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AbstractKinetic energy associated with inertia–gravity waves (IGWs) and other ageostrophic phenomena often overwhelms kinetic energy due to geostrophic motions for wavelengths on the order of tens of kilometers. Understanding the dependencies of the wavelength at which balanced (geostrophic) variability ceases to be larger than unbalanced variability is important for interpreting high-resolution altimetric data. This wavelength has been termed the transition scale. This study uses acoustic Doppler current profiler (ADCP) data along with auxiliary observations and a numerical model to investigate the transition scale in the eastern tropical Pacific and the mechanisms responsible for its regional and seasonal variations. One-dimensional kinetic energy wavenumber spectra are separated into rotational and divergent components, and subsequently into vortex and wave components. The divergent motions, most likely predominantly IGWs, account for most of the energy at wavelengths less than 100 km. The observed regional and seasonal patterns in the transition scale are consistent with those from a high-resolution global simulation. Observations, however, show weaker seasonality, with only modest wintertime increases in vortex energy. The ADCP-inferred IGW wavenumber spectra suggest that waves with near-inertial frequency dominate the unbalanced variability, while in model output, internal tides strongly influence the wavenumber spectrum. The ADCP-derived transition scales from the eastern tropical Pacific are typically in the 100–200-km range.

Abstract: The K-profile parameterization (KPP) is a common method to model turbulent fluxes in regional and global oceanic models. Many versions of KPP exist in the oceanic sciences community, and one of their main differences is how they take the effects of nonbreaking waves into account. Although there is qualitative consensus that nonbreaking waves enhance vertical mixing due to the ensuing Langmuir circulations, there is no consensus on the quantitative aspects and modeling approach. In this paper we use a recently developed method to estimate both components of KPP (the diffusive term, usually called local, and the nondiffusive component, usually called nonlocal) based on numerically simulated turbulent fluxes without any a priori assumptions about their scaling or their shape. Through this method we show that the cubic shape usually used in KPP is not optimal for wavy situations and propose new ones. Furthermore, we show that the formulation for the nondiffusive fluxes, which currently only depend on the presence of surface buoyancy fluxes, should also take wave effects into account. We also investigate how the application of these changes to KPP improves the representation of turbulent fluxes in a diagnostic approach when compared with previous models.

AbstractSurface gravity waves play a major role in the exchange of momentum, heat, energy, and gases between the ocean and the atmosphere. The interaction between currents and waves can lead to variations in the wave direction, frequency, and amplitude. In the present work, we use an ensemble of synthetic currents to force the wave model WAVEWATCH III and assess the relative impact of current divergence and vorticity in modifying several properties of the waves, including direction, period, directional spreading, and significant wave height Hs. We find that the spatial variability of Hs is highly sensitive to the nature of the underlying current and that refraction is the main mechanism leading to gradients of Hs. The results obtained using synthetic currents were used to interpret the response of surface waves to realistic currents by running an additional set of simulations using the llc4320 MITgcm output in the California Current region. Our findings suggest that wave parameters could be used to detect and characterize strong gradients in the velocity field, which is particularly relevant for the Surface Water and Ocean Topography (SWOT) satellite as well as several proposed satellite missions.

Coastal trapped waves (CTWs) transport energy along coastlines and drive coastal currents and upwelling. CTW modes are nonorthogonal when frequency is treated as the eigenvalue, preventing the separation of modal energy fluxes and quantification of longshore topographic scattering. Here, CTW modes are shown to be orthogonal with respect to energy flux (but not energy) when the longshore wavenumber is the eigenvalue. The modal evolution equation is a simple harmonic oscillator forced by longshore bathymetric variability, where downstream distance is treated like time. The energy equation includes an expression for modal topographic scattering. The eigenvalue problem is carefully discretized to produce numerically orthogonal modes, allowing CTW amplitudes, energy fluxes, and generation to be precisely quantified in numerical simulations. First, a spatially uniform K1 longshore velocity is applied to a continental slope with a Gaussian bump in the coastline. Mode-1 CTW generation increases quadratically with the amplitude of the bump and is maximum when the bump's length of coastline matches the natural wavelength of the CTW mode, as predicted by theory. Next, a realistic K1 barotropic tide is applied to the Oregon coast. The forcing generates mode-1 and mode-2 CTWs with energy fluxes of 6 and 2 MW, respectively, which are much smaller than the 80 MW of M2 internal-tide generation in this region. CTWs also produce 1-cm sea surface displacements along the coast, potentially complicating the interpretation of future satellite altimetry. Prospects and challenges for quantifying the global geography of CTWs are discussed. [ABSTRACT FROM AUTHOR]

