Sound channel in an exponentially stratified ocean, with application to SOFAR

For much of the World's oceans, the stability of the water column beneath the thermocline is quite well represented by N2(z) = gρ−1 ∂zρ′ = NO2e−2z/B, where ∂zρ′ is the vertical gradient in potential density, NO ≈ 3 cycles/h is the surface-extrapolated “Brunt-Väisälä” frequency, and B ≈ 1.3 km is the stratification scale. This leads to an idealized sound channel C(z) = C1 1 + ε(η + e−η − 1) = C1 + ε(1/2)η2 − (1/6)η3 + … with a minimum velocity at the axis z = z1, η = (z − z1)/12B being dimensionless depth relative to z1. The parameters ε, z1 are explicitly expressed in terms of the five coefficients α, β, γ, a, b (temperature, salinity, pressure coefficients of C; temperature and salinity coefficients of ρ′), given only the form of N(z) and a representative T, S relation. The up-down asymmetry of the channel, a consequence of the fundamental structure of the oceans, plays a first-order role in the propagation characteristics. As an application, the ray arrivals for an axial source and receiver are computed.