Estimation and evaluation of multi-decadal fire severity patterns using Landsat sensors

Retrospective identification of fire severity can improve our understanding of fire behaviour and ecological responses. However, burnt area records for many ecosystems are non-existent or incomplete, and those that are documented rarely include fire severity data. Retrospective analysis using satellite remote sensing data captured over extended periods can provide better estimates of fire history. This study aimed to assess the relationship between the Landsat differenced normalised burn ratio (dNBR) and field measured geometrically structured composite burn index (GeoCBI) for retrospective analysis of fire severity over a 23 year period in sclerophyll woodland and heath ecosystems. Further, we assessed for reduced dNBR fire severity classification accuracies associated with vegetation regrowth at increasing time between ignition and image capture. This was achieved by assessing four Landsat images captured at increasing time since ignition of the most recent burnt area. We found significant linear GeoCBI–dNBR relationships (R2 = 0.81 and 0.71) for data collected across ecosystems and for Eucalyptus racemosa ecosystems, respectively. Non-significant and weak linear relationships were observed for heath and Melaleuca quinquenervia ecosystems, suggesting that GeoCBI–dNBR was not appropriate for fire severity classification in specific ecosystems. Therefore, retrospective fire severity was classified across ecosystems. Landsat images captured within ~ 30 days after fire events were minimally affected by post burn vegetation regrowth.

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Studies On Hydrogen Bonds: Part IV. Proposed Working Criteria for Assessing Qualitative Strength of Hydrogen Bonds

The data obtained in the earlier parts of this series for the donor and acceptor end parameters of N-H. O and O-H. O hydrogen bonds have been utilised to obtain a qualitative working criterion to classify the hydrogen bonds into three categories: "very good" (VG), "moderately good" (MG) and weak (W). The general distribution curves for all the four parameters are found to be nearly of the Gaussian type. Assuming that the VG hydrogen bonds lie between 0 and ± la, MG hydrogen bonds between ± 1 and ± 2, W hydrogen bonds beyond ± 2 (where is the standard deviation), suitable cut-off limits for classifying the hydrogen bonds in the three categories have been derived. These limits are used to get VG and MG ranges for the four parameters 1 and θ (at the donor end) and ± and ± (at the acceptor end). The qualitative strength of a hydrogen bond is decided by the cumulative application of the criteria to all the four parameters. The criterion has been further applied to some practical examples in conformational studies such as α-helix and can be used for obtaining suitable location of hydrogen atoms to form good hydrogen bonds. An empirical approach to the energy of hydrogen bonds in the three categories has also been presented.

A new type of high-order elements based on the mesh-free interpolations

We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

Cointegration and causal relationships between energy consumption and output: Assessing the evidence from Australia

In this paper, we describe our investigation of the cointegration and causal relationships between energy consumption and economic output in Australia over a period of five decades. The framework used in this paper is the single-sector aggregate production function, which is the first comprehensive approach used in an Australian study of this type to include energy, capital and labour as separate inputs of production. The empirical evidence points to a cointegration relationship between energy and output and implies that energy is an important variable in the cointegration space, as are conventional inputs capital and labour. We also find some evidence of bidirectional causality between GDP and energy use. Although the evidence of causality from energy use to GDP was relatively weak when using the thermal aggregate of energy use, once energy consumption was adjusted for energy quality, we found strong evidence of Granger causality from energy use to GDP in Australia over the investigated period. The results are robust, irrespective of the assumptions of linear trends in the cointegration models, and are applicable for different econometric approaches.

Interfuel substitution in Australia: A way forward to achieve environmental sustainability

This paper examines the possibilities for interfuel substitution in Australia in view of the need to shift towards a cleaner mix of fuels and technologies to meet future energy demand and environmental goals. The translog cost function is estimated for the aggregate economy, the manufacturing sector and its subsectors, and the electricity generation subsector. The advantages of this work over previous literature relating to the Australian case are that it uses relatively recent data, focuses on energy-intensive subsectors and estimates the Morishima elasticities of substitution. The empirical evidence shown herein indicates weak-form substitutability between different energy types, and higher possibilities for substitution at lower levels of aggregation, compared with the aggregate economy. For the electricity generation subsector, which is at the centre of the CO2 emissions problem in Australia, significant but weak substitutability exists between coal and gas when the price of coal changes. A higher substitution possibility exists between coal and oil in this subsector. The evidence for the own- and cross-price elasticities, together with the results for fuel efficiencies, indicates that a large increase in relative prices could be justified to further stimulate the market for low-emission technologies.

