Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere

Nonlinear spectral transfers of kinetic energy and enstrophy, and stationary-transient interaction, are studied using global FGGE data for January 1979. It is found that the spectral transfers arise primarily from a combination, in roughly equal measure, of pure transient and mixed stationary-transient interactions. The pure transient interactions are associated with a transient eddy field which is approximately locally homogeneous and isotropic, and they appear to be consistently understood within the context of two-dimensional homogeneous turbulence. Theory based on spatial wale separation concepts suggests that the mixed interactions may be understood physically, to a first approximation, as a process of shear-induced spectral transfer of transient enstrophy along lines of constant zonal wavenumber. This essentially conservative enstrophy transfer generally involves highly nonlocal stationary-transient energy conversions. The observational analysis demonstrates that the shear-induced transient enstrophy transfer is mainly associated with intermediate-scale (zonal wavenumber m > 3) transients and is primarily to smaller (meridional) scales, so that the transient flow acts as a source of stationary energy. In quantitative terms, this transient-eddy rectification corresponds to a forcing timescale in the stationary energy budget which is of the same order of magnitude as most estimates of the damping timescale in simple stationary-wave models (5 to 15 days). Moreover, the nonlinear interactions involved are highly nonlocal and cover a wide range of transient scales of motion.

The ocean's gravitational potential energy budget in a coupled climate model

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere–ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE, but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing, thus, play complementary roles in sustaining the large scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (-0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by non-linearities in the equation of state.

Thermobaric control of gravitational potential energy generation by diapycnal mixing in the deep ocean

Sources and sinks of gravitational potential energy (GPE) play a rate-limiting role in the large scale ocean circulation. A key source is turbulent diapycnal mixing, whereby irre- versible mixing across isoneutral surfaces is enhanced by turbulent straining of these surfaces. This has motivated international observational efforts to map diapycnal mixing in the global ocean. However, in order to accurately relate the GPE supplied to the large scale circulation by diapycnal mixing to the mixing energy source, it is first necessary to determine the ratio, ξ , of the GPE generation rate to the available potential energy dissipation rate associated with turbulent mixing. Here, the link between GPE and hydro- static pressure is used to derive the GPE budget for a com- pressible ocean with a nonlinear equation of state. The role of diapycnal mixing is isolated and from this a global cli- matological distribution of ξ is calculated. It is shown that, for a given source of mixing energy, typically three times as much GPE is generated if the mixing takes place in bottom waters rather than in the pycnocline. This is due to GPE destruction by cabbelling in the pycnocline, as opposed to thermobaric enhancement of GPE generation by diapycnal mixing in the deep ocean.

Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids

In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction B in steady and transient flows, which reveals that B is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Obstacle avoidance routing scheme through optimal sink movement for home monitoring and mobile robotic consumer devices

In recent years, ZigBee has been proven to be an excellent solution to create scalable and flexible home automation networks. In a home automation network, consumer devices typically collect data from a home monitoring environment and then transmit the data to an end user through multi-hop communication without the need for any human intervention. However, due to the presence of typical obstacles in a home environment, error-free reception may not be possible, particularly for power constrained devices. A mobile sink based data transmission scheme can be one solution but obstacles create significant complexities for the sink movement path determination process. Therefore, an obstacle avoidance data routing scheme is of vital importance to the design of an efficient home automation system. This paper presents a mobile sink based obstacle avoidance routing scheme for a home monitoring system. The mobile sink collects data by traversing through the obstacle avoidance path. Through ZigBee based hardware implementation and verification, the proposed scheme successfully transmits data through the obstacle avoidance path to improve network performance in terms of life span, energy consumption and reliability. The application of this work can be applied to a wide range of intelligent pervasive consumer products and services including robotic vacuum cleaners and personal security robots1.

A cross layer protocol for energy aware and critical data delivered applications using Wireless Sensor Networks

Environment monitoring applications using Wireless Sensor Networks (WSNs) have had a lot of attention in recent years. In much of this research tasks like sensor data processing, environment states and events decision making and emergency message sending are done by a remote server. A proposed cross layer protocol for two different applications where, reliability for delivered data, delay and life time of the network need to be considered, has been simulated and the results are presented in this paper. A WSN designed for the proposed applications needs efficient MAC and routing protocols to provide a guarantee for the reliability of the data delivered from source nodes to the sink. A cross layer based on the design given in [1] has been extended and simulated for the proposed applications, with new features, such as routes discovery algorithms added. Simulation results show that the proposed cross layer based protocol can conserve energy for nodes and provide the required performance such as life time of the network, delay and reliability.

Cross layer based protocols for energy aware and critical data delivery related applications using wireless sensor networks

Wireless Sensor Networks (WSNs) have been an exciting topic in recent years. The services offered by a WSN can be classified into three major categories: monitoring, alerting, and information on demand. WSNs have been used for a variety of applications related to the environment (agriculture, water and forest fire detection), the military, buildings, health (elderly people and home monitoring), disaster relief, and area or industrial monitoring. In most WSNs tasks like processing the sensed data, making decisions and generating emergency messages are carried out by a remote server, hence the need for efficient means of transferring data across the network. Because of the range of applications and types of WSN there is a need for different kinds of MAC and routing protocols in order to guarantee delivery of data from the source nodes to the server (or sink). In order to minimize energy consumption and increase performance in areas such as reliability of data delivery, extensive research has been conducted and documented in the literature on designing energy efficient protocols for each individual layer. The most common way to conserve energy in WSNs involves using the MAC layer to put the transceiver and the processor of the sensor node into a low power, sleep state when they are not being used. Hence the energy wasted due to collisions, overhearing and idle listening is reduced. As a result of this strategy for saving energy, the routing protocols need new solutions that take into account the sleep state of some nodes, and which also enable the lifetime of the entire network to be increased by distributing energy usage between nodes over time. This could mean that a combined MAC and routing protocol could significantly improve WSNs because the interaction between the MAC and network layers lets nodes be active at the same time in order to deal with data transmission. In the research presented in this thesis, a cross-layer protocol based on MAC and routing protocols was designed in order to improve the capability of WSNs for a range of different applications. Simulation results, based on a range of realistic scenarios, show that these new protocols improve WSNs by reducing their energy consumption as well as enabling them to support mobile nodes, where necessary. A number of conference and journal papers have been published to disseminate these results for a range of applications.

Mobile sink based fault diagnosis scheme for wireless sensor networks

Network diagnosis in Wireless Sensor Networks (WSNs) is a difficult task due to their improvisational nature, invisibility of internal running status, and particularly since the network structure can frequently change due to link failure. To solve this problem, we propose a Mobile Sink (MS) based distributed fault diagnosis algorithm for WSNs. An MS, or mobile fault detector is usually a mobile robot or vehicle equipped with a wireless transceiver that performs the task of a mobile base station while also diagnosing the hardware and software status of deployed network sensors. Our MS mobile fault detector moves through the network area polling each static sensor node to diagnose the hardware and software status of nearby sensor nodes using only single hop communication. Therefore, the fault detection accuracy and functionality of the network is significantly increased. In order to maintain an excellent Quality of Service (QoS), we employ an optimal fault diagnosis tour planning algorithm. In addition to saving energy and time, the tour planning algorithm excludes faulty sensor nodes from the next diagnosis tour. We demonstrate the effectiveness of the proposed algorithms through simulation and real life experimental results.