Variable Eddy Viscosity Research Articles

A model of the low-level jet with variable eddy viscosity

A model of the low-level jet with variable eddy viscosity

A model of the low-level jet with variable eddy viscosity

The model of the low-level jet over sloping terrain formulated by Holton (1967) is extended to assess the effects of the diurnal variation of eddy viscosity and of higher harmonics of the thermal driving mechanism. A perturbation expansion leads to analytic solutions which are compared to observations in the south central United States. It is suggested that numerical integration of the fully nonlinear equations is necessary to simulate the virtually simultaneous development of the jet throughout the depth of the planetary boundary layer. DOI: 10.1111/j.2153-3490.1974.tb01633.x

Eddy Viscosity Calculation Along the Chemical Rocket Thrust Chamber Wall Using Turbulent Kinetic Energy

Abstract With introduction of the turbulent kinetic energy equation for the Reynolds stress term, the characteristics of compressible turbulent boundary layers along the wall of a rocket thrust chamber are theoretically solved. This inclusion of the turbulent kinetic energy equation provides the character of chemically reactive flow with mass injection and can exhibit the past history of boundary layers. Results show the variation of eddy viscosity in flow direction including the laminarization tendency in the nozzle convergent section. The results appears to be in good agreement with available experimental data. The eddy viscosity decreases significantly in the reactive hydrogen-oxygen boundary layer when a small amount of hydrogen is injected from the wall.

A Model for Investigating Eddy Viscosity Effects on Mesoscale Cellular Convection

Abstract A mathematical model consisting of a complete set of the Boussinesq equations governing Rayleigh convection in the atmosphere has been solved for the marginal stability case in order to study the geometry and circulation patterns of mesoscale cellular convection. The significant new feature of the model is the inclusion of eddy viscosity variation with height through the convecting layer. Results obtained show that the direction of convection circulations are controlled by the sign of the vertical gradient of eddy viscosity. It is also concluded that variable convective depth has a significant but small effect on the geometry of the convection, with the degree of cell flatness being principally controlled by the degree of anisotropy. Using an assumed periodic form of the perturbation solutions, the problem reduced to solving a sixth-order differential stability equation with variable coefficients and accompanying boundary conditions. By applying the two-variable, small-perturbation technique, the...

Numerical simulation of turbulent flows

Numerical simulation of turbulent flow is of practical importance in geophysics and is useful as a test of turbulence theory. From a basic scale analysis of turbulent flow it is shown that complete simulation is only practicable for two‐dimensional or marginally turbulent three‐dimensional flows. Some examples of such simulations are described. A more useful approach for practical applications is to directly simulate the larger scales of motion and only consider the small unresolved scales with respect to their gross statistical interactions with the larger scales. A variable eddy viscosity model has proved useful for this purpose, although better approximations can be devised. Methods of discretization and numerical integration are discussed, and it is proposed that Galerkin methods are preferred when feasible in order to avoid truncation and aliasing errors.

DIURNAL VARIATIONS IN BOUNDARY LAYER WINDS OVER THE SOUTH-CENTRAL UNITED STATES IN SUMMER

Abstract Analysis of 1 week's data in August 1960 shows significant diurnal variations in surface geostrophic wind over the south-central United States. The oscillation in the southerly component (Vg) is driven by the response of the thermal wind to the diurnal temperature cycle over sloping terrain. A smaller oscillation in Ug derives from spatial variations in the amplitude of the diurnal pressure wave. The amplitude of the oscillation in Vg is about 3 to 5 m sec–1 at the surface, decaying exponentially with height to near 0 at 2 km. Examination of 11 yr of summertime rawinsonde data at Fort Worth, Tex., shows a very regular diurnal variation in boundary layer wind with maximum amplitude of about 3 m sec–1 at 600 m above the ground. This oscillation is forced by periodic variations in both eddy viscosity and geostrophic wind. Using a simplified model of the boundary layer, we obtain solutions for the diurnally periodic wind resulting from “reasonable” variations in eddy viscosity and “observed” variatio...

Combined Forced and Free Turbulent Convection in a Vertical Circular Tube With Volume Heat Sources and Constant Wall Heat Addition

Abstract A study is made of turbulent heat transfer in a vertical circular tube under conditions of combined forced and free convection with uniform heat flux at the wall and volume heat sources. The basic conservation laws are reduced to three coupled, linear integrodifferential equations which are numerically solved by means of a digital computer. An improved expression for eddy viscosity variation with radial distance and degree of turbulence is used in the solution, as is an expression for the ratio of eddy diffusivity of heat to momentum. The parameters in the integrodifferential equations are: Prandtl number, Pr; Rayleigh number, Ra; friction Reynolds number, Re*; and a volume heat source parameter, F. For fixed values of these parameters, the solution results in: the velocity and temperature profiles; the pressure drop parameter, C; mixed-mean-to-wall temperature difference, φm; Nusselt number, Nu; and Reynolds number, Re. The solutions to this fairly general problem compare very closely to solutions of the following special cases (with no volume heat source): pure forced convection, laminar flow; pure forced convection, turbulent flow; and combined forced and free-convection, laminar flow.

Tidal Flow and Mass Transport in a Slowly Converging Estuary

Summary A variable eddy viscosity technique is used to investigate the structure of the semi-diurnal tidal flow in the Humber Estuary. The associated current system is determined theoretically along the river as far as Saltend and compared with observations made in the mid-channel. The tidal solution is then used to estimate the distribution of tidal induced mass transport above the bed of the river. The calculations indicate that there is a convergence of mid-channel mass transport off Grimsby. It is suggested that this mechanism is that primarily responsible for the development of the ‘middle shoal’ in the neighbourhood of Grimsby.

The Ekman Spiral for a Linearly Varying Eddy Viscosity

The Ekman Spiral for a Linearly Varying Eddy Viscosity

The variation of Eddy viscosity with wind velocity and season

The variation of Eddy viscosity with wind velocity and season