Ambient temperature and risk of cardiovascular hospitalization: An updated systematic review and meta-analysis

The association between temperatures and risk of cardiovascular mortality has been recognized but the association drawn from previous meta-analysis was weak due to the lack of sufficient studies. This paper presented a review with updated reports in the literature about the risk of cardiovascular hospitalization in relation to different temperature exposures and examined the dose–response relationship of temperature-cardiovascular hospitalization by change in units of temperature, latitudes, and lag days. The pooled effect sizes were calculated for cold, heat, heatwave, and diurnal variation using random-effects meta-analysis, and the dose–response relationship of temperature-cardiovascular admission was modelled using random-effect meta-regression. The Cochrane Q-test and index of heterogeneity (I2) were used to evaluate heterogeneity, and Egger's test was used to evaluate publication bias. Sixty-four studies were included in meta-analysis. The pooled results suggest that for a change in temperature condition, the risk of cardiovascular hospitalization increased 2.8% (RR, 1.028; 95% CI, 1.021–1.035) for cold exposure, 2.2% (RR, 1.022; 95% CI, 1.006–1.039) for heatwave exposure, and 0.7% (RR, 1.007; 95% CI, 1.002–1.012) for an increase in diurnal temperature. However no association was observed for heat exposure. The significant dose–response relationship of temperature — cardiovascular admission was found with cold exposure and diurnal temperature. Increase in one-day lag caused a marginal reduction in risk of cardiovascular hospitalizations for cold exposure and diurnal variation, and increase in latitude was associated with a decrease in risk of cardiovascular hospitalizations for diurnal temperature only. There is a significant short-term effect of cold exposure, heatwave and diurnal variation on cardiovascular hospitalizations. Further research is needed to understand the temperature-cardiovascular relationship for different climate areas.

Dessy : desktop search and synchronization

Current smartphones have a storage capacity of several gigabytes. More and more information is stored on mobile devices. To meet the challenge of information organization, we turn to desktop search. Users often possess multiple devices, and synchronize (subsets of) information between them. This makes file synchronization more important. This thesis presents Dessy, a desktop search and synchronization framework for mobile devices. Dessy uses desktop search techniques, such as indexing, query and index term stemming, and search relevance ranking. Dessy finds files by their content, metadata, and context information. For example, PDF files may be found by their author, subject, title, or text. EXIF data of JPEG files may be used in finding them. User–defined tags can be added to files to organize and retrieve them later. Retrieved files are ranked according to their relevance to the search query. The Dessy prototype uses the BM25 ranking function, used widely in information retrieval. Dessy provides an interface for locating files for both users and applications. Dessy is closely integrated with the Syxaw file synchronizer, which provides efficient file and metadata synchronization, optimizing network usage. Dessy supports synchronization of search results, individual files, and directory trees. It allows finding and synchronizing files that reside on remote computers, or the Internet. Dessy is designed to solve the problem of efficient mobile desktop search and synchronization, also supporting remote and Internet search. Remote searches may be carried out offline using a downloaded index, or while connected to the remote machine on a weak network. To secure user data, transmissions between the Dessy client and server are encrypted using symmetric encryption. Symmetric encryption keys are exchanged with RSA key exchange. Dessy emphasizes extensibility. Also the cryptography can be extended. Users may tag their files with context tags and control custom file metadata. Adding new indexed file types, metadata fields, ranking methods, and index types is easy. Finding files is done with virtual directories, which are views into the user’s files, browseable by regular file managers. On mobile devices, the Dessy GUI provides easy access to the search and synchronization system. This thesis includes results of Dessy synchronization and search experiments, including power usage measurements. Finally, Dessy has been designed with mobility and device constraints in mind. It requires only MIDP 2.0 Mobile Java with FileConnection support, and Java 1.5 on desktop machines.

