Abstract
In this work, we consider the effect of a small-scale helical driving force on fluid with a stable temperature gradient with Reynolds number . At first glance, this system does not have any instability. However, we show that a large scale vortex instability appears in the fluid despite its stable stratification. In a non-linear mode this instability becomes saturated and gives a large number of stationary spiral vortex structures. Among these structures there is a stationary helical soliton and a kink of the new type. The theory is built on the rigorous asymptotical method of multi-scale development.
Highlights
The importance of the generation processes of large-scale coherent vortex structures in hydrodynamics is well known
Sometimes the appearance of large scale vortex structures is accompanied by the inverse cascade of energy both in the three-dimensional case (AKA-effect [12]), and in quasitwo-dimensional cases as well [3,4,5,6,8,9]
The injection of a helical external force into hydrodynamic systems was considered in many works ([21,22,23,24]), and as a result it was understood that a small-scale turbulence able to generate large-scale perturbations cannot be homogeneous, isotropic and helical [25], but must have additional special properties
Summary
The importance of the generation processes of large-scale coherent vortex structures in hydrodynamics is well known. The generation of large scale slow movements by small scale external forces in a rotating stratified fluid was studied numerically in works [14,15]. In this work we consider the theory of large scale vortex generation in stratified fluid under the impact of small scale helical force. We show in this work that despite stable stratification, a large-scale vortex instability appears in the fluid which leads to the generation of large-scale vortex structures. We devote special attention to stationary, non-linear, periodical vortex structures which appear as a result of the saturation of found instability. Among these structures, there is a spiral vortex soliton and kink of the new type.
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