Lower and Upper Bounds on Internal-Wave Frequencies in Stratified Rotating Fluids

According to classical theories, the frequencies of internal-gravity waves in stratified rotating fluids must lie between the Brunt-Väisälä frequency (a measure of the vertical density stratification) and the Coriolis frequency (equal to twice the rotation rate about the vertical axis). It is shown here that, in the case of the Earth\u27s rotation where the pole-to-pole axis of rotation is almost everywhere not parallel to the local vertical, the range of realizable frequencies is broader. New formulas are derived for the lower and upper bounds of the frequencies

Resonance of internal waves in fjords: A finite-difference model

After the time periodicity is removed from the problem, the spatial distribution of internal waves in a stratified fluid is governed by a hyperbolic equation. With boundary conditions specified all along the perimeter of the domain, information is transmitted in both directions (forward and backward) along every characteristic, and, unlike the typical temporal hyperbolic equation, the internal-wave equation is not amenable to a simple forward integration. The problem is tackled here with a finite-difference, relaxation technique by constructing a time-dependent, dissipative problem, the final steady state of which yields the solution of the original problem. Attempts at solving the problem for arbitrary topography then reveal multiple resonances, each resonance being caused by a ray path closing onto itself after multiple reflections. The finite-difference formulation is found to be a convenient vehicle to discuss resonances and to conclude that their existence renders the problem not only singular but also extremely sensitive to the details of the topography. The problem is easily overcome by the introduction of friction. The finite-difference representation of the problem is instrumental in serving as a guide for the investigation of the resonance problem. Indeed, it keeps the essence of the continuous problem and yet simplifies the analysis enormously. Although straightforward, robust and successful at providing a numerical solution to a first few examples, the relaxation component of the integration technique suffers from lack of efficiency. This is due to the particular nature of the hyperbolic problem, but it remains that numerical analysts could improve or replace the present scheme with a faster algorithm

Northern Adriatic response to a wintertime bora wind event

The unprecedented suite of research activities that focused on the Adriatic in winter 2003 provided a multi-faceted view of bora events and the resulting oceanic response

Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory

The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortice

Introduction to Geophysical Fluid Dynamics, Physical and Numerical Aspects, 2nd Edition Volume 101

The long-awaited second edition of this classic text now combines both physical and numerical aspects of geophysical fluid dynamics -- the principles governing air and water flows on large terrestrial scales --into a single affordable volume

Top-to-bottom Ekman layer and its implications for shallow rotating flows

The analytical solution is derived for rotational frictional flow in a shallow layer of fluid in which the top and bottom Ekman layers join without leaving a frictionless interior.This vertical structure has significant implications for the horizontal flow. In particular, for a layer of water subjected to both a surface wind stress and bottom friction, the vorticity of the horizontal flow is a function not only of the curl of the wind stress (the classical result for deep water known as Ekman pumping) but also of its divergence. The importance of this divergence term peaks for a water depth around 3 times the Ekman layer thickness. This means that a curl-free but non-uniform wind stress on a shallow sea or lake can, through the dual action of rotation and friction, generate vorticity in the wind-driven currents. We also find that the reduction of three-dimensional dynamics to a two-dimensional model is more subtle than one could have anticipated and needs to be approached with utmost care. Taking the bottom stress as dependent solely on the depth-averaged flow, even with some veering, is not appropriate. The bottom stress ought to include a component proportional to the surface stress, which is negligible for large depths but increases with decreasing water depth.Mathematical Physic