Numerical simulation of the interaction of the disturbed boundary layer with an incident shock

Interaction of the disturbed supersonic boundary layer with an incident oblique shock wave is studied numerically with eddy-resolving numerical simulations. Eigenmodes of the linear stability theory are used to generate the inflow boundary layer disturbances. The evolution of unstable boundary-layer disturbances, effects of the incident shock on the disturbances, effects of the disturbances on the boundary layer separation, flow dynamics in the separation zone, and laminar-turbulent transition are studied.

TKE-Based Moist Eddy-Diffusivity Mass-Flux (EDMF) Parameterization for Vertical Turbulent Mixing

A new turbulent kinetic energy (TKE)-based moist eddy-diffusivity mass-flux (EDMF) vertical turbulence mixing scheme (EDMF-TKE) is developed, where the nonlocal transport by large turbulent eddies is represented by a mass-flux (MF) scheme while the local transport by small turbulent eddies is represented by an eddy-diffusivity (ED) scheme, which is given by a function of a prognostic TKE. In the scheme, an MF approach is employed for the stratocumulus-top-driven downdrafts as well as for the thermals in the daytime unstable boundary layer. The scheme includes parameterizations for enhanced buoyancy due to moist adiabatic processes in condensation and for TKE interaction with cumulus convection. A scale-aware parameterization is proposed for the grid sizes where the large turbulent eddies are partially resolved. The single-column model (SCM) tests show that both the EDMF-TKE and the current operational NCEP GFS hybrid EDMF scheme (EDMF-CTL) simulate a daytime dry-convective boundary layer well and agree with a benchmark large-eddy simulation (LES). For a marine stratocumulus-topped boundary layer case, the EDMF-TKE better simulates the liquid water and wind speed profiles than the EDMF-CTL compared to the LES. For a stable boundary layer (SBL) case, the EDMF-TKE also agrees better with the LES than the EDMF-CTL, although it tends to produce a deeper SBL compared to the LES. On the other hand, three-dimensional medium-range forecast experiments show that the EDMF-TKE slightly improves forecast skill in the 500-hPa height anomaly correlation and wind vector, while it has a neutral impact on precipitation forecasts over the continental United States.

Mean flow generation by an intermittently unstable boundary layer over a sloping wall

Direct numerical simulations (DNS) of the flow in various rotating annular confinements have been conducted to investigate the effects of wall inclination on secondary fluid motions due to an unstable boundary layer. The inner wall resembles a truncated cone (frustum) whose apex half-angle is varied from $18^{\circ }$ to $0^{\circ }$ (straight cylinder). The large inner radius $r_{1}$, the mean rotation rate $\unicode[STIX]{x1D6FA}_{0}$ and the kinematic viscosity $\unicode[STIX]{x1D708}$ were kept constant resulting in the constant Ekman number $E=\unicode[STIX]{x1D708}/(\unicode[STIX]{x1D6FA}_{0}r_{1}^{2})=4\times 10^{-5}$. Flows were excited by time-harmonic modulation of the inner wall’s rotation rate (so-called longitudinal libration) by prescribing the amplitude $\unicode[STIX]{x1D700}\unicode[STIX]{x1D6FA}_{0}$ and the forcing frequency $\unicode[STIX]{x1D714}=\unicode[STIX]{x1D6FA}_{0}$. By steepening the inner wall and hence reducing the effect of the local Coriolis force in the boundary layer three different flow regimes can be realized: a rotation-dominated, a libration-dominated and an intermediate regime. In the present study we focus on the libration-dominated regime. For small libration amplitudes (here $\unicode[STIX]{x1D700}=0.2$), a laminar Ekman–Stokes boundary layer (ESBL) is realized at the librating wall. With the aid of laminar boundary layer theory and DNS we show that the ESBL exhibits an oscillatory mass flux along the librating wall (Ekman property) and an oscillatory azimuthal velocity, which resembles a radially damped wave (Stokes property). For large libration amplitudes (here $\unicode[STIX]{x1D700}=0.8$), the DNS results exhibit an intermittently unstable ESBL, which turns centrifugally unstable during the prograde (faster) part of a libration period. This instability is due to the Stokes property and gives rise to Görtler vortices, which are found to be tilted with respect to the azimuth when the librating wall is at a finite angle relative to the axis of rotation. We show that this tilt is related to the Ekman property of the ESBL. This suggests that linear and nonlinear dynamics are equally important for this intermittent instability. Our DNS results indicate further that the Görtler vortices propagate into the fluid bulk where they generate an azimuthal mean flow. This mean flow is notably different from the mean flow driven in the case of the stable ESBL. A diagnostic analysis of the Reynolds-averaged Navier–Stokes (RANS) equations in the unstable flow regime hints at a competition between the radial and axial turbulent transport terms which act as generating and destructing agents for the azimuthal mean flow, respectively. We show that the balance of both terms depends on the wall inclination, that is, on the wall-tangential component of the Coriolis force.

