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<p>A two layer ocean mixed layer model is used to study the relationship between onset of freezing and mixed layer depth, wind forcing, surface buoyancy flux, and temperature and salinity changes between the two layers. Universal non- dimensional parameters for stability and surface forcing are derived and related to the maximum freezing rate. Analytic solutions to the model are found in terms of the universal parameters and the model turbulent mixing tuning constants. Sensitivity studies show the dependence of the freezing rate on the stability as defined by the salinity and temperature jumps, the forcing by wind stress and surface heat flux, and the mixed layer depth. Results show that an increase in heat flux produces a nearly linear increase in the freezing rate. Mixing energy from the wind, proportional to the wind speed cubed, results in a nearly linear decrease in freezing rate. There is a nonlinear relationship between the temperature jump between layers and the freezing rate. Warming of the deeper layer decreases the freezing rate and ultimately prevents freezing. A nonlinear relation was also found between the salinity jump and freezing rate. Increase in the deeper layer salinity causes an increase in the freezing rate and leads to the maximum expected freezing rate. A nearly hyperbolic relationship between the mixed layer depth and freezing rate was found. As the mixed layer depth increases from near zero, the freezing rate increases rapidly and then the maximum expected freezing rate is approached asymptotically.
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<br>Subjects: Dynamics; Temperature.; Oceanography; sea ice; mixed layer modeling; freezing</div>
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Claes, Dennis C.</div>
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