Maneuvering simulations of pusher-barge systems

Pusher-barge systems were studied in nine different configurations. Captive model tests were performed at the Hiroshima University Towing Tank and the hydrodynamic derivatives for the various configurations were obtained. At a service speed of 7 knots, pusher-barge systems with the same number of barges but arranged in a row (shorter length overall but with a larger breadth) require more power to operate than those that were arranged in a line. When the length overall increased, the tactical diameter, advance, and transfer distances also increased, mainly due to the significant increase in the moment of inertia when barges are arranged in a line, rather than in a row. All pusher-barge systems had small first and second overshoot angles. Pusher-barge systems with the same number of barges had a longer response time to the rudder angle of attack and required a longer stopping distance when arranged in a line, mainly due to the increased moment of inertia and reduced resistance when barges are arranged in this way.     

A simple formulation for predicting the ultimate strength of ships

The aim of this study is to derive a simple analytical formula for predicting the ultimate collapse strength of a single- and double-hull ship under a vertical bending moment, and also to characterize the accuracy and applicability for earlier approximate formulations. It is known that a ship hull will reach the overall collapse state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and the tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical equation for calculating the hull ultimate strength is obtained. A comparison between the derived formula and existing expressions is made for largescale box girder models, a one-third-scale frigate hull model, and full-scale ship hulls.List of symbols A _B total sectional area of outer bottom - A _B total sectional area of inner bottom - A _D total sectional area of deck - A _S half-sectional area of all sides (including longitudinal bulkheads and inner sides) - a _s sectional area of a longitudinal stiffener with effective plating - b breadth of plate between longitudinal stiffeners - D hull depth - D _B height of double bottom - E Young's modulus - g neutral axis position above the base line in the sagging condition or below the deck in the hogging condition - H depth of hull section in linear elastic state - I _s moment of inertia of a longitudinal stiffener with effective plating - l length of a longitudinal stiffener between transverse beams - M _E elastic bending moment - M _p fully plastic bending moment of hull section - M _u ultimate bending moment capacity of hull section - M _uh ,M _us ultimate bending moment in hogging or sagging conditions - r radius of gyration of a longitudinal stiffener with effective plating [=(I _s /a _s )^1/2] - t plate thickness - Z elastic section modulus at the compression flange - Z _B ,Z _D elastic section modulus at bottom or deck - slenderness ratio of plate between stiffeners [= (b/t)(_y/E)^1/2] - slenderness ratio of a longitudinal stiffener with effective plating [=(l/r)(_y/E)^1/2] - _y yield strength of the material - _yB , _yB , _yD yield strength of outer bottom, inner bottom - _yS deck, or side - _u ultimate buckling strength of the compression flange - _uB , _uB , _uD ultimate buckling strength of outer bottom - _uS inner bottom, deck, or side     

On the numerical accuracy of the prediction of resistance coefficients in ship stern flow calculations

This article presents a study on the accuracy of the numerical determination of the friction and pressure resistance coefficients of ship hulls. The investigation was carried out for the KVLCC2 tanker at model- and full-scale Reynolds numbers. Gravity waves were neglected, i.e., we adopted the so-called double-model flow. Single-block grids with H–O topology were adopted for all the calculations. Three eddy viscosity models were employed: the one-equation eddy viscosity and the two-equation models proposed by Menter and the TNT version of the two-equation k-ω model. Verification exercises were performed in sets of nearly geometrically similar grids with different densities in the streamwise, normal, and girthwise directions. The friction and pressure resistance coefficients were calculated for different levels of the iterative error and for computational domains of different size. The results show that on the level of grid refinement used, it is possible to calculate the viscous resistance coefficients in H–O grids that do not match the ship contour with a numerical uncertainty of less than 1%. The differences between the predictions of different turbulence models were larger than the numerical uncertainty; however, these differences tended to decrease with increases in the Reynolds number. The pressure resistance was remarkably sensitive to domain size and far-field boundary conditions. Either a large domain or the application of a viscous–inviscid interaction procedure is needed for reliable results. This work was presented in part at the International Conference on Computational Methods in Marine Engineering—MARINE 2007, Barcelona, June 3–4, 2007.     

