Search Results

You are looking at 1 - 10 of 16 items for

  • Author or Editor: T. T. Janssen x
  • Refine by Access: All Content x
Clear All Modify Search
P. B. Smit
and
T. T. Janssen

Abstract

In coastal areas and on beaches, nonlinear effects in ocean waves are dominated by so-called triad interactions. These effects can result in large energy transfers across the wave spectrum and result in non-Gaussian wave statistics, which is important for coastal wave propagation and wave-induced transport processes. To model these effects in a stochastic wave model based on the radiative transfer equation (RTE) requires a transport equation for three-wave correlators (the bispectrum) that is compatible with quasi-homogeneous theory. Based on methods developed in optics and quantum mechanics, the authors present a general approach to derive a transport equation for higher-order correlators. The principal result of this work is a coupled set of equations consisting of the radiative transfer equation with a nonlinear forcing term and a new, generalized transport equation for bispectrum. This study discusses the implications and characteristics of the resulting equations and shows that the model contains various shallow- and deep-water asymptotes for nonlinear wave propagation as special cases.

Full access
P. B. Smit
and
T. T. Janssen

Abstract

The interaction of ocean waves with variable currents and topography in coastal areas can result in inhomogeneous statistics because of coherent interferences, which affect wave-driven circulation and transport processes. Stochastic wave models, invariably based on some form of the radiative transfer equation (or action balance), do not account for these effects. The present work develops and discusses a generalization of the radiative transfer equation that includes the effects of coherent interferences on wave statistics. Using multiple scales, the study approximates the transport equation for the (complete) second-order wave correlation matrix. The resulting model transports the coupled-mode spectrum (a form of the Wigner distribution) and accounts for the generation and propagation of coherent interferences in a variable medium. The authors validate the model through comparison with analytic solutions and laboratory observations, discuss the differences with the radiative transfer equation and the limitations of this approximation, and illustrate its ability to resolve coherent interference structures in wave fields such as those typically found in refractive focal zones and around obstacles.

Full access
T. H. C. Herbers
and
T. T. Janssen

Abstract

Nonlinear effects in Lagrangian sea surface motions are important to understanding variability in wave-induced mass transport, wave-driven diffusion processes, and the interpretation of measurements obtained with moored or free-drifting buoys. This study evaluates the Lagrangian vertical and horizontal motions of a particle at the surface in a natural, random sea state using second-order, finite-depth wave theory. In deep water, the predicted low-frequency (infragravity) surface height fluctuations are much larger than Eulerian bound wave motions and of the opposite sign. Comparison to surface elevation bispectra observed with a moored buoy in steady, high-wind conditions shows good agreement and confirms that—in contrast to the Eulerian sea surface motion with predominant phase coupling between the spectral peak and double-frequency harmonic components—nonlinearity in Lagrangian wave observations is dominated by phase-coupled infragravity motions. Sea surface skewness estimates obtained from moored buoys in deep and shallow sites, over a wide range of wind–sea and swell conditions, are in good agreement with second-order theory predictions. Theory and field data analysis of surface drift motions in deep water reveal energetic [O(10) cm s−1] infragravity velocity fluctuations that are several orders of magnitude larger and 180° out of phase with Eulerian infragravity motions. These large fluctuations in Stokes drift may be important in upper-ocean diffusion processes.

Full access
T. T. Janssen
and
T. H. C. Herbers

Abstract

In this paper, the combined effects of refraction and nonlinearity on the evolution of ocean surface wave statistics are considered and possible implications for the likelihood of extreme waves, also known as freak or rogue waves, are examined. A frequency-angular spectrum model is derived that accounts for cubic nonlinear dynamics and weak lateral homogeneity of the medium. Through Monte Carlo simulations, the evolution of wave statistics in freely developing waves, waves over an opposing shearing current, and waves refracted over an isolated topographical feature is modeled. The simulations show that freely developing, directionally spread wave fields generally maintain near-Gaussian statistics, which was also found in earlier model studies. However, the enhanced nonlinearity caused by the refractive focusing of narrowband wave fields can result locally in strongly non-Gaussian statistics and an associated increased likelihood of extreme wave events.