Irregular, unidirectional surface water waves incident on model ice in an ice tank are used as a physical model of ocean surface wave interactions with sea ice. Results are given for an experiment consisting of three tests, starting with a continuous ice cover and in which the incident wave steepness increases between tests. The incident waves range from causing no breakup of the ice cover to breakup of the full length of ice cover. Temporal evolution of the ice edge, breaking front, and mean floe sizes are reported. Floe size distributions in the different tests are analyzed. The evolution of the wave spectrum with distance into the ice-covered water is analyzed in terms of changes of energy content, mean wave period, and spectral bandwidth relative to their incident counterparts, and pronounced differences are found between the tests. Further, an empirical attenuation coefficient is derived from the measurements and shown to have a power-law dependence on frequency comparable to that found in field measurements. Links between wave properties and ice breakup are discussed. [ABSTRACT FROM AUTHOR]

The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates. [ABSTRACT FROM AUTHOR]

Despite a recent resurgence of observational studies attempting to quantify the ice-induced attenuation of ocean waves in polar oceans, the physical processes governing this phenomenon are still poorly understood. Most analyses have attempted to relate the spatial rate of wave attenuation to wave frequency, but have not considered how this relationship depends on ice, wave, and atmospheric conditions. An in-depth analysis of the wave-buoy data collected during the 2017 Polynyas, Ice Production, and Seasonal Evolution in the Ross Sea (PIPERS) program in the Ross Sea is conducted. Standard techniques are used to estimate the spatial rate of wave attenuation a, and the influence of a number of potential physical drivers on its dependence on wave period T is investigated. A power law is shown to consistently describe the a(T) relationship, in line with other recent analyses. The two parameters describing this relationship are found to depend significantly on sea ice concentration, mean wave period, and wind direction, however. Looking at cross correlations between these physical drivers, three regimes of ice-induced wave attenuation are identified, which characterize different ice, wave, and wind conditions, and very possibly different processes causing this observed attenuation. This analysis suggests that parameterizations of ice-induced wave decay in spectral wave models should be piecewise, so as to include their dependence on local ice, wave, and wind conditions. [ABSTRACT FROM AUTHOR]

Between 5% and 25% of the total momentum transferred between the atmosphere and ocean is transmitted via the growth of long surface gravity waves called ''swell.'' In this paper, we use large-eddy simulations to show that swell-transmitted momentum excites near-inertial waves and drives turbulent mixing that deepens a rotating, stratified, turbulent ocean surface boundary layer. We find that swell-transmitted currents are less effective at producing turbulence and mixing the boundary layer than currents driven by an effective surface stress. Overall, however, the differences between swell-driven and surface-stress-driven boundary layers are relatively minor. In consequence, our results corroborate assumptions made in Earth system models that neglect the vertical structure of swell-transmitted momentum fluxes and instead parameterize all air--sea momentum transfer processes with an effective surface stress. [ABSTRACT FROM AUTHOR]

The effects of nonbreaking surface waves on upper-ocean dynamics enter the wave-averaged primitive equations through the Stokes drift. Through the resulting upper-ocean dynamics, Stokes drift is a catalyst for the fluxes of heat and trace gases between the atmosphere and ocean. However, estimates of the Stokes drift rely crucially on properly resolving the wave spectrum. In this paper, using state-of-the-art spatial measurements (in situ and airborne remote sensing) from a number of different field campaigns, with environmental conditions ranging from 2 to 13ms21 wind speed and significant wave height of up to 4m, we characterize the properties of the surface wave field across the equilibrium and saturation ranges and provide a simple parameterization of the transition between the two regimes that can easily be implemented in numerical wave models. We quantify the error associated with instrument measurement limitations, or incomplete numerical parameterizations, and propose forms for the continuation of these spectra to properly estimate the Stokes drift. Depending on the instrument and the sea state, predictions of surface Stokes drift may be underestimated by more than 50%. [ABSTRACT FROM AUTHOR]

