Ktisis Cyprus University of Technologyhttp://ktisis.cut.ac.cyThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 25 Mar 2019 17:14:10 GMT2019-03-25T17:14:10Z5071Isotropic turbulence in compact spacehttp://ktisis.cut.ac.cy/handle/10488/10538Title: Isotropic turbulence in compact space
Authors: Gravanis, Elias; Akylas, Evangelos
Abstract: Isotropic turbulence is typically studied numerically through direct numerical simulations (DNS). The DNS flows are described by the Navier-Stokes equation in a 'box', defined through periodic boundary conditions. Ideal isotropic turbulence lives in infinite space. The DNS flows live in a compact space and they are not isotropic in their large scales. Hence, the investigation of important phenomena of isotropic turbulence, such as anomalous scaling, through DNS is affected by large-scale effects in the currently available Reynolds numbers. In this work, we put isotropic turbulence - or better, the associated formal theory - in a 'box', by imposing periodicity at the level of the correlation functions. This is an attempt to offer a framework where one may investigate isotropic theories/models through the data of DNS in a manner as consistent with them as possible. We work at the lowest level of the hierarchy, which involves the two-point correlation functions and the Karman-Howarth equation. Periodicity immediately gives us the discrete wavenumber space of the theory. The wavenumbers start from 1.835, 2.896, 3.923, and progressively approach integer values, in an interesting correspondence with the DNS wavenumber shells. Unlike the Navier-Stokes equation, infinitely smooth periodicity is obstructed in this theory, a fact expressed by a sequence of relations obeyed by the normal modes of the Karman-Howarth equation at the endpoints of a unit period interval. Similar relations are imparted to the two-point functions under the condition that the energy spectrum and energy transfer function are realizable. Hence, these relations are necessary conditions for realizability in this theory. Naturally constructed closure schemes for the Karman-Howarth equation do not conform to such relations, thereby destroying realizability. A closure can be made to conform to a finite number of them by adding corrective terms, in a procedure that possesses certain analogies with the renormalization of quantum field theory. Perhaps the most important one is that we can let the spectrum be unphysical (through sign-changing oscillations of decreasing amplitude) for the infinitely large wavenumbers, as long as we can controllably extend the regime where the spectrum remains physical, deep enough in the dissipation subrange so as to be realistically adequate. Indeed, we show that one or two such 'regularity relations' are needed at most for comparisons of the predictions of the theory with the current resolution level results of the DNS. For the implementation of our arguments, we use a simple closure scheme previously proposed by Oberlack and Peters. The applicability of our ideas to more complex closures is also discussed.
Fri, 10 Mar 2017 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/105382017-03-10T00:00:00ZQuasi-steady flow in sloping aquifershttp://ktisis.cut.ac.cy/handle/10488/9239Title: Quasi-steady flow in sloping aquifers
Authors: Akylas, Evangelos; Gravanis, Elias; Koussis, Antonis D.
Abstract: Mass conservation links the storage S and the outflow Q of an aquifer. A relation between them (an S-Q relation) provides then a model governing the evolution of these quantities. In this work we construct an analytical quasi-steady state model which exploits the properties of the exact S-Q relation associated with steady state solutions of the Boussinesq equation for the sloping aquifer (that is, the Henderson and Wooding [1964] solutions). The model is derived by matching the asymptotic forms of the exact S-Q relation which arise for small and large values of the Henderson and Wooding parameter λ. These asymptotic forms provide a novel rederivation of well-known semiempirical S-Q relations of the form Q ∝ S and Q ∝ S2, and they lead to soluble quasi-steady state models. The quadratic asymptotic relation turns out to hold for surprisingly low values of λ. This characteristic and its formal properties allow smooth matching with the linear relation at λ=π2/4=2.47. The obtained model holds over the entire parameter space. An important characteristic of the model, stemming from its derivation, is that it involves only the geometric and hydraulic quantities present in the exact Boussinesq equation. The model is tested by best fitting four data sets from experiments simulating aquifer drainage. The derived curves for the drained volume are in excellent agreement with the data. The estimated values for k and n are also in overall very good agreement with their reference values.
Sun, 01 Nov 2015 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/92392015-11-01T00:00:00ZGeneralized Batchelor functions of isotropic turbulencehttp://ktisis.cut.ac.cy/handle/10488/9389Title: Generalized Batchelor functions of isotropic turbulence
Authors: Gravanis, Elias; Akylas, Evangelos
Abstract: We generalize Batchelor's parameterization of the autocorrelation functions
of isotropic turbulence in a form involving a product expansion with multiple
small scales. The richer small scale structure acquired this way, compared to
the usual Batchelor function, is necessary so that the associated energy
spectrum approximate well actual spectra in the universal equilibrium range. We
propose that the generalized function provides an approximation of arbitrary
accuracy for actual spectra of isotropic turbulence over the universal
equilibrium range. The degree of accuracy depends on the number of higher
moments which are determinable and it is reflected in the number of small
scales involved. The energy spectrum of the generalized function is derived,
and for the case of two small scales is compared with data from high-resolution
direct numerical simulations. We show that the compensated spectra (which
illustrate the bottleneck effect) and dissipation spectra are encapsulated
excellently, in accordance with our proposal.
