#### Abstract

This paper considers the degree of accuracy with which observations from an acoustic Doppler current profiler (ADCP) can determine turbulent horizontal velocity variance. As in a previous paper addressing turbulent vertical velocity variance, we use a combination of techniques, deriving response functions from simple theory and from oceanic observations taken with a VADCP (an ADCP with an additional vertical (V) beam) in two different oceanic turbulent flows, Langmuir supercells (LSC) and unstable convection. In the case of LSC, we also determine response by sampling available Large-Eddy Simulations (LES) with specified beam geometry. In contrast with the previous investigation, where a direct measurement of vertical velocity variance was available from the vertical beam of the VADCP, we lack direct measurements of horizontal velocity variances. Thus the observational response reported here for horizontal variance is an estimate, taken as the ratio of first-order to the (assumed more accurate) second-order variance estimates made possible for the first time by the presence of a vertical beam.The theoretical response function is used to illustrate effects on response of horizontal scale, vertical/horizontal anisotropy and possible quasi-coherent phase structure of the large eddies of the turbulent field, and to predict the impact of changing θ, the angle of slant beams from vertical. Observational estimates show that convective turbulence is characterized by near-unity response throughout the water column for both horizontal velocity variances, in agreement with theoretical prediction. For Langmuir supercells, theoretical responses correctly predict qualitative behavior of the LES-derived response functions, specifically overestimation in the lower part of the water column shifting to underestimation toward the surface. LES-derived responses for different values of θ are also in agreement with theory: both approaches suggest that θ = 30° provides more accurate measurement of horizontal turbulent velocity variance than does θ = 20°, the present commercial standard.For all examined cases of unstable convection and most (normal) LSC cases, observationally estimated response functions generally agree with theoretical (and, where available, LES) predictions. However in a few (abnormal) LSC cases, record-averaged second-order variances are clearly underestimated (most obviously when they are actually negative). We have been unable to assign a cause to this underestimation and advise against use of second-order horizontal velocity variances until this unpredictable effect is understood. Normal LSC cases exhibit overestimation of horizontal variance by a maximum factor of 1.5 (observational estimates) to 3 (LES estimates), a degree of accuracy comparable to that associated with microscale-based estimates of turbulent large-eddy quantities. We suggest ways in which the parameters needed for theoretical prediction of the response function for horizontal velocity can be estimated directly from VADCP measurements.

#### Recommended Citation

Gargett, A. E., A. E. Tejada-Martínez, and C. E. Grosch.
2009.
"Measuring turbulent large-eddy structures with an ADCP. Part 2. Horizontal velocity variance."
*Journal of Marine Research*
67,
(5).
https://elischolar.library.yale.edu/journal_of_marine_research/243