Wave Boundary Layer Turbulence over Surface Waves in a Strongly Forced Condition

Abstract

Accurate predictions of the sea state-dependent air-sea momentum flux require a thorough understanding of the wave boundary layer turbulence over surface waves. A set of momentum and energy equations is derived to formulate and analyze wave boundary layer turbulence. The equations are written in wavefollowing coordinates, and all variables are decomposed into horizontal mean, wave fluctuation, and turbulent fluctuation. The formulation defines the wave-induced stress as a sum of the wave fluctuation stress (because of the fluctuating velocity components) and a pressure stress (pressure acting on a tilted surface). The formulations can be constructed with different choices of mapping. Next, a large-eddy simulation result for wind over a sinusoidal wave train under a strongly forced condition is analyzed using the proposed formulation. The result clarifies how surface waves increase the effective roughness length and the drag coefficient. Specifically, the enhanced wave-induced stress close to the water surface reduces the turbulent stress (satisfying the momentum budget). The reduced turbulent stress is correlated with the reduced viscous dissipation rate of the turbulent kinetic energy. The latter is balanced by the reduced mean wind shear (satisfying the energy budget), which causes the equivalent surface roughness to increase. Interestingly, there is a small region farther above where the turbulent stress, dissipation rate, and mean wind shear are all enhanced. The observed strong correlation between the turbulent stress and the dissipation rate suggests that existing turbulence closure models that parameterize the latter based on the former are reasonably accurate.

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

“…6b). A similar multi-modal curvilinear transformation was first used for a wind-wave interaction numerical model by Chalikov (1978), and more recently by Hara and Sullivan (2015). We note here that experimental results were, up until now, not reported using such coordinate systems.…”

“…In the engineering sector, coupled interfacial gas-liquid dynamics are of interest because they influence the efficiency of chemical reactors, boilers, turbines (Turney and Banerjee 2008;Hewitt 2013). In the 1 3 161 Page 2 of 20 and Fairall 1998;Janssen 1999;Sullivan and McWilliams 2002;Sullivan et al 2008;Yang and Shen 2010;Suzuki et al 2013;Grare et al 2013a;Hara and Sullivan 2015). Airflow separation for example, is the kinematic air-side equivalent to wave breaking in the water (Banner and Melville 1976;Gent and Taylor 1977), a process which is known to generate turbulence and enhance dissipation (Rapp and Melville 1990;Melville et al 2002;Drazen and Melville 2009).…”

Structure of the Airflow above Surface Waves

“…More recently, modelers were able to integrate realistic complex wave fields into largeeddy simulations (LESs) that yielded insight on the instantaneous turbulent structure of the airflow over a wide range of wave ages (Sullivan et al 2014), including very old waves where upward wave-induced momentum flux was observed, as well as wave-driven jets, in agreement with field observations by Smedman et al (1999) and Grachev and Fairall (2001). Using LES within the wave boundary layer over young wind-forced sinusoidal waves, Hara and Sullivan (2015) were able to estimate the wave-induced and turbulent components of the wind stress and their influence on the total drag. Recent field observations have been largely of two kinds.…”

“…Such a multimodal curvilinear transformation was first introduced for a wind-wave interaction numerical model by Chalikov (1978). It is worth mentioning here that while this type of coordinate system is now somewhat frequently used in computational studies (e.g., Hara and Sullivan 2015), experimental studies were, until now, not able to report data using such transformations. 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.…”

“…However, because of high computational costs, DNS studies have been restricted to idealized monochromatic waves. Other modeling efforts focused on parameterizing wind wave momentum fluxes over more realistic wide-spectrum wave fields (e.g., Makin et al 1995;Hara and Belcher 2002;Mueller and Veron 2009). Their results suggest that the turbulent shear stress is reduced by the presence of the wave field and replaced by wave-coherent stress.…”