Cryptographic Software Export Controls in the EU

Certain software products employing digital techniques for encryption of data are subject to export controls in the EU Member States pursuant to Community law and relevant laws in the Member States. These controls are agreed globally in the framework of the so-called Wassenaar Arrangement. Wassenaar is an informal non-proliferation regime aimed at promoting international stability and responsibility in transfers of strategic (dual-use) products and technology. This thesis covers provisions of Wassenaar, Community export control laws and export control laws of Finland, Sweden, Germany, France and United Kingdom. This thesis consists of five chapters. The first chapter discusses the ratio of export control laws and the impact they have on global trade. The ratio is originally defence-related - in general to prevent potential adversaries of participating States from having the same tools, and in particular in the case of cryptographic software to enable signals intelligence efforts. Increasingly as the use of cryptography in a civilian context has mushroomed, export restrictions can have negative effects on civilian trade. Information security solutions may also be took weak because of export restrictions on cryptography. The second chapter covers the OECD's Cryptography Policy, which had a significant effect on its member nations' national cryptography policies and legislation. The OECD is a significant organization,because it acts as a meeting forum for most important industrialized nations. The third chapter covers the Wassenaar Arrangement. The Arrangement is covered from the viewpoint of international law and politics. The Wassenaar control list provisions affecting cryptographic software transfers are also covered in detail. Control lists in the EU and in Member States are usually directly copied from Wassenaar control lists. Controls agreed in its framework set only a minimum level for participating States. However, Wassenaar countries can adopt stricter controls. The fourth chapter covers Community export control law. Export controls are viewed in Community law as falling within the domain of Common Commercial Policy pursuant to Article 133 of the EC Treaty. Therefore the Community has exclusive competence in export matters, save where a national measure is authorized by the Community or falls under foreign or security policy derogations established in Community law. The Member States still have a considerable amount of power in the domain of Common Foreign and Security Policy. They are able to maintain national export controls because export control laws are not fully harmonized. This can also have possible detrimental effects on the functioning of internal market and common export policies. In 1995 the EU adopted Dual-Use Regulation 3381/94/EC, which sets common rules for exports in Member States. Provisions of this regulation receive detailed coverage in this chapter. The fifth chapter covers national legislation and export authorization practices in five different Member States - in Finland, Sweden, Germany, France and in United Kingdom. Export control laws of those Member States are covered when the national laws differ from the uniform approach of the Community's acquis communautaire. Keywords: export control, encryption, software, dual-use, license, foreign trade, e-commerce, Internet

The laminar boundary layer regime for natural convection of air in a square cavity

Numerical predictions are obtained for laminar natural convection of air in a square two dimensional cavity at high Rayleigh numbers. Proper resolution of the core reveals weak multi-cellular structure which varies in a complex manner as the effects of convection are increased. The end of the steady laminar regime is numerically estimated to occur at Ra=2.2x10^8.

Theological Exegesis in the Canonical Context : Brevard S. Childs' Methodology of Biblical Theology

Modern Christian theology has been at pain with the schism between the Bible and theology, and between biblical studies and systematic theology. Brevard Springs Childs is one of biblical scholars who attempt to dismiss this “iron curtain” separating the two disciplines. The present thesis aims at analyzing Childs’ concept of theological exegesis in the canonical context. In the present study I employ the method of systematic analysis. The thesis consists of seven chapters. Introduction is the first chapter. The second chapter attempts to find out the most important elements which exercise influence on Childs’ methodology of biblical theology by sketching his academic development during his career. The third chapter attempts to deal with the crucial question why and how the concept of the canon is so important for Childs’ methodology of biblical theology. In chapter four I analyze why and how Childs is dissatisfied with historical-critical scholarship and I point out the differences and similarities between his canonical approach and historical criticism. The fifth chapter attempts at discussing Childs’ central concepts of theological exegesis by investigating whether a Christocentric approach is an appropriate way of creating a unified biblical theology. In the sixth chapter I present a critical evaluation and methodological reflection of Childs’ theological exegesis in the canonical context. The final chapter sums up the key points of Childs’ methodology of biblical theology. The basic results of this thesis are as follows: First, the fundamental elements of Childs’ theological thinking are rooted in Reformed theological tradition and in modern theological neo-orthodoxy and in its most prominent theologian, Karl Barth. The American Biblical Theological Movement and the controversy between Protestant liberalism and conservatism in the modern American context cultivate his theological sensitivity and position. Second, Childs attempts to dismiss negative influences of the historical-critical method by establishing canon-based theological exegesis leading into confessional biblical theology. Childs employs terminology such as canonical intentionality, the wholeness of the canon, the canon as the most appropriate context for doing a biblical theology, and the continuity of the two Testaments, in order to put into effect his canonical program. Childs demonstrates forcefully the inadequacies of the historical-critical method in creating biblical theology in biblical hermeneutics, doctrinal theology, and pastoral practice. His canonical approach endeavors to establish and create post-critical Christian biblical theology, and works within the traditional framework of faith seeking understanding. Third, Childs’ biblical theology has a double task: descriptive and constructive, the former connects biblical theology with exegesis, the later with dogmatic theology. He attempts to use a comprehensive model, which combines a thematic investigation of the essential theological contents of the Bible with a systematic analysis of the contents of the Christian faith. Childs also attempts to unite Old Testament theology and New Testament theology into one unified biblical theology. Fourth, some problematic points of Childs’ thinking need to be mentioned. For instance, his emphasis on the final form of the text of the biblical canon is highly controversial, yet Childs firmly believes in it, he even regards it as the corner stone of his biblical theology. The relationship between the canon and the doctrine of biblical inspiration is weak. He does not clearly define whether Scripture is God’s word or whether it only “witnesses” to it. Childs’ concepts of “the word of God” and “divine revelation” remain unclear, and their ontological status is ambiguous. Childs’ theological exegesis in the canonical context is a new attempt in the modern history of Christian theology. It expresses his sincere effort to create a path for doing biblical theology. Certainly, it was just a modest beginning of a long process.