The irregular nature of vertical profiles of density in the thermocline appears well described by a Poisson process over vertical scales 2-200 m. To what extent does this view of the thermocline conflict with established models of the internal wavefield? Can a one-parameter Poisson subrange be inserted between the larger-scale wavefield and the microscale field of intermittent turbulent dissipation, both of which require many parameters for their specification? It is seen that a small modification to the Poisson vertical correlation function converts it to the corresponding correlation function of the Garrett--Munk (GM) internal wave spectral model. The linear scaling relations and vertical wavenumber dependencies of the GM model are maintained provided the Poisson constant k0 is equated with the ratio of twice the displacement variance to the vertical correlation scale of the wavefield. Awareness of this Poisson wavefield relation enables higher-order strain statistics to be determined directly from the strain spectrum. Using observations from across the Pacific Ocean, the average Thorpe scale of individual overturning events is found to be nearly equal to the inverse of k0, the metric of background thermocline distortion. If the fractional occurrence of overturning f is introduced as an additional parameter, a Poisson version of the Gregg--Henyey relationship can be derived. The Poisson constant, buoyancy frequency, and f combine to create a complete parameterization of energy transfer from internal wave scales through the Poisson subrange to dissipation. An awareness of the underlying Poisson structure of the thermocline will hopefully facilitate further improvement in both internal wave spectral models and ocean mixing parameterizations. [ABSTRACT FROM AUTHOR]

The irregular nature of vertical density profiles is a ubiquitous characteristic of the ocean thermocline. This distortion can be quantified by tracking a set of constant-density (isopycnal) surfaces over time. Examination of 30 000 km of vertical density profile data from seven Pacific Ocean sites indicates that the statistics of isopycnal vertical separation follow the gamma probability distribution, the continuous representation of a Poisson process. All aspects of this process are specified by a single parameter k0, of order 0.5-2m-1 across the Pacific. When vertical wavenumber spectra of vertical strain are nondimensionalized by k0, the variability in these pan-Pacific spectra reduce from a factor of 20 to a factor of 2. Given that numerous dimensionless metrics such as the Richardson number, Froude number, Burger number, etc., are required to specify dynamical balances in the sea, it is intriguing that a single-parameter model describes all aspects of the statistics of vertical strain over the range of scales ~2-200 m. While both internal wave and vortical motions are present in the data, the waves dominate the strain signal at these sites. The high-wavenumber cutoff in the strain spectrum is set by the nonsinusoidal waveform of short-vertical-scale internal waves. As large-scale numerical models improve in resolution, they should replicate this Poisson structure in order to properly model plankton variability, vertical diffusion, horizontal dispersion, sound propagation, and other fine-scale phenomena. [ABSTRACT FROM AUTHOR]

To clarify characteristics and mechanisms of mesoscale variability in the deep ocean, we conducted a twodimensional observation with a 3 3 3 grid mooring array around site R (308N, 1478E) during 2014-16. We analyze the obtained velocity data together with pastmooring observation data in the northwest Pacific basin and outputs of an ocean general circulation model (OGCM). In our two-dimensional mooring observations, the variability of zonal and meridional velocities at a depth of 4000m was prominent at periods of 174 and 58 days, respectively. The variability at periods of 174 and 58 days propagated to the northwest and west-southwest, respectively, as a single plane wave. The variability at the period of 58 days was considered to be topographic Rossby waves (TRWs) under stratification originated in the Kuroshio Extension region north of site R, as demonstrated by our previous study. At the period of 174 days, zonal and meridional wavenumbers estimated from the phase lag for zonal velocities also satisfied the dispersion relation of TRWs under stratification. Backward ray tracing from site R indicated that energy of TRWs propagated from the eastern slope of the Shatsky Rise to site R almost along f/H contours, where f is the Coriolis parameter and H is water depth. The orientation of major axis of variance ellipses at periods of 174 days and longer, obtained from the past mooring observations and the OGCM outputs, tended to be parallel to f/H contours, being consistent with the direction of energy propagation of TRWs. [ABSTRACT FROM AUTHOR]

Wave streaming is a near-bottom mean current induced by the bottom drag on surface gravity waves. Wave variations include the variations in wave heights, periods, and directions. Here we use numerical simulations to study the effects of wave streaming and wave variations on the circulation that is driven by incident surface waves. Wave streaming induces an inner-shelf Lagrangian overturning circulation, which links the inner shelf with the surf zone. Wave variations cause alongshore-variable wave breaking that produces surf eddies; however, such eddies can be suppressed by wave streaming. Moreover, with passive tracers we show that wave streaming and wave variations together enhance the crossshelf material transport. [ABSTRACT FROM AUTHOR]

