136 1. IntroductIon Most underwater acoustic propagation models are approximated as two dimensional with no interaction between the azimuthal planes. This is a fair approximation, for a basically three-dimensional problem, due to two reasons. One is that three dimensional efects are negligible at shorter ranges and the other is due to non-availability of input data like Sound speed profle, bottom type, etc. along each azimuth. Also, the implementation of a three-dimensional model is computationally expensive for operational purposes. The two important cases where 3D efects are reported in literature are cross-slope propagation over a sloping bottom and propagation around sea mounts 3 . In this study, the efect of an upwelling event on azimuthal acoustic propagation is modelled. Upwelling is a process in which deep colder water rises to the surface, which leads to lowering of sea surface temperature. The change in sound speed profle structure is gradual along the range during an upwelling process 1 . This gradual change in SSP difers along each azimuth and is an ideal scenario to observe 3D efects of acoustic propagation. A 3D parabolic equation model based on implicit fnite diference method is used for this study. This model code has been documented and validated with respect to diferent benchmark cases mentioned by Lee & Schultz 3 . The parabolic equation model developed by Lee and Schultz 3 , can compute acoustic feld for three-dimensional propagation scenario. The 3 D Helmholtz equation in cylindrical coordinates is given by, 2 2 2 2 2 0 2 2 2 2 1 1 (,,) 1 0 k n r z r r r z r ∂∅ ∂∅ ∂∅ ∂∅   + + + + θ − ∅=   ∂ ∂ ∂ ∂θ where θ Azimuth angle. ∅ Spatial portion of the acoustic pressure feld n Index of refraction; n (r,θ, z) = c 0 /c(r, θ, z) c 0 A reference sound speed k 0 2πf/ c 0 , with f being source frequency z Receiver depth r Receiver range. separating the variables as under, ∅ (r,θ, z) = u (r,θ, z) v(r) and solving we get v as Hankel function, and 2 2 0 2 1 (,,) 1 0 r zz u u u k n r z r θθ   + + + θ − =   Dropping frst term in the above equation and rearranging the terms, 2 0 2 0 0 1 (,,) 1 2 2 2 r zz ik i u n r z u u u k kr θθ   = θ − + +   Rewriting the above equation in the operator form, 2 2 2 2 2 0 0 2 2 2 2 1 2 (,,) 1 0 ik k n r z u r r z r ∂ ∂ ∂ ∂   + + + + θ − =   ∂ ∂ ∂ ∂θ Then, defning the operators, Defence Science Journal, Vol. 69, No. 2, March 2019, pp. 136-141, DOI : 10.14429/dsj.69.14220  2019, DESIDOC Efect of Azimuthal Asymmetry Caused by Upwelling on 3D Ocean Acoustic Propagation R.P. Raju * , P. Anand, Dominic Ricky Fernandez, and A. Raghunadha Rao *DRDO-Naval Physical and Oceanographic Laboratory, Kochi - 682 021, India * E-mail: rpraju@npol.drdo.in AbstrACt 3-D underwater parabolic equation model based on implicit fnite diference method has been implemented for South Eastern Arabian Sea (SEAS). The bathymetric and geo-acoustic features have been integrated in the model for a 50 km circular region in SEAS. The model can simulate the efects of azimuthal variation in oceanographic features and compute azimuthally coupled pressure due to an omni-directional source. The azimuthal variation in oceanographic conditions can be observed during an upwelling event. In the frst case study, the efect of upwelling event on three-dimensional acoustic propagation has been studied by using sound speed profle data derived from INS Sagardhwani observations. The diference in Transmission loss mosaic for upslope and downslope propagation is due to bathymetry as well as upwelling. In the second case study, the efect of upwelling only, is studied by running a model corresponding to range independent sound speed profle feld and range dependent bathymetry. It was observed that during this upwelling event, the transmission loss is higher at longer ranges during upslope propagation than downslope propagation. This is due to the increase in the thickness of sonic layer duct as acoustic wave propagates from shallow to deep water. The efect of azimuthal variation in intensity of upwelling is observed in top views of transmission loss mosaics for a given receiver or target depth. Keywords: 3D acoustic propagation; Upwelling; Arabian Sea Received : 07 January 2019, Revised : 06 February 2019 Accepted : 10 February 2019, Online published : 06 March 2019