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Large-scale turbulence in fluid layers and other quasi-two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces a direct energy cascade, while solenoidal planar turbulence…
The presence of stratified layer in atmosphere and ocean leads to buoyant vertical motions, commonly referred to as plumes. It is important to study the mixing dynamics of a plume at a local scale in order to model their evolution and…
This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the opposite…
We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential…
Following the findings in \cite{wangsawijaya2020}, we re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness wavelengths $0.32 \leq S/\overline{\delta} \leq 3.63$, where…
In the stably stratified ocean, small-scale turbulence is important for vertical exchange and hence for the mixing of water masses and suspended matter. To observationally study turbulent motions and the buoyancy- and shear-generators…
Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction…
What do the ocean surface and a swaying flag have in common? Both are deformable surfaces exhibiting chaotic motion when exposed to turbulent flows. Whether such motion is primarily driven by flow turbulence or by nonlinear dynamics…
We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for…
The dissolution of a body into quiescent water leads to density stratifications at the interfaces that drive buoyant flows. Where the stratification is unstable, the flow destabilizes into convective solute plumes. By analogy with the…
We study interfacial waves in a system of two horizontal layers of immiscible inviscid fluids involved into horizontal vibrational motion. We analyze the linear and nonlinear stability properties of the solitons in the system and consider…
Following recent evidence that the vortices in decaying two-dimensional turbulence can be classified into small--mobile, and large--quasi-stationary, this paper examines the evidence that the latter might be considered a `crystal' whose…
The flow structures beneath waves have received significant attention from both theoretical and numerical perspectives. Most studies on this topic assume a flat bottom, leading to questions about the effects of variable bottom topography.…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
The basic building blocks of many forms of optical topologies are particle-like singularities in phase and polarisation, giving rise to lines of darkness that weave complex threads in 3D space. Although known for half a century since…
The homogenization of one-dimensional acoustic or elastic structures of finite extent is considered. A new homogenization method based on transfer matrices is derived. The new homogenization method may account for variable cross sectional…
In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…
The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincar\'e map, is…
We present a comprehensive study of MHD waves and instabilities in a weakly ionised system, e.g., an interstellar molecular cloud. We determine all the critical wavelengths of perturbations across which the sustainable wave modes can change…
Recent observations of Jupiter and Saturn suggest that heavy elements may be diluted in the gaseous envelope, providing a compositional gradient that could stabilise ordinary convection and produce a stably-stratified layer near the core of…