The amplitude of lee waves on the boundary‐layer inversion. (22nd December 2016) - Sachsperger, Johannes; Serafin, Stefano; Grubišić, Vanda; Stiperski, Ivana; Paci, Alexandre
Abstract : This study presents an analytical model for the amplitude of lee waves on the boundary‐layer inversion in two‐dimensional flow. Previous linear lee wave models, in which the amplitude depends on the power spectrum of topography, can be inaccurate if the amplitude is large. Our model incorporates nonlinear effects by assuming that lee waves originate at a region of transition between super‐ and subcritical flow (internal jump) downstream of topography. Energy flux convergence at this location is compensated by the radiation of laminar lee waves. The available energy is estimated using a hydraulic jump model and the resulting wave amplitude is determined from linear theory. According to this model, the amplitude of lee waves depends essentially on their wavelength and on the inversion height difference across the jump. The new amplitude model is verified against numerical simulations and water tank experiments. The agreement between the model and the numerical results is excellent, while the verification with water tank experiments reveals that the accuracy of the model is comparable to that of numerical simulations. Finally, we derive a nonlinearity parameter for interfacial lee waves and discuss the regime transition from lee waves to hydraulic jumps in terms of the Froude number and the non‐dimensional mountain and inversion heights. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This article has been contributed to by a US Government employee and her work is in the public domain in the USA. Abstract : The figure shows results from a laboratory experiment, with a superimposed curve indicating the lee‐wave displacement. Strong vertical motion and low‐level turbulence are often related to large‐amplitude gravity waves in the lee of a mountain. Predictions of the wave amplitude with linear theory are typically inaccurate. By analogy with the theory of free‐surface water waves, we develop a simple analytical nonlinear model of the lee‐wave amplitude. Model results compare well with hydraulic laboratory experiments and numerical simulations. They suggest that, beyond a critical wave amplitude, lee waves are overridden by an internal hydraulic jump.