Modeling of internal tides in fjords

A previous model for the distribution of internal tides above irregular topography is generalized to include arbitrary stratification and a radiation condition at the open boundary. Thanks to a small amount of dissipation, this model remains valid in the presence of resonant internal tides, leading to intense wave-energy beams. An application to a Norwegian fjord correctly reproduces the observed energy pattern consisting of two beams both originating at the 60-meter deep entrance sill and extending in-fjord, one upward toward the surface, the other downward toward the bottom. After correction for the varying width of the fjord, the observed and modelled energy levels are in good agreement, especially in the upper levels where energy is the greatest. Furthermore, the substantial phase lag between these two energy beams revealed by the observations is correctly reproduced by the model. Finally, a third and very narrow energy spike is noted in the model at the level of a secondary bump inward of the sill. This beam is missed by the current meter data, because the current meters were placed only at a few selected depths. But an examination of the salinity profiles reveals a mixed layer at approximately the same depth. The explanation is that high-wave energy leads to wave breaking and vigorous mixing. The model\u27s greatest advantage is to provide the internal-tide energy distribution throughout the fjord. Discrepancies between observations and model are attributed to coarse vertical resolution in the vicinity of the sill and to unaccounted cross-fjord variations

Three-layer flows in the shallow water limit

We formulate and discuss the shallow water limit dynamics of the layered flow with three layers of immiscible fluids of different densities bounded above and below by horizontal walls. We obtain a resulting system of four equations, which may be nonlocal in the non‐Boussinesq case. We provide a systematic way to pass to the Boussinesq limit, and then study those equations, which are first‐order PDEs of mixed type, more carefully. We show that in a symmetric case the solutions remain on an invariant surface and using simple waves we illustrate that this is not the case for nonsymmetric cases. Reduced models consisting of systems of two equations are also proposed and compared to the full system

Nonlinear stability of two-layer shallow water flows with a free surface

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability

Heat transport in rotating convection without Ekman layers

Numerical simulation of rotating convection in plane layers with free slip boundaries show that the convective flows can be classified according to a quantity constructed from the Reynolds, Prandtl and Ekman numbers. Three different flow regimes appear: Laminar flow close to the onset of convection, turbulent flow in which the heat flow approaches the heat flow of non-rotating convection, and an intermediate regime in which the heat flow scales according to a power law independent of thermal diffusivity and kinematic viscosity.Comment: 4 pages, 4 figure

Generation and Structure of Solitary Rossby Vortices in Rotating Fluids

The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical simulations show the formation of anticyclonic vortices in unstable shear flows and ring-like vortices with quiescent cores and vorticity concentrated in a ring. Physical mechanisms that lead to these phenomena and their relevance to turbulence in planetary atmospheres are discussed.Comment: 3 pages in REVTeX, 5 postscript figures separately, submitted to Phys. Rev.

Dynamic Potential Intensity: An improved representation of the ocean's impact on tropical cyclones

To incorporate the effects of tropical cyclone (TC)-induced upper ocean mixing and sea surface temperature (SST) cooling on TC intensification, a vertical average of temperature down to a fixed depth was proposed as a replacement for SST within the framework of air-sea coupled Potential Intensity (PI). However, the depth to which TC-induced mixing penetrates may vary substantially with ocean stratification and storm state. To account for these effects, here we develop a “Dynamic Potential Intensity” (DPI) based on considerations of stratified fluid turbulence. For the Argo period 2004–2013 and the three major TC basins of the Northern Hemisphere, we show that the DPI explains 11–32% of the variance in TC intensification, compared to 0–16% using previous methods. The improvement obtained using the DPI is particularly large in the eastern Pacific where the thermocline is shallow and ocean stratification effects are strong.United States. Department of Energy. Office of Science (part of the Regional and Global Climate Modeling Program)Atlantic Oceanographic and Meteorological Laboratory (base funds

Effects of stencil width on surface ocean geostrophic velocity and vorticity estimation from gridded satellite altimeter data

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90421/1/2011JC007367.pd

Generalized Navier-Stokes equations with nonlinear anisotropic viscosity

The purpose of this work is to study the generalized Navier-Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier-Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.Portuguese Foundation for Science and Technology, PortugalPortuguese Foundation for Science and Technology [UID/MAT/04561/2019][SFRH/BSAB/135242/2017

Influence of topography on tide propagation and amplification in semi-enclosed basins

An idealized model for tide propagation and amplification in semi-enclosed rectangular basins is presented, accounting for depth differences by a combination of longitudinal and lateral topographic steps. The basin geometry is formed by several adjacent compartments of identical width, each having either a uniform depth or two depths separated by a transverse topographic step. The problem is forced by an incoming Kelvin wave at the open end, while allowing waves to radiate outward. The solution in each compartment is written as the superposition of (semi)-analytical wave solutions in an infinite channel, individually satisfying the depth-averaged linear shallow water equations on the f plane, including bottom friction. A collocation technique is employed to satisfy continuity of elevation and flux across the longitudinal topographic steps between the compartments. The model results show that the tidal wave in shallow parts displays slower propagation, enhanced dissipation and amplified amplitudes. This reveals a resonance mechanism, occurring when\ud the length of the shallow end is roughly an odd multiple of the quarter Kelvin wavelength. Alternatively, for sufficiently wide basins, also Poincaré waves may become resonant. A transverse step implies different wavelengths of the incoming and reflected Kelvin wave, leading to increased amplitudes in shallow regions and a shift of amphidromic points in the direction of the deeper part. Including the shallow parts near the basin’s closed end (thus capturing the Kelvin resonance mechanism) is essential to reproduce semi-diurnal and diurnal\ud tide observations in the Gulf of California, the Adriatic Sea and the Persian Gulf