Quasi-Steady Katabatic Winds on Slopes in Wide Valleys: Hydraulic Theory and Observations

Abstract

Theoretical and field observational studies on mean velocity and temperature fields of quasi-steady nocturnal downslope (katabatic) flows on sloping surfaces are reported for the case of very wide valleys in the presence of weak synoptic winds. Because of the lateral constraints on the flow, Coriolis effects are considered negligible. The layer-averaged equations of Manins and Sawford were used for the analysis. It is shown that (i) in the absence of significant turbulent entrainment into the current (i.e., at large Richardson numbers Ri ϭ ⌬h cos␣ /U 2 ) the downslope flow velocity U is related to the slope length (L H ), slope angle (␣), and the buoyancy jump between the current and the background atmosphere (⌬) as U ϭ u (⌬L H sin␣) 1/2 , where u is a constant and h is the flow depth; (ii) on very long slopes h is proportional to L h (tan␣) 1/2 ; and (iii) under highly stable conditions (i.e., Ri Ͼ 1) the katabatic flow exhibits pulsations with period T 0 ϭ 2/N sin␣, where N is the buoyancy frequency of the background atmosphere. These predictions are verified principally using observations made during the Vertical Transport and Mixing Experiment (VTMX) conducted in Salt Lake City, Utah, in October 2000. By assuming the flow follows a straight line trajectory to the nearest ridgeline a good agreement was found between the predictions and observations over appropriate Richardson number ranges. For Ri Ͼ 1.5, u Ϸ 0.2, although u was a decreasing function of Ri at lesser stabilities. Oscillations with period T 0 are simply alongslope (critical) internal-wave oscillations with a slope-normal wavenumber, which are liable for degeneration into turbulence during their reflection. These critical internal waves may be responsible, at least partly, for weak sustained turbulence often observed in complex-terrain nocturnal boundary layer flows.

Mixing efficiency in natural flows

“…The flow was usually weakly stable at the beginning of the night (Ri < 0.1 in this case). At about midnight (figure 2), a local maximum of Ri ≈ 2 was observed owing to a sharp drop of shear and a continuous increase in dT/dz, wherein the flow was dominated by quasi-periodic internal-wave oscillations [44]. Oscillations with longer periods of approximately 2-3 h were also observed [35] that could be attributed to global intermittency associated with periods of intense turbulence production and enhance stability.…”

“…The data (wind velocity and sonic temperature) used in this study were obtained during the vertical transport and mixing experiment (VTMX) in Salt Lake City, Utah conducted from 30 September to 7 October 2000 (see Monti et al [43] and Princevac et al [44] for a general description of the experiment). A meteorological mast at a gentle (approx.…”

Turbulent Mechanical Energy Budget in Stably Stratified Baroclinic Flows over Sloping Terrain

“…The presence of the Brunt-Väisäla frequency and the restoring role of the buoyancy force may tempt us to associate the mechanism described above with pulsations occurring in katabatic winds (e.g., McNider 1982;Princevac et al 2008), gravity waves associated with slope winds (e.g., Chemel et al 2009) and intermittency of turbulence caused by breaking gravity waves (e.g., Staquet 2004). Apparently, these are separate mechanisms that may, but need not necessarily, coexist and affect one another, e.g., by driving changes of shear and stress.…”

Improving mixing length‐scale for stable boundary layers

“…This type of idealized flow reaches its steady state at a time-scale of the order of T ≈ 2π/{N sin(α)}, see e.g. Mahrt (1982), Grisogono (2003), Princevac et al (2008); of course, in reality other effects may disturb this period appreciably (e.g. de Wekker and Whiteman, 2006).…”

“…Hunt et al (1988), Tjernström (1993), Schumann and Gerz (1995), Grisogono and Enger (2004), Princevac et al (2008), etc. However, these studies remained unsure about the relative weight between buoyancy and shearing frequencies, N and |S| respectively, when dividing the local turbulence characteristic speed, u * LOC ≈ (T KE) 1/2 , where TKE is the turbulent kinetic energy, thus yielding the z-less mixing length-scale.…”