| dc.description.abstract | We explore the evolution of the gravest internal Kelvin wave in a two-layer rotating cylindrical
basin, using direct numerical simulations (DNS) with a hyperviscosity/diffusion approach to
illustrate different dynamic and energetic regimes. The initial condition is derived from
Csanady's (J. Geophys. Res., vol. 72, 1967, pp. 4151-4162) conceptual model, which is
adapted by allowing molecular diffusion to smooth the discontinuous idealized solution over a
transition scale, delta(i), taken to be small compared to both layer thicknesses h(l), l = 1, 2. The
different regimes are obtained by varying the initial wave amplitude, eta(0), for the same
stratification and rotation. Increasing eta(0) increases both the tendency for wave steepening
and the shear in the vicinity of the density interface. We present results across several regimes:
from the damped, linear-laminar regime (DLR), for which eta(0) similar to delta(i) and the Kelvin
wave retains its linear character, to the nonlinear-turbulent transition regime (TR), for which the
amplitude eta(0) approaches the thickness of the (thinner) upper layer h(1), and nonlinearity
and dispersion become significant, leading to hydrodynamic instabilities at the interface. In the
TR, localized turbulent patches are produced by Kelvin wave breaking, i.e. shear and
convective instabilities that occur at the front and tail of energetic waves within an internal
Rossby radius of deformation from the boundary. The mixing and dissipation associated with
the patches are characterized in terms of dimensionless turbulence intensity parameters that
quantify the locally elevated dissipation rates of kinetic energy and buoyancy variance. | |