Vibration reduction of main hulls using semiactive absorbers

A semiactive-type absorber for vibration reduction of main hull girders was investigated. The semiactive absorber system includes a moving mass, support springs, dynamic dampers, and a control system. Only a small electrical power supply is needed for control of the damper valve and the operation of the control system. In this paper, the dynamics of the ship's hull and the constraints of the semiactive absorber are described first. Then, a suboptimal operation law is derived based on the properties of the absorber and the theory of optimal vibration reduction. The numerical simulation results show that the semiactive absorber is more efficient in hull vibration reduction than the passive absorber during critical periodical excitation from the propeller. The vibration caused by multifrequency excitation can also be suppressed by the semiactive absorber. In terms of effectiveness, the semiactive absorber is almost as effective as the active absorber. In particular, the performance of the semiactive absorber is excellent in the reduction of high-frequency fluctuations.List of symbols C _h ⁽ⁱ⁾ damping matrices of the segmenti - C _sb structural damping coefficient of bending - C _ss structural damping coefficient of shear - C _v hydrodynamic damping coefficient - EI flexural rigidity - f _a force generated by the absorber - f _ad damper force of the semiactive absorber - f _ext total excitation force - F _ext ⁽ⁱ⁾ generalized load vector in segmenti - teÎ the identity matrix - J performance index - J _r rotatory moment of inertia - k _a stiffness coefficient of the absorber - K _h ⁽ⁱ⁾ stiffnes matrices of the segmenti - K _s A _s G _s shear rigidity - k _v hydrodynamic spring coefficient - l _k length of the segmentk - m _a mass of the absorber - M _ext total exciting moment - M _h ⁽ⁱ⁾ mass matrices of the segmenti - m _v mass moment of inertia - w _h deflection of the center line of the hull - W _h ⁽ⁱ⁾ vertical translation and shear slope of nodes in segmenti - ¯ w _d displacement of the absorber mass relative to the hull - ¯ w _a absolute displacement of the absorber mass - ¯ w (a, t) absolute upward displacement of the hull atx=a - slope deflection due to bending - slope deflection due to shear - Dirac delta function - _k ⁽ⁱ⁾ Kronecker delta function - _k distribution function - shape function vector     

Groups in DEA based cross-evaluation: An application to Asian container ports

In container port performance evaluation, a group of ports in one country is always significantly different from a group of ports in another country. This is noticed as the heterogeneity of port performance. It is therefore necessary to further investigate the impact of the different groups on efficiency evaluation of ports. The cross-evaluation method is a DEA extension tool to identify best performing DMUs and to rank DMUs using cross efficiency scores linked to all DMUs. A factor that possibly reduces the usefulness of the cross efficiency evaluation method is that cross efficiency scores may not be unique due to the presence of alternative optima. Doyle and Green 1 Doyle, J and Green, R. 1994. Efficiency and cross efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45: 567–578. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] propose the use of secondary goals to deal with the non-uniqueness issue by the aggressive/benevolent model formulations. This article extends the model of Doyle and Green by considering the groups of DMUs in the determination of final cross efficiency. A new approach based on cross efficiency evaluation method is developed and applied to efficiency analysis of 28 container ports from 12 countries in Asia. A comparative study between traditional and newly proposed methods is conducted.     

Simple Lagrangian formulation of bubbly flow in a turbulent boundary layer (bubbly boundary layer flow)