IWGDF guidance on the prevention of foot ulcers in at-risk patients with diabetes

Recommendations - 1 To identify a person with diabetes at risk for foot ulceration, examine the feet annually to seek evidence for signs or symptoms of peripheral neuropathy and peripheral artery disease. (GRADE strength of recommendation: strong; Quality of evidence: low) - 2 In a person with diabetes who has peripheral neuropathy, screen for a history of foot ulceration or lower-extremity amputation, peripheral artery disease, foot deformity, pre-ulcerative signs on the foot, poor foot hygiene and ill-fitting or inadequate footwear. (Strong; Low) - 3 Treat any pre-ulcerative sign on the foot of a patient with diabetes. This includes removing callus, protecting blisters and draining when necessary, treating ingrown or thickened toe nails, treating haemorrhage when necessary and prescribing antifungal treatment for fungal infections. (Strong; Low) - 4 To protect their feet, instruct an at-risk patient with diabetes not to walk barefoot, in socks only, or in thin-soled standard slippers, whether at home or when outside. (Strong; Low) - 5 Instruct an at-risk patient with diabetes to daily inspect their feet and the inside of their shoes, daily wash their feet (with careful drying particularly between the toes), avoid using chemical agents or plasters to remove callus or corns, use emollients to lubricate dry skin and cut toe nails straight across. (Weak; Low) - 6 Instruct an at-risk patient with diabetes to wear properly fitting footwear to prevent a first foot ulcer, either plantar or non-plantar, or a recurrent non-plantar foot ulcer. When a foot deformity or a pre-ulcerative sign is present, consider prescribing therapeutic shoes, custom-made insoles or toe orthosis. (Strong; Low) - 7 To prevent a recurrent plantar foot ulcer in an at-risk patient with diabetes, prescribe therapeutic footwear that has a demonstrated plantar pressure-relieving effect during walking (i.e. 30% relief compared with plantar pressure in standard of care therapeutic footwear) and encourage the patient to wear this footwear. (Strong; Moderate) - 8 To prevent a first foot ulcer in an at-risk patient with diabetes, provide education aimed at improving foot care knowledge and behaviour, as well as encouraging the patient to adhere to this foot care advice. (Weak; Low) - 9 To prevent a recurrent foot ulcer in an at-risk patient with diabetes, provide integrated foot care, which includes professional foot treatment, adequate footwear and education. This should be repeated or re-evaluated once every 1 to 3 months as necessary. (Strong; Low) - 10 Instruct a high-risk patient with diabetes to monitor foot skin temperature at home to prevent a first or recurrent plantar foot ulcer. This aims at identifying the early signs of inflammation, followed by action taken by the patient and care provider to resolve the cause of inflammation. (Weak; Moderate) - 11 Consider digital flexor tenotomy to prevent a toe ulcer when conservative treatment fails in a high-risk patient with diabetes, hammertoes and either a pre-ulcerative sign or an ulcer on the distal toe. (Weak; Low) - 12 Consider Achilles tendon lengthening, joint arthroplasty, single or pan metatarsal head resection, or osteotomy to prevent a recurrent foot ulcer when conservative treatment fails in a high-risk patient with diabetes and a plantar forefoot ulcer. (Weak; Low) - 13 Do not use a nerve decompression procedure in an effort to prevent a foot ulcer in an at-risk patient with diabetes, in preference to accepted standards of good quality care. (Weak; Low)

