Lavrentyev Institute of Hydrodynamics, Russia

The given report is devoted to the important problem of internal gravity wave generation in a stratified fluid resulting from the horizontal motion of a submerged body and its associated turbulent wake. Unfortunately, at present there is no definite understanding of all the sources responsible for a generation of internal waves by a towed or self-propelled body. Models used in the 70s and 80s are under reconsideration at the present time (see e.g. (1)) especially at high speed of body motion.

The authors used the model proposed by Kallen (2), where a body together with a turbulent wake is modeled by an infinitely long thin body. Despite the disputability of the model used, the undoubted advantage of the given paper is the proposed effective method of determination of the Green function of a point mass source moving uniformly in a fluid with an arbitrary stable stratification. The asymptotic estimations for near and far field are obtained.

To my point of view, this method will be extremely useful for computation of the flow around the moving solid body of an arbitrary form with a non-flow condition at the body’s surface. Analogously to the computation of the flow around a body submerged under the free surface of homogeneous fluid, it is possible to use the boundary element method demanding a determination of the Green function for the problem and work out of algorithm of its effective calculation. If the problem is solved successfully together with the determination of wave field, the effect of stratification on hydrodynamics loads acting on a body can be estimated.


1. Robey, H.F., “The Generation of Internal Waves by a Towed Sphere and Its Wake in a Thermocline,” Physics of Fluids, Vol. 9, No. 11, 1997, pp. 3353–3367.

2. Kallen, E., “Surface Effects of Vertically Propagating Waves in Stratified Fluid,” Journal of Fluid Mechanics, Vol. 182, 1987, pp. 111–125.


The authors agree with the discusser’s comments.

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