For the theoretical consideration of a system for reducing skin friction, a mathematical model was derived to represent, in a two-phase field, the effect on skin friction of the injection of micro air bubbles into the turbulent boundary layer of a liquid stream. Based on the Lagrangian method, the equation of motion governing a single bubble was derived. The random motion of bubbles in a field initially devoid of bubbles was then traced in three dimensions to estimate void fraction distributions across sections of the flow channel, and to determine local bubble behavior. The liquid phase was modeled on the principle of mixing length. Assuming that the force exerted on the liquid phase was equal to the fluid drag generated by bubble slip, an equation was derived to express the reduction in turbulent shear stress. Corroborating experimental data were obtained from tests using a cavitation tunnel equipped with a slit in the ceiling from which bubbly water was injected. The measurement data provided qualitative substantiation of the trend shown by the calculated results with regard to the skin friction ratio between cases with and without bubble injection as function of the distance downstream from the point of bubble injection.List of symbols B law of wall constant - C _f local coefficient of skin friction - C _f0 local coefficient of skin friction in the absence of bubbles - d _b bubble diameter [m] - g acceleration of gravity [m/s²] - k ₁ k₄ proportional coefficient - k _L turbulent energy of the liquid phase [m²/s²] - L representative length [m] - l _b mean free path of a bubble [m] - m _A added mass of a single bubble [kg] - m _b mass of a single bubble [kg] - N _x ,N _y ,N _z force perpendicular to the wall or ceiling exerted on a bubble adhering to that wall or ceiling [N] - P absolute pressure [Pa] - Q _G rate of air supply [/min] - q _L ⁽ⁱ⁾ turbulent velocity at the ith time increment [m/s] - R> _ex Reynolds number defined by Eq. 32 - T _*L integral time scale of the liquid phase [s] - U velocity of the main stream [m/s] - ,¯v,¯w time-averaged velocity components [m/s] - u,v,w turbulent velocity components [m/s] - û _L ,v_L root mean square values of liquid phase turbulence components in thex- and y-directions [m/s] - V volume of a single bubble [m³] - X,Y,Z components of bubble displacement [m] - x _s ,y _s ,z _s coordinate of a random point on a sphere of unit diameter centered at the coordinate origin - root mean square of bubble displacement in they-direction in reference to the turbulent liquid phase velocity [m] - local void fraction - _m mean void fraction in a turbulent region - regular random number - R _v increment of the horizontal component of the force acting on a single bubble, defined by Eq. 22 [N] - t time increment [s] - ₁ reduction of turbulent stress [N/m²] - _L rate of liquid energy dissipation [m²/s³] - _m coefficient defined by Eq. 30 - law of wall constant in the turbulent region in absence of bubbles - ₁ law of wall constant in the turbulent region in presence of bubbles     

Barriers to progress or windows of opportunity? A study in career path mapping in the maritime industries

The objective of the study was to provide, through a series of interviews with key personnel from a range of European Member States, an overview of the following:

At-sea towing of a Mega-Float unit

A huge floating offshore platform (359m long, 60m wide, and 3m deep) was towed into the Pacific Ocean for a validation experiment for a floating airport. Full-scale measurements of towline tension and the bending strain on the upper-deck were made during towing. The measured bending moment agreed well with numerical calculation without taking the draught and towing speed into consideration.     

Strip method for a laterally drifting ship in waves

Lateral drift occurs due to the effects of wind forces, wave drifting forces, or both on ships sailing in actual seas. It is important therefore to investigate the influence of lateral drift on seakeeping performance for improved ship operation. The velocity potential was expanded as an asymptotic power series in terms of the lateral speed parameter, τ, defined as ω _e V ₀/g, where ω _e is the frequency of wave encounter; V ₀ denotes the lateral velocity, which is assumed to be sufficiently small; and g is the acceleration due to gravity. By combining this technique with the strip method, two sets of motion equations of all the hydrodynamic force coefficients for ship seakeeping were derived. The first set is for ships without lateral drift and is the same as the equations in the new strip method, and the second set is for the additional motions induced by lateral drift. It was found that all ship motion modes except surge are coupled when a ship drifts laterally in waves.     

The numerical friction line

This paper presents a study on the numerical calculation of the friction resistance coefficient of an infinitely thin plate as a function of the Reynolds number. Seven eddy-viscosity models have been selected: the one-equation turbulence models of Menter and Spalart–Allmaras; the k-ω two-equation model proposed by Wilcox and its TNT, BSL and SST variants and the two-equation model. The flow has been computed at 14 Reynolds numbers in sets of seven geometrically similar Cartesian grids to allow a reliable estimation of the numerical uncertainty. The effect of the computational domain size has been reduced to negligible levels (below the numerical uncertainty). And the same holds for the iterative and round-off errors. In the finest grids of each set, the numerical uncertainty of the friction resistance coefficient is always below 1%. Special attention has further been given to the solution behaviour in the laminar-to-turbulent transition region. Curve fits have been applied to the data obtained at the 14 Reynolds numbers and the numerical friction lines are compared with four proposals from the open literature: the 1957 ITTC line, the Schoenherr line and the lines suggested by Grigson and Katsui et al. The differences between the numerical friction lines obtained with the seven turbulence models are smaller than the differences between the four lines proposed in the open literature.     