Full access
P. B. Smit
,
T. T. Janssen
, and
T. H. C. Herbers

Abstract

Refractive focusing of swell waves can result in fast-scale variations in the wave statistics because of wave interference, which cannot be resolved by stochastic wave models based on the radiative transport equation. Quasi-coherent statistical theory does account for such statistical interferences and the associated wave inhomogeneities, but the theory has thus far been presented in a form that appears incompatible with models based on the radiative transfer equation (RTE). Moreover, the quasi-coherent theory has never been tested against field data, and it is not clear how the coherent information inherent to such models can be used for better understanding coastal wave and circulation dynamics. This study therefore revisits the derivation of quasi-coherent theory to formulate it into a radiative transport equation with a forcing term that accounts for the inhomogeneous part of the wave field. This paper shows how the model can be nested within (or otherwise used in conjunction with) quasi-homogeneous wave models based on the RTE. Through comparison to laboratory data, numerical simulations of a deterministic model, and field observations of waves propagating over a nearshore canyon head, the predictive capability of the model is validated. The authors discuss the interference patterns predicted by the model through evaluation of a complex cross-correlation function and highlight the differences with quasi-homogeneous predictions. These results show that quasi-coherent theory can extend models based on the RTE to resolve coherent interference patterns and standing wave features in coastal areas, which are believed to be important in nearshore circulation and sediment transport.

Full access
P. B. Smit
,
T. T. Janssen
, and
T. H. C. Herbers

Abstract

Estimation of second-order, near-surface wave kinematics is important for interpretation of ocean surface remote sensing and surface-following instruments, determining loading on offshore structures, and understanding of upper-ocean transport processes. Unfortunately, conventional wave theories based on Stokes-type expansions do not consider fluid motions at levels above the unperturbed fluid level. The usual practice of extrapolating the fluid kinematics from the unperturbed free surface to higher points in the fluid is generally reasonable for narrowband waves, but for broadband ocean waves this results in dramatic (and nonphysical) overestimation of surface velocities. Consequently, practical approximations for random waves are at best empirical and are often only loosely constrained by physical principles. In the present work, the authors formulate the governing equations for water waves in an incompressible and inviscid fluid, using a boundary-fitted coordinate system (i.e., sigma or s coordinates) to derive expressions for near-surface kinematics in nonlinear random waves from first principles. Comparison to a numerical model valid for highly nonlinear waves shows that the new results 1) are consistent with second-order Stokes theory, 2) are similar to extrapolation methods in narrowband waves, and 3) greatly improve estimates of surface kinematics in random seas.

Full access
Pieter B. Smit
and
Tim T. Janssen

Abstract

The propagation of ocean swells from generating regions to remote coastlines is affected by submesoscale turbulence in the surface flow field. The presence of submesoscale velocity variations results in random scattering of wave rays. While the interactions with these flow fields are weak, cumulative effects over oceanic scales are significant and result in observable changes in the wave field. Using geometrical optics and statistical mechanics we derive a framework to express these scattering effects on the mean wave statistics directly in terms of the variance spectrum of the submesoscale current field. The theoretical results are presented in Lagrangian and Eulerian forms, where the latter takes the form of a radiative transport equation augmented with a diffusive term in directional space. The theoretical results are verified through Monte Carlo simulations with a geometrical optics model. We show that including submesoscale scattering on ocean wave evolution can explain observed delays in swell arrivals, accelerated wave height decay, and much larger directional spreading of the wave field than predicted by geometrical spreading alone.

