Numerical wind wave model with a dynamic boundary layer

Abstract

Abstract.A modern version of a numerical wind wave model of the fourth generation is constructed for a case of deep water. The following specific terms of the model source function are used: (a) a new analytic parameterization of the nonlinear evolution term proposed recently in Zakharov and Pushkarev (1999); (b) a traditional input term added by the routine for an atmospheric boundary layer fitting to a wind wave state according to Makin and Kudryavtsev (1999); (c) a dissipative term of the second power in a wind wave spectrum according to Polnikov (1991). The direct fetch testing results showed an adequate description of the main empirical wave evolution effects. Besides, the model gives a correct description of the boundary layer parameters' evolution, depending on a wind wave stage of development. This permits one to give a physical treatment of the dependence mentioned. These performances of the model allow one to use it both for application and for investigation aims in the task of the joint description of wind and wave fields.

A Semi-phenomenological Model for Wind-Induced Drift Currents

“…In ( 5), c ph (ω) is the phase velocity as function of frequency, taken at the peak frequency of wind-wave spectrum, ω p ; and W 10 is the wind speed at the standard horizon, z=10 m. Herewith, in Wu (1975) it was clearly shown that the drift velocity, U d , decreases with the wave-fetch increasing, what is in a good agreement with the known variability of the friction velocity (see survey of data in (Polnikov et al, 2003) and detailed parametrization in (Polnikov , 2013)).…”

“…It can be assumed that all the dependences of drift velocity on the wave state are "hidden" in the direct proportionality between U d and friction velocity *a u , whilst the latter, as is well known, depends explicitly on the above-mentioned wave parameters: H, ε and A (see references in Polnikov et al (2003), Polnikov (2013)). However, the absence of direct empirical dependences of U d on wave parameters, in our opinion, requires its justification basing on specialized experiments for their determination.…”

Ocean Wave Prediction Using Numerical and Neural Network Models

“…By modifying the wind wave model -WAM, a series of numerical experiments [5,37] are carried out for verification of a proposed source function. Verification is done on the basis of comparison of the results of wave simulation for a given wind field with the buoy observation data obtained in three oceanic regions (Barents Sea, eastern and western parts of North Atlantic Ocean).…”

Effects of nonlinear energy transfer on short surface waves

“…as proposed by Jenkins and Phillips [2001] on dimensional grounds, this formulation for the nonlinear energy transfer term is equivalent to the diffusion approximation of Polnikov [2002] and Polnikov et al [2002]. Equation ( 5) is also valid when surface tension effects are included, in which case it can be written as…”

“…Jenkins and Phillips [2001] showed that a nonlinear source term of the form conserves energy, action, and momentum for any function ψ ( k ) that goes to zero rapidly enough as k → 0 and k → ∞. Using the gravity wave dispersion relation and defining as proposed by Jenkins and Phillips [2001] on dimensional grounds, this formulation for the nonlinear energy transfer term is equivalent to the diffusion approximation of Polnikov [2002] and Polnikov et al [2002]. is also valid when surface tension effects are included, in which case it can be written as where τ is the ratio of the surface tension to the density of water.…”