On the computation of planetary boundary layer height using the bulk Richardson number method

Experimental data from four intensive field campaigns are used to explore the variability of the critical bulk Richardson number, which is a key parameter for calculating the planetary boundary layer height (PBLH) in numerical weather and climate models with the bulk Richardson method. First, the PBLHs of three different thermally-stratified boundary layers (i.e., strongly stable boundary layer, weakly stable boundary layer, and unstable boundary layer) from the four field campaigns are determined using the turbulence method, the potential temperature gradient method, the low-level jet method, or the modified parcel method. Then for each type of boundary layer, an optimal critical Richardson numbers is obtained through linear fitting and statistical error minimization methods so that the bulk Richardson method with this optimal critical bulk Richardson number yields similar estimates of PBLHs as the methods mentioned above. We find that the optimal critical bulk Richardson number increases as the atmosphere becomes more unstable: 0.24 for strongly stable boundary layer, 0.31 for weakly stable boundary layer, and 0.39 for unstable boundary layer. Compared with previous schemes that use a single value of critical bulk Richardson number for calculating the PBLH, the new values of critical bulk Richardson number that proposed by this study yield more accurate estimate of PBLH.

Global stability of swept flow around a parabolic body: the neutral curve

The onset of transition in the leading-edge region of a swept blunt body depends crucially on the stability characteristics of the flow. Modelling this flow configuration by swept compressible flow around a parabolic body, a global approach is taken to extract pertinent stability information via a DNS-based iterative eigenvalue solver. Global modes combining features from boundary-layer and acoustic instabilities are presented. A parameter study, varying the spanwise disturbance wavenumber and the sweep Reynolds number, showed the existence of unstable boundary-layer and acoustic modes. The corresponding neutral curve displays two overlapping regions of exponential growth and two critical Reynolds numbers, one for boundary-layer instabilities and one for acoustic instabilities. The employed global approach establishes a first neutral curve, delineating stable from unstable parameter configurations, for the complex flow about a swept parabolic body with corresponding implications for swept leading-edge flow.

Global stability of swept flow around a parabolic body: features of the global spectrum

The global temporal stability of three-dimensional compressible flow about a yawed parabolic body of infinite span is investigated using an iterative eigenvalue technique in combination with direct numerical simulations. The computed global spectrum provides a comprehensive picture of the temporal perturbation dynamics of the flow, and a wide and rich variety of modes has been uncovered for the investigated parameter choices: stable and unstable boundary-layer modes, different types of stable and unstable acoustic modes, and stable wavepacket modes have been found. A parameter study varying the spanwise perturbation wavenumber and the sweep Reynolds number reproduced a preferred spanwise length scale and a critical Reynolds number for a boundary-layer or acoustic instability. Convex leading-edge curvature has been found to have a strongly stabilizing effect on boundary-layer modes but only a weakly stabilizing effect on acoustic modes. Furthermore, for certain parameter choices, the acoustic modes have been found to dominate the boundary-layer modes.