A dense water outflow from the Ross Sea, Antarctica: Mixing and the contribution of tides

We use hydrographic, current, and microstructure measurements, and tide-forced ocean models, to estimate benthic and interfacial mixing impacting the evolution of a bottom-trapped outflow of dense shelf water from the Drygalski Trough in the northwestern Ross Sea. During summer 2003 an energetic outflow was observed from the outer shelf ( 500 m isobath) to the  1600 m isobath on the continental slope. Outflow thickness was as great as  200 m, and mean speeds were  0.6 m s^− 1 relative to background currents exceeding  1 m s^− 1 that were primarily tidal in origin. No outflow was detected on the slope in winter 2004, although a thin layer of dense shelf water was present on the outer shelf. When the outflow was well-developed, the estimated benthic stress was of order one Pascal and the bulk Froude number over the upper slope exceeded one. Diapycnal scalar diffusivity (K_z) values in the transition region at the top of the outflow, estimated from Thorpe-scale analysis of potential density and measurements of microscale temperature gradient from sensors attached to the CTD rosette, were of order 10^− 3−10^− 2 m² s^− 1. For two cases where the upper outflow boundary was particularly sharply defined, entrainment rate w_e was estimated from K_z and bulk outflow parameters to be  10^− 3 m s^− 1 ( 100 m day^− 1). A tide-forced, three-dimensional primitive equation ocean model with Mellor-Yamada level 2.5 turbulence closure scheme for diapycnal mixing yields results consistent with a significant tidal role in mixing associated with benthic stress and shear within the stratified ocean interior.     

Robust aspects in dependable filter design for alignment of a submarine inertial navigation system

The strapdown inertial navigation system (SINS) is able to provide continuous estimates of a vehicle??s velocity, position and attitude. As a rule, the SIMS component known as a high accuracy strapdown inertial measurement unit (SIMU) is an exceptionally expensive system. Less expensive SIMUs comprised of low cost sensors suffer from degraded performance, but this can be compensated for, in part, by addition of a velocity data recorder (VDR) to accompany the SINS. In this configuration, the need frequently arises to align the SINS of a submarine to in order to avoid a long run-up of the inertial system before a start command is issued. This in-motion alignment (IMA) can be accomplished by integrating SINS data with some external aiding source, such as the VDR, by using some form of measurement matching method. Accordingly, this paper demonstrates a consistent IMA scheme for a low-cost SIMU using a robust Kalman/ $ H_{\infty } $ filter structure. An error model of the SINS is derived in which the state vector includes attitude, velocity, position and sensor errors. Velocity information from the VDR is used as a measurement to the proposed filter. All significant equations concerning navigation are presented in conjunction with argument. Results show the advantages of the approach and emphasize diverse aspects of the SINS.     

Distribution of void fraction in bubbly flow through a horizontal channel: Bubbly boundary layer flow, 2nd report

