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On Langmuir Circulations in Unsteady Free Surface Flows

Author(s): Ming Zhao; Mohamed S. Ghidaoui; Zhenhua Huang

Linked Author(s): Mohamed S. Ghidaoui

Keywords: Langmuir circulations; Coastal water; Stability analysis

Abstract: Langmuir circulations (LCs) are parallel counter-rotating vortical structures adjacent to the water surface and oriented approximately along the current. The presence of LCs is most readily marked by the parallel streaks of materials that float on the water surface of large lakes, shallow lagoons, rivers and seas. LCs play an important role in turbulence modeling; deepening of mixed layers; transfer of mass, momentum and energy between air and water; re-suspension and transport of sediments, pollutants and organisms; formation of―boils‖; accumulation of floating materials (e.g., leafs, bubbles, oil slicks, algae and thermal releases) along rows; and the behavior of internal waves including the possibility of Bragg-like resonance. An important primary mechanism for LCs is the Craik and Leibovich hydrodynamic instability, often called CL-II mechanisms. This mechanism recognizes that longitudinal velocity fluctuation produces vertical vorticity which then gets bend in the stream-wise direction by the stokes drift resulting in streamwise vorticity. The downwelling and upwelling action of this streamwise vorticity, in turn, generates vertical vorticity by tilting the horizontal (spanwise) vorticity of the current in the vertical direction. This process of positive feedback, where vertical vorticity interacts with stokes drift to generate streamwise vorticity, which in turn, interacts with the current to intensify vertical vorticity, leads to the CL-II instability. The method of transient growth is ideal for instabilities that are due to vortex tilting and provides a rigorous approach for investigating the onset of LCs under unsteady forcing and various types of fluctuations. In this paper, the method of transient growth method is formulated, validated and used to understand the relative importance of the various forcing of LCs, the role of algebraic growth instability on the formation of LCs and the sensitivity of the initiation of LCs to the type of perturbation. The formation of LCs in unsteady flows due to both impulsively and linearly accelerated wind is examined and the results are compared to field observation and laboratory experiments.

DOI:

Year: 2010

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