms and small molecules—have resonances above 300 nm and shift the bulk of the reflected light into the green and orange region of the spectrum. In water, the wavelength range is compressed in the long-wavelength part of the spectrum due to water’s high absorption of red and infrared light (Fig. 1). But in water, too, direct light is relatively richer in shortwave light. Neglecting the finer differences in the spectral content of light, this general distinction between direct and reflected light could be the cue that allows an animal to differentiate such basically different habitats as open spaces, shadowed areas, spaces rich in food, hiding places, etc.

Relation between the angular dependence of scattering and the statistical properties of optical surfaces

Abstract: A relation from vector scattering theory has been used to predict the angular distribution of scattered light from optical surfaces as a function of the wavelength, optical constants of the material, and spectral density function. For calculations of one-dimensional (two-dimensional) scattering, the spectral density function of the surface roughness is obtained from the Fourier transform (Hankel transform) of the autocovariance function, which in turn is determined from surface-profile data. Measured statistics presented for various types of optical surfaces indicate that there are three basic components of surface structure: long-range waviness, short-range random roughness, and periodicity; one or more of which may be present on a given surface. Averaged and unaveraged surface-profile data for the same surface are shown to be consistent. Experimental data are presented that yield an exponential autocovariance function, and give a reasonably good fit to a Poisson distribution of zero crossings. Finally, angular scattering values calculated using measured surface statistics with vector scattering theory are compared to scattering values measured on the same surface. The shapes of the measured and calculated curves are similar, but the magnitudes are not. However, the rms surface roughnesses calculated from total integrated scattering measurements are in excellent agreement with values measured directly on these same surfaces.

The effect of orbital motions on synthetic aperture radar imagery of ocean waves

Abstract: The formation of wave-like patterns in synthetic aperture radar (SAR) images of the ocean surface caused by orbital motions is investigated. Furthermore, the degradation in azimuthal resolution due to these motions is calculated by applying a least square fit to the phase history. Formulas are given which describe the variation of intensity in azimuthal direction in the image plane as well as the degradation in azimuthal resolution as a function of ocean wave amplitude, wave frequency, direction of wave propagation, and radar wavelength, incidence angle, and integration time.

A model for predicting acoustic material signatures

Abstract: Unique acoustic material signatures (AMS) may be obtained in the reflection acoustic microscope. The proposed model shows that they result from interference between two components reradiated into the immerson fluid at the materials critical Rayleigh angle ϑR. The characteristic period ΔzN of this interference signature varies as the square of the Rayleigh wave velocity and is empirically given by ΔzN=λR/sinϑR, where λR is the Rayleigh wavelength. Materials covering a greater than 3 : 1 velocity range agree well with this physical model. Substitution of the longitudinal wave velocity in the expression extends the range of measurable AMS to acoustically slower materials. A variety of applications for AMS is suggested.

The Non-Linear Theory of Free Electron Lasers and Efficiency Enhancement

Abstract: The development of lasers in which the active medium is a relativistic stream of free electrons has recently evoked much interest. The potential advantages of such free-electron lasers include, among other things, continuous frequency tunability, very high operating power, and high efficiency. The free-electron laser (FEL) is characterized by a pump field, for example, a spatially periodic magnetic field which scatters from a relativistic-electron beam. The scattered radiation has a wavelength much smaller than the pump wavelength, depending on the electron-beam energy. The authors present a general self-consistent nonlinear theory of the FEL process. The nonlinear formulation of the temporal steady-state FEL problem results in a set of coupled differential equations governing the spatial evolution of the amplitudes and wavelength of the radiation and space-charge fields. These equations are readily solved numerically since the amplitude and wavelength vary on a spatial scale which is comparable to a growth length of the output radiation. A number of numerical and analytical illustrations are presented, ranging from the optical to the submillimeter-wavelength regime. Our nonlinear formulation in the linear regime is compared with linear theory, and agreement is found to be excellent. Analytical expressions for the saturated efficiency and radiation amplitude are alsomore » shown to be in very good agreement with our nonlinear numerical solutions. Efficiency curves are obtained for both the optical and submillimeter FEL examples with fixed magnetic-pump parameters. It is shown that these intrinsic efficiencies can be greatly enhanced by appropriately contouring the magnetic-pump period. In the case of the optical FEL, the theoretical single-pass efficiency can be made greater than 20% by appropriately decreasing the pump period and increasing the pump magnetic field.« less