A method of enveloping the hull with a sheet of microbubbles is discussed. It forms part of a study on means of reducing the skin friction acting on a ship's hull. In this report, a bubble traveling through a horizontal channel is regarded as a diffusive particle. Based on this assumption, an equation based on flow flux balance is derived for determining the void fraction in approximation. The equation thus derived is used for calculation, and the calculation results are compared with reported experimental data. The equation is further manipulated to make it compatible with a mixing length model that takes into account the presence of bubbles in the liquid stream. Among the factors contained in the equation thus derived, those affected by the presence of bubbles are the change of mixing length and the difference in the ratio of skin friction between cases with and without bubbles. These factors can be calculated using the mean void fraction in the boundary layer determined by the rate of air supply into the flow field. It is suggested that the ratio between boundary layer thickness and bubble diameter could constitute a significant parameter to replace the scale effect in estimating values applicable to actual ships from corresponding data obtained in model experiments.List of symbols a ₁ proportionality constant indicating directionality of turbulence - B law-of-the-wall constant - C _f local skin-friction coefficient in the presence of bubbles - C _f0 local skin-friction coefficient in the absence of bubbles - d _b bubble diameter (m) - g acceleration of gravity (m/s²) - j _g flow flux of gas phase accountable to buoyancy (m/s) - j _t flow flux of gas phase accountable to turbulence (m/s) - k ₄ constant relating reduction of liquid shear stress by bubble presence to decrease of force imparted to bubble by its displacement due to turbulence - l _b mixing length of gas phase (m) - l _m mixing length of liquid phase (m) - l _mb diminution of liquid phase mixing length by bubble presence (m) - Q _G rate of air supply to liquid stream (l/min) - q _/g velocity of bubble rise (m/s) - 2R height of horizontal channel (m) - T _* integral time scale (s) - U _m mean stream velocity in channel (m/s) - U friction velocity in channel (m/s) - V volume of a bubble (m³) - u, ¯ v time-averaged stream velocities inx- andy-directions, respectively (m/s) - u, v turbulent velocity components inx- andy-directions, respectively (m/s) - v root mean square of turbulence component in they-direction (m/s) - root mean square of bubble displacement iny-direction with reference to turbulent liquid phase velocity (m) - y displacement from ceiling (m) - local void fraction - _m mean void fraction in boundary layer - _m constant relating local void fraction to law-of-the-wall constant - _t reduction of turbulent stress (N/m²) - law-of-the-wall constant in turbulent liquid region in absence of bubbles - ₁ law-of-the-wall constant in turbulent liquid region in presence of bubbles - ₂ law-of-the-wall constant in gas phase - _m constant indicating representative turbulence scale (m) - viscosity (Pa × s) - v kinematic viscosity (m²/s) - density (kg/m³) Suffixes G gas - L liquid - 0 absence of bubbles     

Surf-riding and oscillations of a ship in quartering waves

The behavior of a ship encountering large regular waves from astern at low frequency is the object of investigation, with a parallel study of surf-riding and periodic motion paterns. First, the theoretical analysis of surf-riding is extended from purely following to quartering seas. Steady-state continuation is used to identify all possible surf-riding states for one wavelength. Examination of stability indicates the existence of stable and unstable states and predicts a new type of oscillatory surf-riding. Global analysis is also applied to determine the areas of state space which lead to surf-riding for a given ship and wave conditions. In the case of overtaking waves, the large rudder-yaw-surge oscillations of the vessel are examined, showing the mechanism and conditions responsible for loss of controllability at certain vessel headings.List of symbols c wave celerity (m/s) - C(p) roll damping moment (Ntm) - g acceleration of gravity (m/s²) - GM metacentric height (m) - H wave height (m) - I _x ,I _z roll and yaw ship moments of inertia (kg m²) - k wave number (m^–1) - K _H ,K _W ,K _R hull reaction, wave, rudder, and propeller - K _p forces in the roll direction (Ntm) - m ship mass (kg) - n propeller rate of rotation (rpm) - N _H ,N _W ,N _R hull reaction, wave, rudder, and propeller - N _P moments in the yaw direction (Ntm) - p roll angular velocity (rad/s) - r rate-of-turn (rad/s) - R(,x) restoring moment (Ntm) - Res(u) ship resistance (Nt) - t time (s) - u surge velocity (m/s) - U vessel speed (m/s) - v sway velocity (m/s) - W ship weight (Nt) - x longitudinal position of the ship measured from the wave system (m) - x _G ,z _G longitudinal and vertical center of gravity (m) - x _S longitudinal position of a ship section (S), in the ship-fixed system (m) - X _H ,X _W ,X _R hull reaction, wave, rudder, and propeller - X _P forces in the surge direction (Nt) - y transverse position of the ship, measured from the wave system (m) - Y _H ,Y _W ,Y _R hull reaction, wave, rudder, and propeller - Y _p forces in the sway direction (Nt) - z _Y vertical position of the point of action of the lateral reaction force during turn (m) - z _W vertical position of the point of action of the lateral wave force (m) Greek symbols angle of drift (rad) - rudder angle (rad) - wavelength (m) - position of the ship in the earth-fixed system (m) - water density (kg/m³) - angle of heel (rad) - heading angle (rad) - _e frequency of encounter (rad/s) Hydrodynamic coefficients K roll added mass - N _v ,N _r yaw acceleration coefficients - N _v N _r N _rr N _rrv ,N _vvr yaw velocity coefficients K. Spyrou: Ship behavior in quartering waves - X _u surge acceleration coefficient - X _u X _vr surge velocity coefficients - Y _v ,Y _r sway acceleration coefficients - Y _v ,Y _r ,Y _vv ,Y _rr ,Y _vr sway velocity coefficients European Union-nominated Fellow of the Science and Technology Agency of Japan, Visiting Researcher, National Research Institute of Fisheries Engineering of Japan     

