Nonlinear amplification of ocean waves in straits

Abstract

Using the exact Hasselmann equation, we study wind-driven deep-water ocean waves in a strait with the wind directed orthogonally to the shore. The strait has “dissipative” shores with no reflection from the shorelines. We show that the evolution of wave turbulence can be divided into two different regimes in time. During the first regime, waves propagate with the wind, and the wind-driven sea can be described by self-similar solutions of the Hasselmann equation. The second regime starts after a sufficiently significant accumulation of wave energy at the downwind boundary. From this instant, an ensemble of waves propagating against the wind starts to form. Moreover, waves orthogonal to the wind arise and propagate along the strait. The wave system eventually reaches an asymptotic stationary state in which two types of wave motion coexist: an ensemble of self-similar waves propagating with the wind and quasimonochromatic waves propagating almost orthogonally to the wind direction and tending to slant against the wind at the angle of 15° with respect to the shore of turbulence origination. These “secondary waves” arise only as a result of an intensive nonlinear wave interaction. The total wave energy exceeds its expected value approximately by a factor of two compared with the energy calculated in the absence of shores. We expect that this amplification increases substantially in the presence of reflective shores. We propose calling this “secondary” laser-like mechanism “nonlinear ocean wave amplification” (abbreviated NOWA).