Open access
T. H. C. Herbers
,
P. F. Jessen
,
T. T. Janssen
,
D. B. Colbert
, and
J. H. MacMahan

Abstract

Surface-following buoys are widely used to collect routine ocean wave measurements. While accelerometer and tilt sensors have been used for decades to measure the wave-induced buoy displacements, alternative global positioning system (GPS) sensor packages have been introduced recently that are generally smaller, less expensive, and do not require calibration. In this study, the capabilities of several GPS sensors are evaluated with field observations in wind-sea and swell conditions off the California coast. The GPS buoys used in this study include Datawell Directional Waverider and Mini Directional Waverider buoys equipped with a specialized GPS Doppler shift sensor, and a low-cost experimental drifter equipped with an “off the shelf” GPS receiver for absolute position tracking. Various GPS position receivers were attached to the Waverider buoys to evaluate their potential use in low-cost wave-resolving drifters. Intercomparisons between the Datawell GPS-based buoys, the experimental GPS drifter, and a conventional Datawell buoy with an accelerometer–tilt–compass sensor package, show good agreement in estimates of wave frequency and direction spectra. Despite the limited (several meters) absolute accuracy of the GPS position receivers, the horizontal wave orbital displacements are accurately resolved, even in benign (significant wave height less than 1 m) swell conditions. Vertical sea surface displacements were not well resolved by the GPS position receivers with built-in or small patch antennas, but accurately measured when an external precision antenna was attached to the drifter. Overall, the field tests show excellent agreement between Datawell buoys using GPS and motion-sensor packages, and demonstrate the feasibility of observing ocean surface waves with low-cost GPS-tracked drifters.

Full access
I. A. Houghton
,
P. B. Smit
,
D. Clark
,
C. Dunning
,
A. Fisher
,
N. J. Nidzieko
,
P. Chamberlain
, and
T. T. Janssen

Abstract

A distributed sensor network of over 100 free-drifting, real-time marine weather sensors was deployed in the Pacific Ocean beginning in early 2019. The Spotter buoys used in the network represent a next-generation ocean weather sensor designed to measure surface waves, wind, currents, and sea surface temperature. Large distributed sensor networks like these provide much needed long-dwell sensing capabilities in open-ocean regions. Despite the demand for better weather forecasts and climate data in the oceans, direct in situ measurements of marine surface weather (waves, winds, currents) remain exceedingly sparse in the open oceans. Because of the large expanse of Earth’s oceans, distributed paradigms are necessary to create sufficient data density at global scale, similar to advances in sensing on land and in space. Here we discuss initial findings from this long-dwell open-ocean distributed sensor network. Through triple-collocation analysis, we determine errors in collocated satellite-derived observations and model estimates. The correlation analysis shows that the Spotter network provides wave height data with lower errors than both satellites and models. The wave spectrum was also further used to infer wind speed. Buoy drift dynamics are similar to established drogued drifters, particularly when accounting for windage. We find a windage correction factor for the Spotter buoy of approximately 1%, which is in agreement with theoretical estimates. Altogether, we present a completely new open-ocean weather dataset and characterize the data quality against other observations and models to demonstrate the broad value for ocean monitoring and forecasting that can be achieved using large-scale distributed sensor networks in the oceans.

Open access
G. Janssens-Maenhout
,
B. Pinty
,
M. Dowell
,
H. Zunker
,
E. Andersson
,
G. Balsamo
,
J.-L. Bézy
,
T. Brunhes
,
H. Bösch
,
B. Bojkov
,
D. Brunner
,
M. Buchwitz
,
D. Crisp
,
P. Ciais
,
P. Counet
,
D. Dee
,
H. Denier van der Gon
,
H. Dolman
,
M. R. Drinkwater
,
O. Dubovik
,
R. Engelen
,
T. Fehr
,
V. Fernandez
,
M. Heimann
,
K. Holmlund
,
S. Houweling
,
R. Husband
,
O. Juvyns
,
A. Kentarchos
,
J. Landgraf
,
R. Lang
,
A. Löscher
,
J. Marshall
,
Y. Meijer
,
M. Nakajima
,
P. I. Palmer
,
P. Peylin
,
P. Rayner
,
M. Scholze
,
B. Sierk
,
J. Tamminen
, and
P. Veefkind
Full access