Dmitry Chalikov

Source Terms in a Third-Generation Wind Wave Model

Abstract A new third-generation ocean wind wave model is presented. This model is based on previously developed input and nonlinear interaction source terms and a new dissipation source term. It is argued that the dissipation source term has to be modeled using two explicit constituents. A low-frequency dissipation term analogous to wave energy loss due to oceanic turbulence is therefore augmented with a diagnostic high-frequency dissipation term. The dissipation is tuned for the model to represent idealized fetch-limited growth behavior. The new model results in excellent growth behavior from extremely short fetches up to full development. For intermediate to long fetches results are similar to those of WAM, but for extremely short fetches the present model presents a significant improvement (although the poor behavior of WAM appears to be related to correctable numerical constraints). The new model furthermore gives smoother results and appears less sensitive to numerical errors. Finally, limitations of...

Development and implementation of wind-generated ocean surface wave models at NCEP

Abstract A brief historical overview of numerical wind wave forecast modeling efforts at the National Centers for Environmental Prediction (NCEP) is presented, followed by an in-depth discussion of the new operational National Oceanic and Atmospheric Administration (NOAA) “WAVEWATCH III” (NWW3) wave forecast system. This discussion mainly focuses on a parallel comparison of the new NWW3 system with the previously operational Wave Model (WAM) system, using extensive buoy and European Remote Sensing Satellite-2 (ERS-2) altimeter data. The new system is shown to describe the variability of the wave height more realistically, with similar or smaller random errors and generally better correlation coefficients and regression slopes than WAM. NWW3 outperforms WAM in the Tropics and in the Southern Hemisphere, and they both show fairly similar behavior at northern high latitudes. Dissemination of NWW3 products, and plans for its further development, are briefly discussed.

New approach to calculation of atmospheric model physics: accurate and fast neural network emulation of longwave radiation in a climate model

Abstract A new approach based on a synergetic combination of statistical/machine learning and deterministic modeling within atmospheric models is presented. The approach uses neural networks as a statistical or machine learning technique for an accurate and fast emulation or statistical approximation of model physics parameterizations. It is applied to development of an accurate and fast approximation of an atmospheric longwave radiation parameterization for the NCAR Community Atmospheric Model, which is the most time consuming component of model physics. The developed neural network emulation is two orders of magnitude, 50–80 times, faster than the original parameterization. A comparison of the parallel 10-yr climate simulations performed with the original parameterization and its neural network emulations confirmed that these simulations produce almost identical results. The obtained results show the conceptual and practical possibility of an efficient synergetic combination of deterministic and statist...

Numerical and laboratory investigation of breaking of steep two-dimensional waves in deep water

The paper extends a pilot study into a detailed investigation of properties of breaking waves and processes responsible for breaking. Simulations of evolution of steep to very steep waves to the point of breaking are undertaken by means of the fully nonlinear Chalikov–Sheinin model. Particular attention is paid to evolution of nonlinear wave properties, such as steepness, skewness and asymmetry, in the physical, rather than Fourier space, and to their interplay leading to the onset of breaking. The role of superimposed wind is also investigated. The capacity of the wind to affect the breaking onset is minimal unless the wind forcing is very strong. Wind is, however, important as a source of energy for amplification of the wave steepness and ultimately altering the breaking statistics. A detailed laboratory study is subsequently described. The theoretical predictions are verified and quantified. In addition, some features of the nonlinear development not revealed by the model (i.e. reduction of the wave period which further promotes an increase in steepness prior to breaking) are investigated. Physical properties of the incipient breaker are measured and examined, as well as characteristics of waves both preceding and following the breaker. The experiments were performed both with and without a superimposed wind, the role of which is also investigated. Since these idealized two-dimensional results are ultimately intended for field applications, tentative comparisons with known field data are considered. Limitations which the modulational instability mechanism can encounter in real broadband three-dimensional environments are highlighted. Also, substantial examination of existing methods of breaking onset detection are discussed and inconsistencies of existing measurements of breaking rates are pointed out.

Freak waves: Their occurrence and probability

This paper describes the results of more than 4000 long-term (up to thousands of peak wave periods) numerical simulations of nonlinear gravity surface waves performed for the investigation of properties and estimation of statistics of extreme (“freak”) waves. The method of solution of two-dimensional potential wave equations based on conformal mapping is applied to the simulation of wave behavior assigned by different initial conditions, defined by the Joint North Sea Wave Observation Project and Pierson–Moskowitz spectra. It is shown that nonlinear wave evolution sometimes results in the appearance of very big waves. There are no predictors for the appearance of extreme waves; however, the height of dimensional waves is proportional to the significant wave height. The initial generation of extreme waves can occur simply as a result of linear group effects, but in some cases the largest wave suddenly starts to grow. It is followed sometimes by a strong concentration of wave energy around a peak vertical. ...

