Flows in the oceans and the atmosphere often involve the horizontal shearing of stably stratified density layers. These shear layers are subject to hydrodynamic instabilities that cause the transition from laminar to turbulent flow. When a density interface is sharper than the velocity interface, the Holmboe instability can arise. In this thesis, the dynamics and mixing of the Holmboe instability are investigated theoretically, numerically and in the laboratory.

First, the spatial evolution of the Holmboe instability along an arrested salt wedge is investigated both in laboratory experiments and using linear stability analysis. The spatial evolution is dependent on the variation in the mean velocity and density profiles along the length of the salt wedge. The linear stability analysis incorporates this variation and predicts the growth rate, wavelength, phase speed and wave steepness of the Holmboe instability along the length of the salt wedge. These predictions are consistent with the laboratory measurements.

The Reynolds stress ellipses associated with Holmboe instabilities are investigated using linear stability analysis, single wavelength simulations, multiple wavelength simulations, and a laboratory experiment. Conventionally, only the statistics of horizontal and vertical velocity perturbation pairs, (u',w'), are used to show the degree of anisotropy in perturbation fields. Here, a theory-based approach is used to investigate this anisotropy. Linear stability analysis predicts the aspect ratio of the major and minor axes and the orientation angle of the Reynolds stress ellipses, and thus predicts the resultant Reynolds stresses.

Finally, the influence of initial perturbations on the mixing generated by Holmboe instabilities is examined. Initial perturbations are commonly used in direct numerical simulations to stimulate the shear instability of stratified fluids. The amplitudes of the primary and subharmonic Holmboe modes determine the development of the Holmboe instabilities. The excitation of the subharmonic mode induces the merging of the primary Holmboe mode, and further increases the amplitude of Holmboe waves and the overall mixing.