Direct numerical simulations and hydrodynamic stability problems in the upper oceanic mixed layer
Langmuir circulations are longitudinal rolls driven by the wind and appear beneath the surface of the ocean. The author models these as an instability of the mean current due to its interaction with averaged effect of the surface waves. Perturbations are allowed for in three dimensions for a layer of finite depth. Linear stability analysis shows that two-dimensional rolls are most unstable for unstratified flow as in previous two-dimensional studies. In presence of stratification three-dimensional modes are most unstable. At low and high values of the Reynolds number, the most unstable modes are nearly two-dimensional. At intermediate values, three dimensionality is important. The angular deviation from the wind direction of the most unstable modes increases with stratification in the range considered. Two-dimensional simulations are done at different values of stratification for unconstrained and constrained sidewall boundary conditions. These show good agreement qualitatively and quantitatively with the weakly nonlinear dynamics of the governing equations in two-dimensions. A secondary stability (Floquet) analysis is performed to determine the range of stability of unstratified steady Langmuir rolls and elicit the streamwise length scales when rolls become unstable. Eckhaus and Oscillatory mechanisms of instability are found to be important at a moderate value of Reynolds number. Subsequent direct numerical simulations are performed for corresponding instabilities. Oscillatory instability sets in as streamwise traveling waves. As one of the destabilizing parameters is increased, quasi-periodic motion is observed, with a low frequency vacillating mode. At lower values of Reynolds number, the secondary instability thresholds for the forcing are higher and steady rolls are stable in a large domain of parameter space. Simulations at high forcing at low Reynolds number show defect traveling wave solutions.
- Research Organization:
- Cornell Univ., Ithaca, NY (United States)
- OSTI ID:
- 5547389
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
OCEANIC CIRCULATION
COMPUTERIZED SIMULATION
SURFACE WATERS
AIR-WATER INTERACTIONS
BOUNDARY CONDITIONS
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REYNOLDS NUMBER
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TWO-DIMENSIONAL CALCULATIONS
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