Critical Layer Depth and its Implication on the Wave Growth Parameter for the Southern Ocean

We explore the physics behind the open ocean wind wave interaction by analyzing the behavior of the wave growth parameter based on the shear flow theory proposed by Miles in 1957. Based on a logarithmic wind profile we find the critical layer height (z_c) at which the mean wind speed (U₁₀) matches the phase speed of the waves (c(ω)). We find the average critical height to be O(10¹) [m], with maximum values of O(10⁰) [m]. For growing seas the rate of energy input from wind to waves is calculated by the integration of the work done by the wave induced momentum flux against the wind velocity profile. Integration is carried from the roughness length (z_o) to z_c. Inside this layer the wave induced stress is assumed to exponentially decay with height. We then calculate the wave growth parameter and use the classical Plant 82 parametrization for comparison porpoises. We also present direct spectral estimates from the SOGASEX 08 cruise which we use to validate our approach. We find good agreement between methods and propose that the Miles 57 theory's crucial step lies on the definition of the critical height, where the wave induced stress dominates the total momentum flux. We finally explore the wave growth parameter as a function of the wind steepness (Donelan et.al 2006) and hypothesize on the implications of varying wave conditions (i.e. wave slope) on the Miles 57 shear flow model.