Turbulence in the atmospheric wave boundary layer
Date
2020
Authors
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Publisher
University of Delaware
Abstract
The air-sea momentum and energy exchanges in the presence of surface waves play an integral role in coupling the atmosphere and the ocean and, consequently, in determining the sea state, weather patterns, and climate. In the current study, we present a detailed laboratory investigation of the air-sea momentum and energy budgets over wind-generated surface waves. To this end, quantitative airside velocity measurements above wind waves were acquired in the laboratory using a combination of particle image velocimetry and laser-induced fluorescence techniques. The experiments were performed for several forcing conditions corresponding to equivalent 10 m wind speeds ranging from 0.89 to 16.59 m/s. The acquired velocity fields were separated into mean, wave-coherent, and turbulence components using a linear decomposition technique. The corresponding momentum and energy fluxes are then explored in detail. ☐ To explicitly examine the near-surface airflow structures above surface wind waves, we employ a wave-following coordinate system. The governing equations of fluid flow, including conservation of mass, momentum, and energy balance, are first derived in an orthogonal curvilinear coordinate system relevant to surface water waves. All equations are further decomposed to extract mean, wave-induced, and turbulent components. The dynamical governing equations were further simplified by considering the flow over periodic quasi-linear surface waves wherein the wavelength of the disturbance is large compared to the wave amplitude. The quasi-linear analysis is employed to express the boundary layer equations in the orthogonal wave-following curvilinear coordinates with the corresponding decomposed equations for the mean, wave, and turbulent fields. ☐ In the wave boundary layer, the phase-averaged turbulent stress is intense (weak) and positive downwind (upwind) of the crests. The wave-induced stress is also positive on the windward and leeward sides of wave crests but with asymmetric intensities. These regions of positive wave stress are intertwined with regions of negative wave stress just above wave crests and downwind of wave troughs. Likewise, at the interface, the viscous stress exhibits along-wave phase-locked variations with maxima upwind of the wave crests. As a general trend, the mean profiles of the wave-induced stress decrease to a negative minimum from a near-zero value far from the surface and then increase rapidly to a positive value near the interface where the turbulent stress is reduced. Far away from the surface, however, the turbulent stress is nearly equal to the total stress. Closer to the surface, within the viscous sublayer, the wave and turbulent stresses vanish, and the stress is supported by the viscosity. ☐ Over wind waves, the turbulent kinetic energy (TKE) production is positive at all heights with a sharp peak near the interface, indicating the transfer of energy from the mean shear to the turbulence. Away from the surface, however, the TKE production approaches zero. Similarly, the wave kinetic energy (WKE) production is positive in the lower portion of the wave boundary layer representing the transfer of energy from the mean flow to the wave-coherent field. In the upper part of the boundary layer, WKE production becomes slightly negative, wherein the energy is transferred from the wave perturbation to the mean flow. The viscous and Stokes layer heights emerge as natural vertical scales for the TKE and WKE productions, respectively. Finally, the wave-turbulence interaction term shows a transfer of energy from the wave to turbulence in the bulk of the wave boundary layer and a transfer of energy from the turbulence to the wave in a thin layer near the interface.
Description
Keywords
Air-sea interactions, Surface gravity waves, Turbulent boundary layers, Wave-turbulence interactions, Wind-wave interactions