The Gulf Stream, rings and North Atlantic eddy structures from remote sensing (Altimeter and SeaWiFS)

Seasonal SeaWiFS chlorophyll a concentrations cycles and annual changes of altimeter Sea Level Anomaly are derived for the subtropical North Atlantic near  35°N and along a Gulf Stream axis. Spatial structure of SeaWiFS, is defined in terms of deviations from a local seasonal cycle and examined in relation to altimeter eddy structure. In the subtropical region near 35°N, SeaWiFS structure is evident during the spring bloom period with a scale of  430 km, or about twice the eddy scale. A Gulf Stream axis has been selected as a region where the Sea Level Anomaly variance is a maximum. Eddy propagation speeds and scales are examined. Cold-core (cyclonic) rings correspond to areas of high SeaWiFS chlorophyll a. Warm-core (anticyclonic) rings relate to areas of low chlorophyll concentration. Both SeaWiFS structure and eddy structure have a spatial scale of  450 km or twice the ring scale along the Gulf Stream axis. SeaWiFS chlorophyll anomalies and Altimeter Sea Level Anomaly structure have an overall negative correlation coefficient of r = − 0.34. Swirl currents between eddies redistribute surface chlorophyll concentrations and can spatially bias maximum and minimum concentration levels off eddy centre.     

A pseudofield model approach to simulate compartment-fire phenomena for marine fire safety design

In order to prevent the spread of marine compartment fires, it is necessary to understand the governing factors or characteristics of fire-spread phenomena. We present a pseudofield model approach to this problem. We first described a field model of turbulent heat convection based on a standard k – turbulence model. Two-dimensional numerical simulations of a two-linked compartment fire were carried out in order to predict the turbulent convection flow induced by the heat released from the fire. Then a more complicated fire-spread problem of multilinked compartment fires was analyzed by means of a zone model, in which the amounts of oxygen consumption and gas generation were solved by a gas-balance equations system. The effect of threshold conditions on fire propagation and the effect of the thickness of the heat insulation were investigated with numerical simulations.     

The distribution of the benefits of waterfront reform

In this paper we introduce, for the first time, a methodology from the most recent literature of finance to reveal the duration of shipping cycles and then show the benefit of the use of this information to make more successful shipping loans. This is so as banks are willing to finance, during boom periods, shipping loans for new buildings but by this way ‘create’ oversupply and thus depress the freight market by their own actions. The information about cycles, especially their forecasting, is mostly important as shipping loans are based on project financing/cash flow financing, which means that ship revenue is of utmost importance. The Rescaled Range Analysis is applied here to 379 monthly freight trips—made stationary—between 1971 and 2002 (July), due to Hurst 1 Hurst, HE. 1950. Long-term storage capacity of reservoirs. April1950. pp.770–808. American Society of Civil Engineers. Paper No. 2447 [Google Scholar] and elaborated and popularized by Mandelbrot 2 Mandelbrot, BB. 1975. Stochastic models for the earth's relief, the shape and the fractal dimensions of the coastlines, and the number-area rule for islands. Proceedings of the National Academy of Sciences. 1975, USA 72. pp.3825–3828. [Crossref] , [Google Scholar]. The most important effect, however, is that shipping freight series exhibit non-normality and long-run dependence rendering the use of random walk models such as GARCH (Generalized Autoregressive Conditional Heteroscedasticity) problematic. Thus an adequate literature review is carried out with criticism against the models used. The cycles have been calculated as equal to 4.5 years and 2.25 years. This is almost compatible with the most recent paper of Stopford 3 Stopford, M. 21 September 2001. “Forecasting the dry bulk, tanker and container markets”. In Maritime Cyprus 21 September,  [Google Scholar]. The Hurst exponent was found equal to 0.93, alternating over the periods examined (0.65, 0.73, 0.62, 0.59 and 0.55) and indicating long-term persistence but seriously away from normal/random walk domain. Most studies have said the same using the Jarque--Bera test for normality but provided no alternative.