Internal waves from a body accelerating in a thermocline

Many papers study the steady wave system around bodies moving in thermoclines but little attention has been given to unsteady wave systems. This paper concentrates on the unsteady wave systems around accelerating bodies in thermoclines. The wave shapes are calculated using a theory derived from a dispersion relation based on an exp-tanh density profile. All modes of oscillation can be determined and it is shown that for the lowest mode both oblique and transverse waves occur whereas for the higher modes the presence of transverse waves depends on the background conditions and on the speed of the body. Cauchy-Poisson impulsive start waves are included. The theoretical wave shapes compare quite well with those calculated using finite-difference formulations of the full Navier-Stokes equations when a body accelerates from rest.It is also shown how the dispersion relation =N sin together with the WKB approximation can produce the same plan-view wave forms as those obtained using the thermocline wave dispersion relation given by 17, 30].