The hydrodynamics of flagellar propulsion: helical waves

Abstract: The swimming of a micro-organism by the propagation of helical waves on a long slender flagellum is analysed. The model developed by Higdon (1979) is used to study the motion of an organism with a spherical cell body (radius A) propelled by a cylindrical flagellum (radius a, length L).The average swimming speed and power consumption are calculated for helical waves (amplitude α, wavenumber k). A wide range of parameter values is considered to determine the optimal swimming motion. The optimal helical wave has ak ≈ 1, corresponding to a pitch angle of 45°. The optimum number of waves on the flagellum increases as the flagellar length L/A increases, such that the optimum wavelength decreases as L/A increases. The efficiency is relatively insensitive to the flagellar radius a/A. The optimum flagellar length is L/A ≈ 10.The results are compared to calculations using two different forms of resistance coefficients. Gray-Hancock coefficients overestimate the swimming speed by approximately 20% and underestimate the power consumption by 50%. The coefficients suggested by Lighthill (1976) overestimate the swimming speed for large cell bodies (L/A 15) by 10%. The Lighthill coefficients underestimate the power consumption up to 50% for L/A 10. Overall, the Lighthill coefficients are superior to the Gray-Hancock coefficients in modelling swimming by helical waves.

The effects of terrain shape on nonlinear hydrostatic mountain waves

Abstract: Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength. Nonlinear lower and upper (radiative) boundary conditions are utilized and found to have a strong influence on the wave structure at large amplitudes. The results for symmetric and asymmetric mountain profiles reveal that the wave amplitude and wave drag are significantly enhanced for mountains with gentle windward and steep leeward slopes. These results confirm and explain those obtained by Raymond (1972) using a different solution method. Several results obtained by Smith (1977) from perturbation analysis are also confirmed and extended to large amplitudes. The methods are also applied to investigate the nonlinear nature of the singularity predicted by linear theory for flow over a step.

Third-harmonic generation in argon, krypton, and xenon: Bandwidth limitations in the vicinity of Lyman-α

Abstract: Using experimentally determined oscillator strengths and photoionization cross-sectional data, we compute the dispersion characteristics of Ar, Kr, and Xe up to their first ionization levels and determine the spectral regions in the VUV where these gases exhibit negative dispersion and so can be efficiently used for frequency tripling. We then investigate the bandwidths over which efficient tripling can be achieved in phase-matched gas mixtures. The bandwidth is limited by the rapidly varying dispersion in the vicinity of resonance transitions in the gases. In particular, we look at the case of frequency tripling 3647 A radiation to 1215.7 A (hydrogen Lyman-α) and show, that for fundamental wavelength bandwidths as narrow as 1 A, the rapid change in refractive index with wavelength can preclude phase matching over the entire bandwidth of the radiation.

Tailoring zero chromatic dispersion into the 1.5-1.6 μm low-loss spectral region of single-mode fibres

Abstract: We have designed and fabricated single-mode silica fibres that have zero chromatic dispersion within the 1.5-1.6 μm low-loss spectral region by controlling their waveguide dispersion and dopant-dependent material dispersion. These fibres have small core diameters and large core-cladding refractive-index differences, n = 0.018, corresponding to a 13 mole % GeO2 dopant concentration in the core. The zero-dispersion wavelength was shifted from -0 = 1.375 = to =0 = 1.54 = by decreasing the fibre core diameter from 7 μm to 4.8 μm. This ability to tailor the minimum dispersion wavelength to the ultra-low-loss region near 1.55 μm is important for designing single-mode fibres for very long distance and very high capacity optical transmission.

Temperature‐compensated surface‐acoustic‐wave devices with SiO2 film overlays

Abstract: Temperature‐stable surface‐acoustic‐wave (SAW) devices have been fabricated with an rf‐sputtered SiO3. film overlay on YZ LiTaO2. The material properties of this composite structure relevant to surface‐acoustic‐wave propagation have been thoroughly studied. For an SiO2 film thickness of approximately one‐half of an acoustic wavelength, a piezoelectric coupling coefficient of 0.014 is present and the temperature stability of phase delay is similar in magnitude to that of bulk acoustic waves in AT‐cut quartz. A variation in delay of less than one part in 105 is observed over the temperature range −40 to 80 °C. The film‐overlay structure is dispersive and the nature of this dispersion has been fully characterized. The dependence of the phase and group delay on temperature and frequency has been measured. For most characteristics, theoretical as well as experimental values have been determined. In addition to YZ LiTaO3, five other cuts of LiTaO3 have been analyzed theoretically. To demonstrate potential appli...

