Effect of wall friction on oscillation of velocity at the head of the gravity current

Velocity oscillations at the head of the gravity current were investigated in experiments and numerical simulations of a locked-exchange flow.A comparison of the experimental and numerical simulations showed that the depth and volume of the released fluid affected the oscillations in the velocity of the gravity current.At the initial stage,the head moved forward at a constant velocity,and velocity oscillations occurred.The head maximum thickness increased at the same time as the head,which did not have a round,and accumulated buoyant fluid due to the buoyancy effect intrusion force.The period of accumulation and release of the buoyant fluid was almost the same as that observed for the head movement velocity;the head movement velocity was faster when the buoyant fluid accumulated and slower when it was released.At the viscous stage,the forward velocity decreased proportionally to the power of 1/2 of time,since the head was not disturbed from behind.As the mass concentration at the head decreased,the gravity current was slowed by the viscous stage in its effect.At the viscous stage,the mass concentration at the head was no longer present,and the velocity oscillations also decreased.

Capturing the baroclinic effect in non-Boussinesq gravity currents

Direct numerical simulations of two-dimensional gravity currents with small and medium density variations are performed using different non-Boussinesq buoyancy approximations. Taking the full low-Machnumber approximation as the reference, the accuracy of several buoyancy terms are examined. It is found that all considered buoyancy terms performed well in the cases with small density variation. In the cases with medium density variation, the classical gravitational Boussinesq’s buoyancy term showed the lack of accuracy, and a simple correction did not make any improvement. In contrast, the recently introduced second-order buoyancy term showed a significantly higher accuracy. The present results and our previous derivations indicate that simple algebraic buoyancy approximations extended from the Boussinesq’s gravitational buoyancy are unlikely to achieve an accuracy beyond first order. Instead, it seems necessary to solve at least one extra Poisson equation for buoyancy terms to capture the higher-order baroclinic effect. An approximate analysis is also provided to show the leading term of the non-Boussinesq effect corresponding to gravity.

Simulation of Gravity Currents Using VOF Model

By the Volume of Fluid (VOF) multiphase flow model two-dimensional gravity currents with three phases including air are numerically simulated in this article. The necessity of consideration of turbulence effect for high Reynolds numbers is demonstrated quantitatively by LES (the Large Eddy Simulation) turbulence model. The gravity currents are simulated for h not equal H as well as h = H, where h is the depth of the gravity current before the release and H is the depth of the intruded fluid. Uprising of swell occurs when a current flows horizontally into another lighter one for h not equal H. The problems under what condition the uprising of swell occurs and how long it takes are considered in this article. All the simulated results are in reasonable agreement with the experimental results available.

Turbulent Evolution and Energetics of Lock-Release Gravity Currents

Turbulence modeling by use of the renormalization group （RNG） κ-ε model for Reynolds-stress closure is carried out to reveal the evolution dynamics for lock release gravity currents with the so-called slumping, inviscid and viscous phases. Field evolution of the turbulent current is investigated, and time transition of global energy balance is presented between the terms of potential energy, averaged kinetic energy, turbulent kinetic energy, turbulent dissipation and viscous dissipation. It is well illustrated that turbulent dissipation and viscous force are respectively dominant in the inviscid and viscous phases, while inertia effect accounts for the slumping.

Numerical Solution of Lock-Release Gravity Current with Viscous Self-Similar Regime

Lock-release gravity currents with a viscous self-similar regime are simulated by use of the renormalization group (RNG) k-ε model for Reynolds-stress closure. Besides the turbulent regime with initially a slumping phase of a constant current front speed and later an inviscid self-similar phase of front speed decreasing as t -1/3 (where t is the time measured from release), the viscous self-similar regime is satisfactorily reproduced with front speed decreasing as t -4/5, consistent with well known experimental observations.

NUMERICAL SIMULATION OF TWO-PHASE GRAVITY CURRENTS OVER A POROUS SUBSTRATE

Based on shallow-water approximations the governing equations for twodimensional two-phase gravity currents over a porous substrate and some appropriate boundaryconditions were introduced. With on characteristic interpolations the numerical boundary conditionswere introduced and a series of exact solutions were constructed. Numerical a-nalysis were made byusing the two-step Lax scheme, second-order TVD scheme, third-order ENO scheme and fifth-order WE NOscheme combined with second- and third-order TVD-Runge-Kutta method is given. It is found that forpractice applications the second-order TVD scheme combined with the second-order TVD- Runge- Kuttamethod is an economical and suitable choice.

