Estimated Flow Noise Levels due to a Thin Line Digital Towed Array Unnikrishnan K.C., V. Pallayil, M.A. Chitre and S. Kuselan Acoustic Research Laboratory, Tropical Marine Science Institute National University of Singapore,12A Kent Ridge Road, Singapore-119223 Email: unni@arl.nus.edu.sg Abstract—Flow noise levels for a digital thin line towed array for normal operating speeds of an AUV were estimated using em- pirical models and towing experiments. The wavenumber filtering associated with the finite size and distribution of hydrophones in acoustic element of DTLA was applied to the empirical models of turbulent wall pressure spectra to estimate the expected flow noise levels. The empirical results were then compared with the noise spectra measured during towing experiments conducted in a quiet lake. The results showed rapid loss of flow noise energy with increase in frequency arising due to the very nature of turbulent noise spectra and flow noise averaging introduced by the finite size of the hydrophone. I. I NTRODUCTION With the advent of the Autonomous Underwater Vehicles (AUV) and Unmanned Surface Vehicles (USV) there has been an increased demand for the development of very light weight thin line towed arrays for applications like littoral water surveillance and survey, marine mammal studies etc. Acous- tic Research laboratory (ARL) of Tropical Marine Science Institute, National University of Singapore has developed a digital thin line array (DTLA) that consists of 11 acoustic elements, a pressure sensor, a tilt-corrected heading sensor and associated digitizing and power conditioning circuitry packaged inside a 10 mm diameter PVC tube. One of the major concerns for the application of DTLA have been that a reduction in array diameter will increase the proximity and hence susceptibility of acoustic sensors to pressure fluctuations in the turbulent boundary layer (TBL). This could deteriorate the signal to noise ratio (SNR) of thin line arrays especially at low frequencies due to high levels of flow noise getting coupled to the sensors. In this paper, we discuss the empirical estimates of expected flow noise levels for the ARL DTLA and compare them with those estimated from an experiment conducted. II. EMPIRICAL ESTIMATES OF FLOW NOISE Flow noise estimates for the DTLA were arrived at based on empirical model of frequency-wavenumber (F-K) spectrum of turbulent boundary layer (TBL) wall pressure fluctuations. Ex- tensive studies have been conducted in the past to understand the characteristics of wall pressure fluctuation in turbulent boundary layers in flows over cylinders and plates as it is one of the key factors in design of aircraft fuselages, ship and submarine domes and towed array sonars [1]. Many of the observed structural features of the cylindrical boundary layer are similar to those observed in flat-plate turbulent boundary layers even though turbulence intensities for cylinder are lower than that for a flat plate case for most of the boundary layer (outer regions) as the small surface area of the cylinder limits the amount of vorticity introduced in to the fluid [2]. In this paper we use the frequency-wavenumber spectrum of TBL wall pressure fluctuations given by Carpenter and Kewley [3] as expressed in (1).This model was obtained modifying the chase spectrum [4] to express the wall pressure spectra on a cylinder as a function of frequency and wave number component along the axis of cylinder. P (k, ω)= Cρ 2 v 2 * a 2 (12k 2 a 2 + 1) 12  (ωa - ucka) 2 h 2 v 2 * + k 2 a 2 + b -2  -2.5 (1) In equation (1), ρ is the fluid density; U is the tow velocity; u c =0.68U is the convection velocity of turbulence; v * is the friction velocity; and the constants are C =0.063,h = 3.17,b =1.08. The value of v * was evaluated from the drag values measured during tank testing of the array[5] as 0.038U which is very close to the 0.04U used by Carpenter and Kew- ley [3].Application of this model is limited to the cases where δ >> a where δ is the boundary layer thickness and a is the radius of array tube. For the ARL DTLA, δ value under normal operating speed of 2-5 knots is about 100 mm.The frequency spectra of wall pressure fluctuations at DTLA tube surface for different tow speeds were then estimated by integrating P (k,ω) from (1) over the wavenumber range of interest. Another independent estimate of wall pressure spectra on DTLA was obtained by scaling the non-dimensional spectra by Cipolla and Kieth [6]. The wall pressure spectra they measured on a full scale experimental towed array for different tow speeds collapsed well in to a single curve when scaled using tow velocity and array tube diameters as scaling variables. Fig1 shows the frequency spectra of wall pressure fluctuations at DTLA tube surface for different tow speed estimated using two methods described above. Even though the frequency spectrum obtained from empirical F-K model in (1) is ap- proximately 10dB lower than the spectra obtained using the non-dimensional spectra reported by Cipolla and Kieth [6], the energy distribution across the frequencies follow the same trend. Each acoustic ’super-element’ in ARL DTLA consisted of 6 numbers of 8 mm long 2.3 mm diameter piezo-ceramic