Numerical solution of the exact equations for capillary-gravity waves

Abstract: A numerical method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The dynamic boundary equation is used in its exact nonlinear form. The procedure involves a boundary-integral formulation coupled with a Newtonian iteration. Solutions of high accuracy can be achieved over much of the range of wavelengths and heights including limiting waves. A number of different continuous families of solutions have been produced, all of which ultimately exhibit closed bubbles at their troughs. The so-called critical wavelengths are less important than have been previously assumed; the number of possible wave forms does increase with increasing wavelength, however.

A high-order cnoidal wave theory

Abstract: A method is outlined by which high-order solutions are obtained for steadily progressing shallow water waves. It is shown that a suitable expansion parameter for these cnoidal wave solutions is the dimensionless wave height divided by the parameter m of the cn functions: this explicitly shows the limitation of the theory to waves in relatively shallow water. The corresponding deep water limitation for Stokes waves is analysed and a modified expansion parameter suggested.Cnoidal wave solutions to fifth order are given so that a steady wave problem with known water depth, wave height and wave period or length may be solved to give expressions for the wave profile and fluid velocities, as well as integral quantities such as wave power and radiation stress. These series solutions seem to exhibit asymptotic behaviour such that there is no gain in including terms beyond fifth order. Results from the present theory are compared with exact numerical results and with experiment. It is concluded that the fifth-order cnoidal theory should be used in preference to fifth-order Stokes wave theory for wavelengths greater than eight times the water depth, when it gives quite accurate results.

Infrared‐to‐optical image conversion by Bragg reflection from thermally induced index gratings

Abstract: We have observed efficient reproduction at visible wavelengths of 1.06‐μ images. We employed a phase‐matched four‐wave mixing process in which three waves at ν, ν, and ω mix to generate a fourth wave at ω, with no resonant conditions in either frequency. The image conversion was seen with each of the 14 liquids tried as a nonlinear medium and also with a glass. Thermal index changes were the dominant mechanism.

Large amplitude progressive interfacial waves

Abstract: This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Pade approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

Resonance Anomalies in the Lamellar Grating

Abstract: The problem of diffraction by a perfectly conducting lamellar grating is examined numerically and analytically by use of a modal expansion technique. At various complex wavelengths, with a positive imaginary part, individual mode amplitudes have poles which give rise to resonance effects in the orders at nearby real wavelengths. These are the well-known resonance anomalies. We determine the trajectories of these poles as functions of groove depth, finding that as this parameter increases they move in the complex wavelength plane to a mode threshold, or cut-off wavelength—from a Rayleigh wavelength in the case of S -polarization and from zero wavelength in the case of P -polarization. It is emphasized that the modal expansion technique is particularly valuable in gaining an understanding of the dynamics of diffraction gratings, and that the resonance poles are perhaps the basic dynamical objects determining their behaviour.

Angular distribution of fluorescence from liquids and monodispersed spheres by evanescent wave excitation

Abstract: Experimental data on the angular distribution of fluorescence from thick liquid dye layers excited by evanescent waves are found to agree well with Fresnel theory and with an effective thickness formulation. Qualitative agreement of theory with fluorescence data obtained from monodispersed spherical particles having diameters comparable to the wavelength of the incident evanescent radiation and impregnated with dye molecules is also attained. From our results, the optimum incident and observation angles and polarizations to enhance the contrast and SNR for inelastic ATR reemission spectroscopy applied to studying micron or submicron layers of particulates can be predicted.

Magnetopause Kelvin-Helmholtz instability

Abstract: The Kelvin-Helmholtz instability as it applies to the dayside magnetopause is reviewed. Simple theory suggests the boundary should generally be unstable to waves moving at a large angle to the Earth's field. Nonlinear effects, how amplitudes might be limited, and what dynamic role the instability could have in boundary regions in stimulating mass and momentum transfer are discussed. Examination of data from a particular ISEE spacecraft pass shows relatively small amplitude (750 km) waves present on the boundary. Corresponding wavelength estimates show wave momentum is not significant at the time of the pass.

