Numerical Modeling of Internal Waves Generated by Turbulent Wakes Behind Self-Propelled and Towed Bodies in Stratified Media

Dynamics of turbulent wake with small excess momentum in stratified media

“…This indicates the weak influence of small excess momentum on the pattern of internal waves generated by turbulent wakes in stratified fluid. There is significant distinction between the evolution of axisymmetric turbulent wakes past towed [21][22][23] and past self-propelled bodies (or bodies with small excess momentum). In the wakes behind towed bodies in homogeneous fluid the production of turbulent energy due to the average flow has significant effect.…”

“…The choice of this model of turbulence is due to the following reasons: it is close to the standard e-e model of turbulence and we can take into account the anisotropy of the turbulence characteristics in the wakes in a stratified fluid. In [22], a similar mathematical model is used to study internal waves generated by turbulent wakes behind self-propelled and towed bodies in a stratified fluid. A weak dependence of the internal wave characteristics on the applied mathematical model has been shown as well (see, for example [5]).…”

“…Based on the model including modified algebraic representations of triple correlations of the velocity field and the transfer equation for the dissipation rate, a numerical investigation of a far momentumless wake in a linearly stratified fluid was carried out in [19]. The internal waves generated by the turbulent wakes of self-propelled and towed bodies moving in a stable stratified fluid were studied numerically in [5,16,[21][22][23][24]. The turbulent wake behind a towed body was shown to generate internal waves of substantially larger amplitude than those behind a self-propelled body.…”

Passive scalar dynamics in turbulent wakes of bodies moving in a linearly stratified medium

“…5) In these equations the value U d = U 0 −U is the defect of the averaged longitudinal velocity component; U , V , W are the velocity components of the averaged motion along the x-, y-, z-axes, respectively; p 1 is the pressure deviation from hydrostatic pressure due to the stratification ρ s (z); U 0 is the velocity of an incident undisturbed flow; g is the gravity acceleration, ρ 1 is the averaged density defect: ρ 1 = ρ − ρ s , ρ s = ρ s (z) is the density of an undisturbed fluid that is assumed to be linear: ρ s (z) = ρ 0 (1 − az), a = const > 0; the prime indicates the pulsation components, · is the averaging. 5) In these equations the value U d = U 0 −U is the defect of the averaged longitudinal velocity component; U , V , W are the velocity components of the averaged motion along the x-, y-, z-axes, respectively; p 1 is the pressure deviation from hydrostatic pressure due to the stratification ρ s (z); U 0 is the velocity of an incident undisturbed flow; g is the gravity acceleration, ρ 1 is the averaged density defect: ρ 1 = ρ − ρ s , ρ s = ρ s (z) is the density of an undisturbed fluid that is assumed to be linear: ρ s (z) = ρ 0 (1 − az), a = const > 0; the prime indicates the pulsation components, · is the averaging.…”

“…Particular attention in [4,14] was given to numerical modelling of anisotropic decay of turbulence in a long momentumless turbulent wake in a linearly stratified medium. In [4,5] the characteristics of internal waves generated by turbulent wakes both behind self-propelled [4,5] and towed bodies [5] have been thoroughly studied. A series of investigations [12,13] deal with numerical modelling of the propagation of a passive scalar from an instantaneously localized source in a turbulent mixing plane in a stable stratified medium.…”