Sun, 11 Jan 2015 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/93892015-01-11T00:00:00ZEarly-time solution of the horizontal unconfined aquifer in the buildup phasehttp://ktisis.cut.ac.cy/handle/10488/12598Title: Early-time solution of the horizontal unconfined aquifer in the buildup phase
Authors: Gravanis, Elias; Akylas, Evangelos
Abstract: We derive the early-time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.
Sun, 01 Oct 2017 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/125982017-10-01T00:00:00ZInfluence of spatial variability on rock slope reliability using 1-D random fieldshttp://ktisis.cut.ac.cy/handle/10488/4931Title: Influence of spatial variability on rock slope reliability using 1-D random fields
Authors: Pantelidis, Lysandros; Gravanis, Elias; Griffiths, D.V.
Abstract: In this work, the theory of random fields is used to account for the influence of spatial
variability on slope reliability. Within this framework the friction coefficient along a
discontinuity is treated as a Gaussian random field which is fully described by its mean value,
standard deviation and spatial correlation length. The random field is simulated using the
Local Average Subdivision (LAS) method. As shown by the examples presented herein, the
spatial correlation of shear strength along a failure plane can have an important influence on
slope performance, as expressed by the failure probability. This is a significant observation
since ignoring the influence of spatial correlation in design may lead to non-conservative
estimations of slope reliability. The planar mode of failure is considered.
Thu, 01 Jan 2015 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/49312015-01-01T00:00:00ZStationarity of linearly forced turbulence in finite domainshttp://ktisis.cut.ac.cy/handle/10488/7684Title: Stationarity of linearly forced turbulence in finite domains
Authors: Gravanis, Elias; Akylas, Evangelos
Abstract: A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the "linear forcing," which amounts to a force term that is linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence toward a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS, the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to rewrite the problem as one of decaying turbulence with a decreasing viscosity. Its late-time behavior can then be studied by scaling symmetry considerations. The evolution of the system in the description of "decaying" turbulence can be understood as the gradual symmetry breaking of a larger approximate symmetry to a smaller symmetry that is exact at late times. The latter symmetry implies a stationary state: In the original description all correlators are constant in time, while, in the "decaying" turbulence description, that state possesses constant Reynolds number and integral length scale. The finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times: In linear forcing there is no other large scale than the domain size, therefore, it is the only scale available to set the magnitude of the necessarily constant integral length scale in the stationary state. A high degree of local isotropy is implied by the late-time exact symmetry, the symmetries of the domain itself, and the solenoidal nature of the velocity field. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy that is necessarily broken at the large scale by the finiteness of the domain. Indeed, to strengthen this conclusion somewhat, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view. Simultaneously, the naturalness of the Taylor microscale as a self-similarity scale in this system is emphasized. In this context the stationary state emerges as a stable fixed point. We also note that self-preservation seems to be the reason behind a noted similarity of the third-order structure function between the linearly forced and freely decaying turbulence, where, again, the finiteness of the domain plays a significant role.
Sat, 01 Jan 2011 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/76842011-01-01T00:00:00ZAn analytical solution in probabilistic rock slope stability assessment based on random fieldshttp://ktisis.cut.ac.cy/handle/10488/4918Title: An analytical solution in probabilistic rock slope stability assessment based on random fields
Authors: Gravanis, Elias; Pantelidis, Lysandros; Griffiths, D. V.
Abstract: An analytical solution for calculating the probability of failure of rock slopes against planar sliding is proposed. The method in based on the theory of random fields accounting for the influence of spatial variability on slope reliability. In this framework, both the cohesion and friction coefficient along a discontinuity are treated as Gaussian random fields which are fully described by their mean values View the MathML source, standard deviations View the MathML source, spatial correlation lengths View the MathML source, and the parameters View the MathML source which account for the cross-correlation between cohesion and coefficient of friction. As shown by the examples presented herein, the spatial correlation of shear strength can have an important influence on slope performance expressed by the probability of failure. This is a significant observation, since ignoring the influence of spatial correlation in design may lead to unconservative estimations of slope reliability.
Wed, 01 Oct 2014 00:00:00 GMThttp://ktisis.cut.ac.cy/handle/10488/49182014-10-01T00:00:00Z