Wave-Coherent Fields in Air Flow over Ocean Waves: Identification of Cooperative Behavior Buried in Turbulence

Abstract

We present a method to study the coupling and synchronization of two chaotic systems -the surface gravity waves in the open ocean and the turbulent air flow above. Our approach employs an eikonallike representation of the wave field based on the concept of an analytic signal and the Hilbert transform. We identify a wave-coherent component in the air flow which is phase locked with the waves and deeply buried in turbulence. That component contributes most of the wind-wave energy and momentum exchange, so its identification from actual data is of primary interest. We define and obtain the phase shifts of the wave-coherent fields and discuss their roles in the wind wave exchange.[S0031-9007(98)07829-6] PACS numbers: 92.10. Hm, 47.27.Eq, 47.35. + i, 47.52. + j Cooperative behavior plays a major role in a variety of chaotic systems, but it may be hard to identify and quantify. A good example is the coupling between ocean surface waves (which are not periodic) and the randomly fluctuating turbulent wind above, where a small (relative to the turbulent fluctuations) wave-coherent component in the wind is believed to carry most of the wind-wave interaction. Today's climate and weather forecasting models are built on assumptions (many of which are untested experimentally, [1]) about the mechanisms and intensity of the exchange of kinetic energy and momentum between the ocean and the atmosphere. In spite of decades-long efforts, starting from Jeffreys in 1924 [2], expanded by Miles [3] and Phillips [4], and recent advances in [5,6], current knowledge regarding wind-wave interactions is limited due to experimental and theoretical difficulties [1,7,8]. The wide inconsistency among the experimental estimates for the wind-wave energy exchange [8], possibly amplified by the lack of technique to extract the wave-coherent component in the air flow, as well as the absence of field data for the wave-induced Reynolds stresses (which impedes the closure modeling) are some of those difficulties. Laboratory experiments on wind-wave coupling do not reproduce the scales and conditions over the open ocean [9], so the field experiments remain as relevant and necessary components of this research. In this study we use data from the marine boundary layers experiment, which took place 50 kilometers off the coast of California on the stable floating instrument platform (FLIP). The instruments were positioned at fixed heights from 2.7 to 18.1 m above the interface and the wave height was registered directly beneath them.Intuitively, one might expect that the fluctuations of velocity and pressure in the air flow over waves are of two kinds, originating either from the shear-driven turbulence, or induced by the underlying waves. Assuming that the two kinds of fluctuations are weakly coupled, the flow velocity u ϵ ͑u, y, w͒ and pressure p can be decomposed into mean, turbulent, and wave-induced components, u u 1 u 0 1ũ and p p 1 p 0 1p. The turbulent pressure fluctuations p 0 can lead to wave growth through a random walk process [4], but their c...

Structure of the Airflow above Surface Waves

“…Above the critical height, f hw ; 0. This phase difference df ; 2p/2 across the critical layer is in agreement with the predictions of the critical layer theory (Miles 1957;Davis 1970;Miles 1993) and consistent with the field observations of Hristov et al (2003) and Grare et al (2013a). For the younger waves with C p /u * 5 3.7, df ; 2p, also in agreement with the critical layer theory.…”

“…Wave phase detection within the PIV field of view was achieved for wind waves by applying a Hilbert transform (Oppenheim and Schafer 2013;Melville 1983) directly to the LFV wave profiles. Further details of this technique applied to surface waves were presented in Hristov et al (1998). The phases f in the abscissa of Fig.…”

“…The first, focused on turbulent flux measurements and efforts to parameterize drag as a function of wind speed (e.g., Edson et al 2013), were motivated by a need to rapidly improve operational forecasting and climate modeling (see, e.g., the COARE momentum flux model; Webster and Lukas 1992). Others, concerned with the fundamental physics of wave generation and growth mechanisms, were able to relate their flux measurements to the phase of the waves, thereby estimating wave-coherent fluxes, which provided evidence of Miles's critical layer mechanism for a certain range of wave ages (Hristov et al 2003;Grare et al 2013a). However, these field studies, challenged by the technical difficulties involved with the study of small-scale dynamics in the open ocean near a highly dynamic interface, were limited to fixed-height vertical profile measurements some distance above the level of the highest wave crest.…”

Airflow measurements at a wavy air–water interface using PIV and LIF

“…(Lumley and Terray 1983;Thais and Magnaudet 1996;Hristov et al 1998;Veron et al 2008;Grare et al 2013a). This is in part due to the technical difficulty associated with making measurements close to the air water interface in the laboratory or the field, and the difficulty in modeling the complex non-linear interactions between the turbulence and the surface waves.…”

“…Janssen 1989; Komen et al 1994;Belcher and Hunt 1998;Hristov et al 1998; Abstract Physical phenomena at an air-water interface are of interest in a variety of flows with both industrial and natural/environmental applications. In this paper, we present novel experimental techniques incorporating a multi-camera multi-laser instrumentation in a combined particle image velocimetry and laser-induced fluorescence system.…”