Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

Presence of Holmboe waves in particle-laden intrusive gravity current

The present study evaluates the prevalence of Holmboe waves in an intrusive gravity current (IGC) containing particles, employing large Eddy simulation (LES). Holmboe waves, a type of stratified shear layer-generated wave, are characterised by a relatively thin density interface compared to the thickness of the shear layer. The study demonstrates the occurrence of secondary rotation, wave stretching over time, and fluid ejection at the interface between the IGC and a lower gravity current (LGC). Results indicate that, aside from J and R, the density difference between the IGC and the LGC has an impact on Holmboe instability. However, a reduction in the density difference does not manifest consistently in the frequency, growth rate, and phase speed, though it does cause an increase in the wavelength. It is important to note that small particles do not affect the Holmboe instability of the IGC, while larger particles cause the current to become unstable and vary the characteristics of Holmboe instability. Moreover, an increase in the particle diameter size results in an increment in the wavelength, growth rate, and phase speed; but is accompanied by a decrease in frequency. Additionally, the enlargement of the bed slope angle makes the IGC more unstable, encouraging the growth of Kelvin-Helmholtz waves; however, this causes Holmboe waves to disappear on inclined beds. Finally, a range for the instabilities of both Kelvin-Helmholtz and Holmboe is provided.

Vertical Shear Processes in River Plumes: Instabilities and Turbulent Mixing

In this paper, the problem of vertical shear flow instabilities at the base of a river plume and their consequences in terms of turbulent energy production and mixing is addressed. This study was carried out using 2D non-hydrostatic simulations and a linear stability analysis. The initial conditions used in these simulations were similar to those observed in river plumes near estuaries. Unstable stratified sheared flows follow three stages of evolution: (i) the generation of billows induced by vertical shear instabilities, (ii) intensification, and (iii) elongation. The elongation of the generated billows is related to the strain intensity, which depends on the physical setting involved (velocity shear, stratification thickness, and bottom slope). Two vertical shear instabilities were found in our study: the Holmboe and Kelvin–Helmholtz instabilities. The Kelvin–Helmholtz instability has a smaller growth time and longer wavelengths; the Holmboe instability is characterized by a longer growth time and shorter wavelengths. The Kelvin–Helmholtz instability is intensified when the bottom is sloped and for large shears. The Holmboe instability is stronger when the stratification thickness is reduced compared to the shear thickness and when the bottom is sloped. For mixing, the flow can be: (i) pre-turbulent, (ii) quasi-turbulent, or (iii) turbulent. The pre-turbulent flow corresponds to more mass mixing than momentum mixing and to more Eddy Kinetic Energy dissipation than Eddy Available Potential Energy dissipation. Such a flow is encountered over a flat bottom whatever the initial shear is. The quasi-turbulent and turbulent flows are reached when the bottom is sloped and when the stratification thickness is reduced. Using turbulent mixing statistics (mixing coefficients, mixing efficiency, Eddy Kinetic Energy, and Eddy Available Potential Energy dissipation rates), we showed that, despite their slow growth, Holmboe instabilities contribute more efficiently to turbulent mixing than Kelvin–Helmholtz instabilities. Holmboe instabilities are the only source of turbulent mixing when sharp density gradients are observed (small buoyancy thickness experiment). Our simulations highlight the contribution of the Holmboe instability to turbulent mixing.