Turbulent Patch Identification in Microstructure Profiles: A Method Based on Wavelet Denoising and Thorpe Displacement Analysis

Abstract

A new method based on wavelet denoising and the analysis of Thorpe displacements d_T profiles is presented for turbulent patch identification. Thorpe profiles are computed by comparing the observed density profile ρ(z) and the monotonic density profile ρ_m(z), which is constructed by reordering ρ(z) to make it gravitationally stable. This method is decomposed in two main algorithms. The first, based on a wavelet denoising procedure, reduces most of the noise present in the measured profiles. This algorithm has been tested from theoretical profiles and has demonstrated a high efficiency in noise reduction, only some limitations were detected in very low-density gradient conditions. The second algorithm is based on a semiquantitative analysis of the Thorpe displacements. By comparing each displacement d_T with its potential error E_dT, it is possible to classify samples in three possible states: Z (d_T = 0), U (d_T < E_dT), and S (d_T > E_dT). This classification makes it possible to compute two statistical indexes: the displacement index I_D, the quotient between the number of S values and the number of averaging points; and the uncertainty index I_U, the quotient between the number of points on state U and the number of averaging points. The displacement index I_D has been used as the parameter for turbulent patch identification, identifying the patches as segments with strict positive I_D values. To illustrate the method, a number of field profiles covering a wide density gradient range were analyzed. Turbulent patches were validated following the tests proposed by Moum and Galbraith and Kelley. The high percentage of validating patches indicates that the proposed method is very efficient even at very low-density gradients where the potential error on d_T is high, and shows that it is a powerful tool for turbulent patch identification.