By Cedrick Ansorge
This thesis offers a research of sturdy stratification and turbulence cave in within the planetary boundary layer, starting a brand new street during this box. it's the first paintings to check all regimes of stratified turbulence in a unified simulation framework with out a holiday within the paradigms for illustration of turbulence.
To date, advances in our figuring out and the parameterization of turbulence within the sturdy boundary layer were hampered through problems simulating the strongly stratified regime, and the research has essentially been according to box measurements. The content material offered the following alterations that paradigm via demonstrating the facility of direct numerical simulation to deal with this challenge, and via doing so that you can eliminate the uncertainty of turbulence versions from the research. using a stably stratified Ekman layer as a simplified actual version of the strong boundary layer, the 3 stratification regimes saw in nature— weakly, intermediately and strongly stratified—are reproduced, and the knowledge is accordingly used to reply to key, long-standing questions.
The major a part of the e-book is geared up in 3 sections, specifically a accomplished advent, numerics, and physics. The thesis ends with a transparent and concise end that distills particular implications for the examine of the sturdy boundary layer. This constitution emphasizes the actual effects, yet even as supplies relevance to the technical facets of numerical schemes and post-processing instruments. the choice of the suitable literature in the course of the creation, and its use alongside the paintings safely combines literature from learn groups: fluid dynamics, and boundary-layer meteorology.
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Extra info for Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer
1, and it quantifies the splitting error to be of first order. In a physical sense this means, the pressure term is utilized to enforce the physical constraint of incompressibility (Sect. 1). This is done through a projection of an intermediate momentum field—namely that where all the source and sink terms for momentum act but the pressure gradient force—onto an incompressible flow field that fulfills the boundary conditions. In the set of Eqs. 8c), the operator L occurs twice. Mathematically, this is correct since part of the linear tendency is integrated explicitly.
13d) where Pr = 1, as defined above, is used. Therefore, L + O contains information about the stability character in the near-wall region. Large L + O implies a small Ri G and hence turbulence can develop in the lower part of the SBL. In Ekman flow over a surface at fixed temperature, both L O and Ri G are not external parameters to the problem, but they are time-dependent measures describing the evolution of the system. For that reason Ri B is used as control parameter. Besides the strength of stratification, the profile of stratification imposed as the initial condition has a significant impact during the initial phase: the initial profile determines the duration of the initial transient.
E. maximize, its stability region and to allow for larger time steps. e. the level of parallelization required (cf. Chap. 4). Based on the available schemes, the decision on the numerical algorithm is detailed in Sect. 4. e. un+1 = f (un ). The simplest of such schemes is the explicit Euler-forward integration where un+1 = un + τ F(un ). 3) Explicit methods may have several sub-stages and involve several evaluations of F; they are generalized in the class of Runge–Kutta schemes. In general, a Runge– Kutta scheme requires enough memory to store the full fields of every sub-stage until the end of the evaluation.