Geomagnetopause surface fluctuations observed by Voyager 1

Abstract: Moving out of the dawnside of the earth's magnetosphere, Voyager 1 crossed the magnetopause apparently seven times, despite the high spacecraft speed of 11 km/sec. Normals to the magnetopause and their associated error cones were estimated for each of the crossings using a minimum variance analysis of the internal magnetic field. The oscillating nature of the ecliptic plane component of these normals indicates that most of the multiple crossings were due to a wave-like surface disturbance moving tailward along the magnetopause. The wave, which was aperiodic, was modeled as a sequence of sine waves. The amplitude, wavelength, and speed were determined for two pairs of intervals from the measured slopes, occurrence times, and relative positions of six magnetopause crossings. The magnetopause thickness was estimated to lie in the range 300 to 700 km with higher values possible. The estimated amplitude of these waves was obviously small compared to their wavelengths.

Turbulent Taylor vortex flow

Abstract: The wavelength of turbulent Taylor vortices at very high Taylor numbers up to 40000Tc , has been measured in long fluid columns with radius ratios η = 0·896 and η = 0·727. Following slow acceleration procedures the wavelength (in units of the gap width) of turbulent axisymmetric vortices was found to be λ = 3·4 ± 0·1 with the small gap and about λ = 2·4 ± 0·1 with the larger gap, and thus in both cases substantially larger than the critical wavelength of laminar Taylor vortices. In the narrow and wide gap the wavelength was, within experimental error, independent of the Taylor number for T > 100Tc . In the experiments with the narrow gap a clear dependence of the value of the wavelength of the turbulent vortices on initial conditions was found. After sudden starts to Taylor numbers > 700Tc the wavelength of steady axisymmetric turbulent vortices was only 2·4 ± 0·05, being then the same as the wavelength of the vortices after sudden starts in the wide gap, and being, within the experimental error, independent of the Taylor number. In the narrow gap all values of the wavelength between λmax = 3·4 and λmin = 2·4 can be realized as steady states through different acceleration procedures. In the wide gap the dependence of the wavelength on initial conditions is just within the then larger experimental uncertainty of the measurements.

Optical Constants of Polycrystalline 3d Transition Metal Oxides in the Wavelength Region 350 to 1200 nm

Abstract: The refractive index and the extinction coefficient of polycrystalline oxides of Ti, V, Mn, Fe, Co, Cu, and Zn are determined from the measurement of the ratio of the reflection coefficients for incident light polarized parallel and perpendicular to the plane of incidence. The absorption coefficient and the reflectivity for light of normal incidence are calculated from the data. Among these oxides, CuO has a large extinction coefficient and a rather small refractive index, and hence a large absorption coefficient and a medium reflectivity, over the solar spectrum.

A Generalized Method of Resolving Transient Disturbances into Standing and Traveling Waves by Space-Time Spectral Analysis

Abstract: Space-time spectral formulas are generalized to partition the time power spectrum of transient disturbances consisting of multiple wavenumbers into standing and traveling parts by assuming that these parts are incoherent with each other. This technique is useful in interpreting the spatial variation of wave amplitude in terms of standing and traveling waves. An example of its application to the analysis of transient planetary waves is given.

Resonances in electromagnetic scattering by objects with negative absorption

Abstract: This is a numerical study of electromagnetic scattering by particles exhibiting negative absorption, i.e., with refractive index m = n(1 + κi), where the time dependence is exp(+iωt). The particle is a homogeneous circular cylinder. The stimulating incident plane wave travels perpendicularly to the cylinder axis. The scattering, amplification, and extinction cross sections as well as the differential scattering cross sections were evaluated for n = 1.50 over the nκ = 0.001–1 range for the size parameter up to α = 50, where α = 2πa/λ (a is the radius and λ is the wavelength). In some cases results were obtained for much larger values of α. The most remarkable finding was the occurrence of sharp resonances. Not only does this provide for large amplification of the scattered radiation traveling outward as spherical waves (for 3-D objects) or as cylindrical waves (for 2-D objects), but, because of the occurrence of negative extinction cross sections, it may also result in amplification of the incident plane wave. The present formalism (Lorenz-Mie for spheres; Rayleigh for cylinders) implies a particular and highly contrived mechanism for pumping and stimulation. However, the formalism may be extended to other particular mechanisms.