Penetration of solar radiation in the upper few meters of the ocean creates a near-surface, stratified diurnal warm layer. Wind stress accelerates a diurnal jet in this layer. Turbulence generated at the diurnal thermocline, where the shear of the diurnal jet is concentrated, redistributes heat downward via mixing. New measurements of temperature and turbulence from fast thermistors on a surface-following platform depict the details of this sequence in both time and depth. Temporally, the sequence at a fixed depth follows a counterclockwise path in log-logN parameter space. This path also captures the evolution of buoyancy Reynolds number (a proxy for the anisotropy of the turbulence) and Ozmidov scale (a proxy for the outer vertical length scale of turbulence in the absence of the free surface). Vertically, the solar heat flux always leads to heating of fluid parcels in the upper few meters, whereas the turbulent heat flux divergence changes sign across the depth of maximum vertical temperature gradient, cooling fluid parcels above and heating fluid parcels below. In general, our measurements of fluid parcel heating or cooling rates of order 0.18Ch-1 are consistent with our estimates of heat flux divergence. In weak winds (<2ms-1), sea surface temperature (SST) is controlled by the depth-dependent absorption of solar radiation. In stronger winds, turbulent mixing controls SST. [ABSTRACT FROM AUTHOR]

The equatorial deep jets (EDJ) are a striking feature of the equatorial ocean circulation. In the Atlantic Ocean, the EDJ are associated with a vertical scale of between 300 and 700 m, a time scale of roughly 4.5 years, and upward energy propagation to the surface. It has been found that the meridional width of the EDJ is roughly 1.5 times larger than expected based on their vertical scale. Here, the authors use a shallow-water model for a high-order baroclinic vertical normal mode to argue that mixing of momentum along isopycnals can explain the enhanced width. A lateral eddy viscosity of 300 m2 s−1 is found to be sufficient to account for the width implied by observations. [ABSTRACT FROM AUTHOR]

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ultimately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a nonlinear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter. [ABSTRACT FROM AUTHOR]

The residual effect of surface gravity waves on mean flows in the upper ocean is investigated using thickness-weighted mean (TWM) theory applied in a vertically Lagrangian and horizontally Eulerian coordinate system. Depth-dependent equations for the conservation of volume, momentum, and energy are derived. These equations allow for (i) finite amplitude fluid motions, (ii) the horizontal divergence of currents, and (iii) a concise treatment of both kinematic and viscous boundary conditions at the sea surface. Under the assumptions of steady and monochromatic waves and a uniform turbulent viscosity, the TWM momentum equations are used to illustrate the pressure- and viscosity-induced momentum fluxes through the surface, which are implicit in previous studies of the wave-induced modification of the classical Ekman spiral problem. The TWM approach clarifies, in particular, the surface momentum flux associated with the so-called virtual wave stress of Longuet-Higgins. Overall, the TWM framework can be regarded as an alternative to the three-dimensional Lagrangian mean framework of Pierson. Moreover, the TWM framework can be used to include the residual effect of surface waves in large-scale circulation models. In specific models that carry the TWM velocity appropriate for advecting tracers as their velocity variable, the turbulent viscosity term should be modified so that the viscosity acts only on the Eulerian mean velocity. [ABSTRACT FROM AUTHOR]

Solutions of barotropic coastal-trapped waves in the shallow-water context are discussed for different shapes of the bottom topography. In particular, an infinite family of topographic waves over continental shelves characterized by a shape parameter is considered. The fluid depth is proportional to xs, where x is the offshore coordinate and s is a real, positive number. The model assumes the rigid-lid approximation and a semi-infinite domain 0 ≤ x ≤ ∞. The wave structure and the dispersion relation depend explicitly on the shape parameter s. Essentially, waves over steeper shelves possess higher frequencies and phase speeds. In addition, the wave frequency is independent of the alongshore wavenumber k, implying a zero group velocity component along the coast. The advantages and limitations of this formulation, as well as some comparisons with other models, are discussed in light of numerical simulations for waves over arbitrary topography within a finite domain. The numerical calculations show that the frequency of the waves present a nondispersive regime at small wavenumbers (observed by several authors), followed by a constant value predicted by the analytical solutions for larger k. It is concluded that these frequencies can be considered as an upper limit reached by barotropic coastal-trapped waves over the infinite family of xs-bottom profiles, regardless of the horizontal and vertical scales of the system. The modification of the dispersion curves in a stratified ocean is briefly discussed. [ABSTRACT FROM AUTHOR]