Pyhä Teresa ja keskiajan mystiikan teoriat

In my dissertation I have studied St Teresa (1515-1582) in the light of medieval mystical theories. I have two main levels in my research: historical and theological. On the historical level I study St Teresa s personal history in the context of her family and the Spanish society. On the theological level I study both St Teresa s mysticism and her religious experience in the light of medieval mysticism. St Teresa wrote a book called Life , which is her narrative autobiography and story about her mystical spiritual formation. She reflected herself through biblical texts interpreting them in the course of the biblical hermeneutics like allegory, typology, tropology and anagogy. In addition to that she read others life stories from her period of time, but reflected herself only slightly through the sociological point of view. She used irony as a means to gain acceptance to her authority and motive to write. Her position has been described as a double bind because of writing at the request of educated men and to the non-educated women as she herself was uneducated. She used irony as a means to achieve valuation to women, to gain negative attributes connected to them and to gain authority to teach them mystical spirituality, the Bible and prayer. In this ironic tendency she was a feminist writer. In order to understand medieval mysticism I have written in the first chapter a review of the main trends in medieval mysticism in connection with the classical emotional theories. Two medieval mystical theories show an important role in St Teresa s mysticism. One is love mysticism and the other is the three partite way of mysticism (purification, illumination and union). The classic-philosophical emotional theories play a role in both patterns. The theory of love mysticism St Teresa interpreted in the traditional way stressing the spiritual meaning of love in connexion with God and neighbors. Love is an emotion, which is bound with other emotions, but all objects of love don t strengthen spiritual love. In the three partite way of mysticism purification means to find biblical values in life and to practice meditative self-knowledge theologically interpreted. In illumination human understanding has to be illuminated by God and united to mystical knowledge from God. St Teresa considered illumination a way to learn things. Illumination has also psychological aspects like recognition of many trials and pains, which come from life on earth. Theologically interpreted in illumination one should die to oneself, let oneself be transformed and renewed by God. I have also written a review of the modern philosophical discussion on personal identity where memory and mental experiences are important creators of personal identity. St Teresa bound medieval mystical teaching together with her personal religious experience. Her personal identity is by its character based on her narrative life story where mental experiences play important role. Previous researchers have labelled St Teresa as an ecstatic person whose experiences produced ecstatic phenomena to the mysticism. These phenomena combined with visions have in one respect made of her a person who has brought physical and visionary tendencies to theology. In spite of that she also represents a modern tendency trying to give words to experiences, which at first seem to be exceptional and extreme and which are easily interpreted as one-sided either physical or sexual or unsaid. In other respect I have stressed the personality of St Teresa that was represented as both strong and weak. The strong personality for her is demonstrated by religious faith and in its practice. The weak personality was for her a natural personal identity. St Teresa saw a unifying aspect in almost all. Firstly, her mysticism was aimed towards union with God and secondly, the unifying aspects and common rules in human relations in community life were central. Union with God is based on the fact that in a soul God is living in its centre, where God is present in the Trinitarian way. The picture of God in ourselves is a mirror but to get to know God better is to recognize his/her presence in us. When the soul recognizes itself as a dwelling place of God, it knows itself as God knows him/herself. There is equality between God and the soul. To be a Christian means to participate in God in his Trinitarian being. The participation to God is a process of divinization that puts a person into transformation, change and renewal. The unitive aspect concludes also knowledge of opposites between experience of community and solitude as well as community and separateness. As a founder of monasteries St Teresa practiced theology of poverty. She renewed the monastic life founding a rule called discalced that stressed ascetic tendencies. Supporters of her work were after the difficulties in the beginning both society and churchly leaders. She wrote about the monasteries including in her description at times seriousness at times humor and irony. Her stories are said to be picaresque histories that contain stories of ordinary laymen and many unexpected occasions. She exercised a kind of Bakhtinian dialogue in her letters. St Teresa stressed the virtues like sacrifice, determination and courage in the monastic life. Most of what she taught of virtues is based on biblical spirituality but there are also psychological tendencies in her writings. The theological pedagogical advice is mixed with psychology, but she herself made no distinction between different aspects in her teaching. To understand St Teresa and her mysticism is to recognize that she mixes her personal religious experience and mysticism, which widens mysticism to religious experience in a new way, although this corresponds also the very definition of mysticism. St Teresa concentrated on mental-spiritual experiences and the aim of her mystical teaching was to produce a human mind well cured like a garden that has God as its gardener.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.