Vertical propagation of waves in the solar atmosphere. I. Observations of phase delays

Abstract: The Sacramento Peak Observatory Tower Vacuum Telescope, echelle spectrograph, and diode array were used to simultaneously measure velocities and intensities in three spectral lines and the continuum. According to our contribution function calculations, these wavelengths are formed at heights from the low photosphere to the chromosphere. The phase velocities of the intensity and velocity oscillations between the various heights, and the phase relations between intensity and velocity at one height were determined as a function of frequency in the range 0--11.1 mHz. The oscillations are found to be predominantly evanescent in nature for frequencies less than 4 mHz and propagating upward at higher frequencies, with phase velocities approaching the sound speed at approximately 6 mHz. We calculated the upward mechanical flux in the observed waves at two atmospheric heights by an integration in frequency, and we show that in the chromosphere the propagated power is centered at 6 MHz but is still much too small to heat the overlying atmosphere.

A theory for wave-power absorption by two independently oscillating bodies

Abstract: In a recent paper (Evans 1976) a theory was presented for the behaviour of an oscillating two-dimensional cylinder of any shape which was capable of absorbing energy from a given regular sinusoidal wave. In particular an expression was derived for the efficiency of power absorption of the cylinder when oscillating in a single mode in terms of properties of the solution of the so-called radiation problem in which the cylinder is forced to oscillate in the appropriate mode in the absence of the incident wave train. In the present paper this theory is extended to two independent cylinders of arbitrary shape each oscillating in a single mode and capable of absorbing energy in that mode. A general expression for the efficiency is derived which depends on properties of the solution to a new radiation problem, in which one cylinder is forced to oscillate in the presence of the other cylinder, which is held fixed in its equilibrium position. In this case, the efficiency also depends on cross-coupling coefficients related to the force on the fixed cylinder due to the motion of the oscillating cylinder. It is shown that the cylinders can be tuned to absorb all the incident wave energy at a given frequency even for symmetric cylinders, in contrast to the single symmetric cylinder, for which the maximum efficiency has been shown to be 50%. The general solution to the new radiation problem is derived in terms of the solution to the radiation problem for a single cylinder, by assuming that the cylinders are far enough apart for local wave effects to be negligible. The special case of two widely spaced rolling vertical plates is considered in detail and curves showing the variation of efficiency with wavelength are given for a variety of plate spacings and points of rotation.

Edge waves on complex beach profiles

Abstract: In order to interpret field data in terms of edge wave modes, investigators usually assume that the beach profile is linear, allowing the use of simple analytical solutions for edge wave structure and wavelength. The validity of this assumption is checked by using a numerical model to find the edge wave modes on a typical concave beach. Results show that estimates of edge wave wavelength using the plane beach assumption can be wrong by ±100% at a fixed mean sea level with a further error of ±50% introduced by the tides. Greatly improved estimates can be made if the value of beach slope is chosen to reflect suitably the offshore extent of the edge wave. A rule of thumb for calculating the effective beach slope βe is , where h is the water depth at distance x′ from shore, L is the edge wave wavelength, and n is the edge wave mode number. The motion of the offshore profile of the edge wave due to a change of tidal elevation is dramatically different on a concave beach than on a plane beach. The tendency for the profile to move offshore for a drop in tide is compensated by the decrease in mean beach slope and hence reduction in wavelength and offshore extent of the wave. For a fixed instrument a drop in tide may lead to a profile shift onshore or offshore or no shift at all. Edge wave damping on a concave beach is shown to change as a function of tide. At low tide the surf zone width is increased while edge wave wavelength is decreased, both factors increasing damping. Thus edge wave spectra taken at low tide may be less energetic than those at high tide, particularly at high frequencies.

A model for the interpretation of wave ripple-marks using their wavelength, textural composition, and shape

Abstract: Two graphs based on field and experimental data assembled from a variety of sources are given showing how the wavelength, flatness (vertical form-index or ripple index), and grain size of wave ripple marks in the stratigraphic record can be interpreted in terms of the near-bed water particle orbital diameter and maximum orbital velocity induced by progressive surface waves. The graphs lead to estimates of wave period, from which the environmental setting and possible water depths and wave heights can be judged. Wave ripple-marks are the response of a mobile bed to multi component currents that are more complex than is generally recognized. The asymmetry and slow translation of the structures is shown empirically to depend on the relative importance of 2 of the 3 minimum recognizable components.