Simulation of Wave Breaking in One-Dimensional Spectral Environment

Results of numerical investigations, based on full dynamic equations, are presented for wave breaking in a one-dimensional environment with a wave spectrum. The breaking is defined as a process of irreversible collapse of an individual wave in physical space, and the incipient breaker is a wave that reached a dynamic condition of the limiting stability where the collapse has not started yet but is inevitable. The main attention is paid to documenting the evolution of different wave characteristics before the breaking commences. It is shown that the breaking is a localized process that rapidly develops in space and time. No single characteristic, such as wave steepness, wave height, and asymmetry, can serve as a predictor of the incipient breaking. The process of breaking is intermittent; it happens spontaneously and is individually unpredictable. The evolution of geometric, kinematic, and dynamic characteristics of the breaking wave describes the process of breaking itself rather than indicating an imminent breaking. It is shown that the criterion of breaking, valid for the breaking due to modulation instability in one-dimensional waves trains, is not universal if applied to the conditions of spectral environment. In this context, the development of algorithms for parameterization of breaking for wave prediction models and for direct wave simulations is more important.

Numerical simulation of the Benjamin-Feir instability and its consequences

Full nonlinear equations for one-dimensional potential surface waves were used for investigation of the evolution of an initially homogeneous train of exact Stokes waves with steepness AK=0.01–0.42. The numerical algorithm for the integration of nonstationary equations and the calculation of exact Stokes waves is described. Since the instability of the exact Stokes waves develops slowly, a random small-amplitude noise was introduced in initial conditions. The development of instability occurs in two stages: in the first stage the growth rate of disturbances was close to that established for small steepness by Benjamin and Feir [J. Fluid. Mech. 27, 417 (1967)] and for medium steepness [McLean, J. Fluid Mech. 114, 315 (1982)]. For any steepness, the Stokes waves disintegrate and create random superposition of waves. For AK 0.13, one of the waves increases its height,...

Numerical investigation of turbulence generation in non‐breaking potential waves

Theoretically, potential waves cannot generate the vortex motion, but the scale considerations (Babanin 2006) indicate that if the steepness of waves is not too small, the Reynolds number can exceed the critical values. This means that in presence of initial non-potential disturbances, the orbital velocities can generate the vortex motion and turbulence. This problem has been investigated by means of linear instability theory (Benilov et al. 1993). It was shown that pure two-dimensional motion always remains potential because one-dimensional vortex (in vertical plane) does not interact with the orbital motion. The waves can generate the vortex in horizontal plane, and further development of vorticity occurs due to exchange of energy between the components of vorticity. Then, due to nonlinearity, motion at smaller scales and more or less developed turbulent regime arise. This problem was investigated numerically on basis of full two-dimensional (x–z) equations of potential motion with the free surface in cylindrical conformal coordinates. It was assumed that all variables are a sum of the 2-D potential orbital velocities and 3-D non-potential disturbances. Because the energy of waves is much larger than energy of turbulence, currently it was assumed that only one-way interaction exists: Non-potential motion takes the energy from potential waves. The non-potential motion is described directly with 3-D Euler equations, with very high resolution. The interaction between potential orbital velocities and non-potential components is accounted through additional terms which include the components of vorticity. The effects of turbulence are incorporated with a use of subgrid turbulent energy evolution equation. The turbulent scale is assumed to be proportional to grid resolution (LES technique). For small waves, the approach turns into a direct simulation method. Numerical scheme is based on 2-D Fourier transform method in ‘horizontal’ (in conformal coordinates) plane and on second-order approximation in the ‘vertical’. The pressure is calculated by means of Poisson equation in cylindrical conformal coordinates derived through covariant components of velocity. Poisson equation was solved with three-diagonal matrix algorithm (TDMA). Initial conditions for the elevations and the surface potential for waves were assigned according to the linear theory, and 3-D non-potential velocity components were inserted as a small-amplitude noise. Long-term numerical integration of the system of equations was done for different wave steepness. The vorticity and turbulence usually occurred in vicinity of wave crests (where the velocity gradients reach their maximum) and then spreads over upwind slope and downward. Specific feature of the wave turbulence is its strong intermittency: The turbulent patches are mostly isolated, and intermittency grows with the decrease of the wave amplitude. The maximum values of energy of turbulence are in qualitative agreement with experimental data. The results suggest that even non-breaking potential waves can generate the turbulence, which thus enhance the turbulence created by the shear current. Further investigation of this process will include the effect of tangential stress on a sea surface and flux of turbulent energy from the surface generated by breaking waves.

Modulational Instabilities and Breaking Strength for Deep-Water Wave Groups

Progressionofnonlinear wave groups to breakingwasstudiednumericallyand experimentally. Evolution ofsuchwavegroupparametersasafunctionofdistancetobreakingandmodulationdepth—theheightratio of the highest and the lowest waves in the group—was described. Numerical model results demonstrated good agreement with experimental results in describing the behavior of the distance to breaking and modulation depth as functions of initial wave steepness. It was shown that energy loss appears to be a function of the modulation depth at the breaking onset. Energy loss grows with modulation depth up to a certain threshold of the latter. It was also shown that breaking probability for wave groups with modulation depth below 2.2 is very low.

Influence of Wind Forcing on Modulation and Breaking of One-Dimensional Deep-Water Wave Groups

AbstractEvolution of nonlinear wave groups to breaking under wind forcing was studied by means of a fully nonlinear numerical model and in a laboratory experiment. Dependence of distance to breaking and modulation depth (height ratio of the highest and the lowest waves in a group) on wind forcing was described. It was shown that in the presence of a certain wind forcing both distance to breaking and modulation depth decrease; the latter signifies slowing down of the instability growth. It was also shown that wind forcing significantly reduces the energy loss in a single breaking event.