STATISTICS OF SHEAR AND TURBULENT DISSIPATION PROFILES IN RANDOM INTERNAL WAVE-FIELDS

Because breaking internal waves produces most of the turbulence in the thermocline, the statistics of epsilon, the rate of turbulent dissipa tion, cannot be understood apart from the statistics of internal wave shear. The statistics of epsilon and shear are compared for two sets o f profiles from the northeast Pacific. One set, PATCHEX, has internal wave shear close to the Garrett and Munk model, but the other set, PAT CHEX north. has average 10-m shear squared, [S-10(2)] about four times larger than the model. The 10-m shear components, S(x) and S(y), were measured between 1 and 9 MPa and referenced to a common stratificatio n by WKB scaling. The scaled components, S(x) and S(y), are found to b e independent and normally distributed with zero means, as assumed by Garrett and Munk. This readily leads to analytic forms for the probabi lity densities of S-10(2) and S-10(4). The observed probability densit ies of S-10(2) and S10(4) are close to the predicted forms, and both a re strongly skewed. Moreover, sigma(lnS10(2)) and sigma(lnS10(4)) are constants, independent of the standard deviations of S(x) and S(y). Th e probability density of the inverse Richardson number, Ri10(-1) = S-1 0(2)/[N2], is a scaled version of the probability density of S-10(2). The PATCHEX distribution cuts off near Ri10(-1) = 4, as found by Eriks en, but the PATCHEX north distribution extends to higher values, as pr edicted analytically. Consequently, a cutoff at Ri10(-1) = 4 is not a universal constraint. Over depths where [N2] is nearly uniform, the pr obability density of 0.5-m epsilon can be approximated, to varying deg rees of accuracy, as the sum of a noise variate with an empirically de termined distribution and a lognormally distributed variate whose para meters can be estimated using a minimum chi-square fitting procedure. The 0.5-m epsilon, however, are far from being uncorrelated, a circums tance not considered by Baker and Gibson in their analysis of microstr ucture statistics. Obtaining approximately uncorrelated samples requir es averaging over 10 m for PATCHEX and 15 m for PATCHEX north. These l engths correspond approximately to reciprocals of the wavenumbers at w hich the respective shear spectra roll off. After correcting the uncor related epsilon samples for noise and then scaling to remove the depen dence on stratification, the scaled dissipation rates, epsilon = epsil on(N-0(2)/[N2]), are lognormally distributed. (Without noise correctio n and [N2] scaling the data are not lognormal; e.g., noise correction and scaling with [N1] and [N3/2] do not produce lognormality.) It is h ypothesized that the approximate lognormality of bulk ensembles of eps ilon results from generation of turbulence in proportion to S-10(4). L ognormality is well established for isotropic homogeneous turbulence ( Gurvich and Yaglom), and Yamazaki and Lueck show that it also occurs w ithin individual turbulent patches. Bulk ensembles from the thermoclin e, however, include samples from many sections lacking turbulence as w ell as from a wide range of uncorrelated turbulent events at different evolutionary stages. Consequently, the bulk data do not meet the crit eria used to demonstrate lognormality under more restricted conditions . If the authors are correct, the high-amplitude portion of [N2]-scale d bulk ensembles is lognormal or nearly so owing to generation of the turbulence by a highly skewed shear moment. As another consequence, si gma(lnS10(4)) = 2.57 should be an upper bound for 10 m sigma(lnepsilon ) when the turbulence is produced by the breaking of random internal w aves. Because many parts of the profile lack turbulence, sensor noise limits the epsilon distribution to smaller spreads than those of S-10( 4). In practice we observe sigma(lnepsilon) almost-equal-to 1.2 when S 10(2) equals GM76, and sigma(lnepsilon) almost-equal-to 1.5 when S-10( 2) is about three times GM76. For the larger spread, 95% confidence li mits require n almost-equal-to 60 for accuracies of +/- 100%, n almost -equal-to 140 for +/-50%, and n almost-equal-to 2000 for +/-10%. Owing to instrumental uncertainties in epsilon estimates, the authors sugge st accepting less restrictive confidence limits at one site and sampli ng at multiple sites to estimate average dissipation rates in the ther mocline.