Research on Characteristics of Density Current Under the Action of Waves

In this paper, the characteristics of density current under the action of waves are described with the help of flume experiment and theoretical analysis. The study shows that turbid water under the action of the waves can present three types of motion, i. e. significant stratification, fragile stratification and strong mixing. The motion gf turbid;,ater presents significant stratification when (H/D)/root Delta rho/rho less than or equal to 4.5, generally this state is known as density current. The formulas of motion velocity, thickness, and discharge of density current moving on horizontal bottom are derived by use of basic equations such as momemtum equation, equation of energy conservation and continuity equation of fluid. The time-average velocity and the thickness of density current under the action of waves have a relationship with such parameters as relative density (Delta rho/rho), wave height (H), and water depth (D). When these parameters are determined, the time-average thickness and motion velocity of density current are also determined. The relative thickness of density current (D-t/D) decreases with the increase of Delta rho/rho and increases with the increase of H/D. On the other hand, the motion velocity of density current increases with the increase of Delta rho/rho and decreases with the increase of the relative thickness (D-t/D) of density current. It is shown that the calculated results are in agreement with those of the flume experiment.

Structure of Thunderstorm Gust Fronts with Topographic Effects

Surface meteorological observations, associated with gust fronts produced by thunderstorm outflows over Tehran, an area surrounded by mountains, have been analyzed. Distinctive features are sudden drop in air temperature, up to 10°C, sharp increase in wind speed, up to 30 m s?1, with wind shift, to northwesterly, pressure jump, up to 4 hPa, humidity increase, up to 40%, and rain after some 20 min. Gust fronts which often occur in spring time, have a typical thickness of about 1.5 km and produce vertical wind shear of the order of 10?2s?1. Although these features seem to be common for most of the events, their intensities differ from one event to another, indicating that the gust fronts may occur in different sizes and shapes. Apart from a dominant effect on the formation of the original thunderstorms, topography appears to break up the frontal structure of the gust fronts. The internal Rossby radius of deformation for these flows is small enough (～ 100 km) for rotational effects to be minor. A laboratory model of the gust front (gravity current) also shows that it initially has a distinctive head with a turbulent wake, and can be broken up by topography. It is shown that when the environment is stratified, turbulence due to lobes and clefts instabilities near the nose of the current is suppressed. When the ground is rough, these instabilities are highly amplified and the internal Froude number of the flow is reduced. The bottom slope in the presence of rough topography leads to the break up of the current head and produces a broad and highly non-uniform head, recognized in the density signals. Key words Frontal structure - Gravity current - Meteorological data - Outflows

Turbulence Modelling of A Lock-Release Oil Slick

The motion of a lock-release oil slick as an immiscible two-fluid gravity current is numerically studied by a finite dif ference algorithm based on the volume of fluid （VOF） method for the basic formulation and a rigid cover approximation for the open free surface. Detailed numerical simulation with careful model validation reveals the existence of turbulence and the adaptability of the renormalization group （RNG） k - ε model for the Reynolds-stress closure in the case of the oil slick. The time evolution and spatial distribution of the mean velocity, turbulence kinetic energy and turbulent viscosity are characterized. The mechanism for the transition from an initial gravity-inertial phase to a second gravity-vinous phase is shown to be the relaminarization effect of the initially highly turbulent slick. Compared well with known theoretical analyses and experimental observations, the turbulence modeling results in self-similar spreading laws in terms of the fact that the oil slick passes through the initial gravity-inertial phase with the front speed decreasing as t ^-1/3（where t is the time measured from lock release） and the second gravity-viscous phase with the front speed decreasing as t^-5/8.

Experimental study on the origin of lobe-cleft structures in a sand storm

Lobes and clefts are characteristic structures at the front of sand storms.In this paper,their original formation mechanism and geometric features are studied experimentally and theoretically.A rotatable lock-exchange tank is utilized to avoid the strong local disturbances existing in the conventional horizontal apparatus,and the original lobe size is selected as the dominant spanwise wavelength by a statistical method instead of the mean lobe size used in the literature.It is shown that at the initial formation stage,the measured lobe sizes for different tank geometries and density differences(or Atwood numbers)have a 1/3 scaling law with the Grashof number(Gr)as predicted by a Rayleigh-Taylor(RT)model,especially at moderate Gr range,and substantially depend on the diffusion effect represented by the Schmidt number.Furthermore,using turbulent Schmidt number and eddy viscosity for atmosphere in the RT model predicts large scale dominant lobes,whose sizes agree qualitatively with those observed in a real sand storm,revealing that the underlying control mechanism for these lobe and cleft structures is intrinsically related to the RT instability.