On the Relationship Between Spectral Models of Ice Drift and Wind Turbulence

Abstract

Abstract At present, there is quite limited research activity related to mathematical models of the ice drift spectrum. The intention of this work is to propose a novel mathematical model of a generalized ice drift speed spectrum to describe the ice drift behavior in the frequency domain. The drift of sea ice is naturally influenced by external forces such as wind stress at the air-ice interface, water stress at the water-ice interface, the Coriolis force, pressure gradients due to sea surface tilting, and internal stress within the sea ice itself. Typically, wind dominates the ice drift at higher frequencies, while current is likely to play an important role in the lower frequency range. This is due to the slow rate of change for the ocean current. Typically, sea ice will drift at approximately 2–3% of the wind speed as referred to a height of 10-meter above the ocean surface in the Arctic region. The magnitude of the ice drift speed can approximately be predicted by the Nansen number corresponding to the drift speed magnitude as a percentage of the wind speed. The physical connection between the wind speed and the ice drift speed is presently utilized in order to generate a generalized ice drift spectrum. The ice drift data is collected from local subsurface measurements by means of acoustic Doppler current profilers (ADCP) in the Beaufort Sea. The frequency spectra of the wind speed and ice drift speed are calculated by application of the Fourier transform (as implemented in the WAFO software) based on the measured time series. It is found that the sea ice drifts at around 2.5% of the wind speed in the winter season (which corresponds to non-free drift conditions). However, during the summer season the sea ice tends to drift faster than 2.5% of the wind speed (which corresponds to free drift conditions). According to the scaling relationship between the ice drift speed and the wind speed, the Kaimal turbulence spectra are adopted to describe the ice drift behavior. This provides a good match for the winter season. However, the empirical ice drift spectrum contains higher energy levels than the Kaimal turbulence spectra in the high frequency range during the summer season. Accordingly, a generalized ice drift spectrum is proposed in the present paper, which is developed based on expressions for the general turbulence spectrum. The corresponding expression is more flexible in order to capture the ice drift behavior in the high frequency range for both the winter and the summer seasons. The generalized ice drift spectrum is found to provide a better match to the empirical spectra from ADCP measurements than the Kaimal turbulence spectrum.