Integrated Model for a Wave Boundary Layer

Abstract

In the paper a new version of semi-phenomenological model is constructed, which allows to calculate the friction velocity u* via the spectrum of waves S and the wind at the standard horizon, W. The model is based on the balance equation for the momentum flux, averaged over the wave-field ensemble, which takes place in the wave-zone located between troughs and crests of waves. Derivation of the balance equation is presented, and the following main features of the model are formulated. First, the total momentum flux includes only two physically different types of components: the "wave" part τ w associated with the energy transfer to waves, and the "tangential" part τ t that does not provide such transfer. Second, component τ w is split into two constituents having different mathematical representation: (a) for the low-frequency part of the wave spectrum, the analytical expression of momentum flux τ w is given directly via the local wind at the standard horizon, W; (b) for the high-frequency part of the wave spectrum, flux τ w is determined by friction velocity u*. Third, the tangential component of the momentum flux is parameterized by using the similarity theory, assuming that the wave-zone is an analogue of the traditional friction layer, and in this zone the constant eddy viscosity is realized, inherent to the wave state. The constructed model was verified on the basis of simultaneous measurements of two-dimensional wave spectrum S and friction velocity u*, done for a series of fixed values of W. It is shown that the mean value of the relative error for the drag coefficient, obtained with the proposed model, is 15-20%, only.

A Semi-phenomenological Model for Wind-Induced Drift Currents

“…Here, first of all, it is necessary to represent the facts confirming both the existence of a three-layer interface structure, mentioned in the introduction, and the physical expediency of accounting such a structure in further theoretical constructions. First, in order to visualize the fact of existing the wave-zone, (WZ), which should have its own physical properties, we represent here figures 1(a, b) taken from (Polnikov, 2010(Polnikov, , 2011. In Second, as it was demonstrated for the first time in Polnikov(2011), basing on the analysis of numerical simulations executed in (Chalikov & Rinechik, 2011), the profile of average windvelocity, W(z), differs in the wave-zone significantly from the traditional logarithmic one.…”

“…First, in order to visualize the fact of existing the wave-zone, (WZ), which should have its own physical properties, we represent here figures 1(a, b) taken from (Polnikov, 2010(Polnikov, , 2011. In Second, as it was demonstrated for the first time in Polnikov(2011), basing on the analysis of numerical simulations executed in (Chalikov & Rinechik, 2011), the profile of average windvelocity, W(z), differs in the wave-zone significantly from the traditional logarithmic one. It varies linearly with the height from level z ≈ -h to level z of the order of 3h , relative to the mean water level (Fig.…”

“…where, on the right-hand side, there is the friction velocity in the air, It is physically clear (for the justification, see, for example, Janssen, 1991;Polnikov, 2011) that only the certain part,…”

“…In works of the author (Polnikov, 2011(Polnikov, , 2013, where quantity t  is called as "the tangential component" of the total flux, the model was proposed for calculating magnitudes of each terms in (7), as functions of wind speed W 10 and previously mentioned wave parameters. This model is not used here, but it is important to note that value t  can be further considered as the known one.…”

“…Here, first of all, it is necessary to represent the facts confirming both the existence of a three-layer interface structure, mentioned in the introduction, and the physical expediency of accounting such a structure in further theoretical constructions. First, in order to visualize the fact of existing the wave-zone, (WZ), which should have its own physical properties, we represent here figures 1(a, b) taken from (Polnikov, 2010(Polnikov, , 2011. In Fig.…”