An analysis of airborne wave observations collected in the Gulf of Tehuantepec is presented. The data include lidar measurements of the surface displacement as a function of two horizontal dimensions in fetch-limited conditions, with fetches between 20 and 500 km and winds between 10 and 20 m s−1. The spatial data have an advantage over the commonly used single-point time series measurements, allowing direct estimates of the wavelength and wave slope, including spatial information such as the lengths of crests exceeding various thresholds. This study presents an analysis of several statistical wind wave parameters, including the joint probability distribution function (pdf) of wave amplitudes and wavelengths; the pdf of wave heights, wavenumber vectors, and wave slopes; as well as the statistics of the lengths of crests exceeding threshold wave heights and slopes. The empirical findings from the lidar data are compared against analytical theories in the literature, including some that had not been tested previously with field data such as the work by M. S. Longuet-Higgins describing the length of contours surrounding large wave heights per unit surface area. The effect of second-order nonlinearities on the distribution of crest lengths per unit surface area is investigated with analytical approximations and stochastic numerical simulations from computed directional wavenumber spectra. The results show that second-order nonlinearities can increase the crest-length distribution of large waves by a factor of 2 or more. [ABSTRACT FROM AUTHOR]

Based on Monte Carlo simulations of the nonlinear Schrödinger equation in two horizontal dimensions, the dependence of the kurtosis on the directional energy distribution of the initial conditions is examined. The parametric survey is carried out to obtain the behavior of the kurtosis as function of the Benjamin-Feir index and directional spread in directional sea states. As directional dispersion effect becomes significant, the kurtosis monotonically decreases in comparison with the unidirectional waves. A parameterization of the kurtosis estimated from directional spectra is proposed here; the error of the parameterization is at most 10%%. The parameterization is verified against laboratory data, and good agreement is obtained. [ABSTRACT FROM AUTHOR]

A turbulent airflow with a centerline velocity of 4 m s−1 above 2.5-Hz mechanically generated gravity waves of different amplitudes has been studied in experiments using the particle image velocimetry (PIV) technique. Direct measurements of the instantaneous flow velocity fields above a curvilinear interface demonstrating flow separation are presented. Because the airflow above the wavy water surface is turbulent and nonstationary, the individual vector fields are conditionally averaged sampled on the phase of the water elevation. The flow patterns of the phase-averaged fields are relatively smooth. Because the averaged flow does not show any strongly nonlinear effects, the quasi-linear approximation can be used. The parameters obtained by the flow averaging are compared with the theoretical results obtained within the theoretical quasi-linear model of a turbulent boundary layer above the wavy water surface. The wave-induced pressure disturbances in the airflow are calculated using the retrieved statistical ensemble of wind flow velocities. The energy flux from the wind to waves and the wind-wave interaction parameter are estimated using the obtained wave-induced pressure disturbances. The estimated values of the wind-wave interaction parameter are in a good agreement with the theory. [ABSTRACT FROM AUTHOR]

Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations. A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett--Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky--Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime. The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence. [ABSTRACT FROM AUTHOR]

Tropical cyclones (TCs) Katrina and Rita moved as major hurricanes over energetic geostrophic ocean features in the Gulf of Mexico. Increased and reduced oceanic mixed layer (OML) cooling was measured following the passage of both storms over cyclonic and anticyclonic geostrophic relative vorticity ζg, respectively. This contrasting thermal response is investigated here in terms of the evolution of the storms’ near-inertial wave wake in geostrophic eddies. Observational data and ray-tracing techniques in realistic geostrophic flow indicate that TC-forced OML near-inertial waves are trapped in regions of negative ζg, where they rapidly propagate into the thermocline. These anticyclonic-rotating regimes coincided with the distribution of reduced OML cooling because rapid downward dispersion of near-inertial energy reduced the amount of kinetic energy available to increase vertical shears at the OML base. By contrast, TC-forced OML near-inertial waves were stalled in upper layers of cyclonic circulations, which strengthened vertical shears and entrainment cooling. Upgoing near-inertial energy propagation dominated inside a geostrophic cyclone that interacted with Katrina; the salient characteristics of these upward-propagating waves were the following: (i) they were radiated from the ocean interior because of geostrophic adjustment following upwelling–downwelling processes; (ii) rather than with the buoyancy frequency, they amplified horizontally as they encountered increasing values of f + ζg/2 during upward propagation; and (iii) they produced episodic vertical mixing through shear instability at a critical layer underneath the OML. To improve the prediction of TC-induced OML cooling, models must capture geostrophic features and turbulence closures must represent near-inertial wave processes such as dispersion and breaking between the OML base and the thermocline. [ABSTRACT FROM AUTHOR]