Large eddy simulation of sea breeze and scaling of its horizontal extent

Sea breeze is horizontal circulation that is derived by differential heating between sea and land surface. A non-linear theory of horizontal convection shows that there exist three kinds of flow regimes, a gravity wave regime, a gravity current regime, and diffusion regime, each of which has a self-similar solution depending on strafication and elapsed time from the start of the differential heating. The theory assumed that the both spatially and temporally coefficients of turbulent mixing are both spatially and temporally constant. In the real atmosphere the coefficients of turbulent mixing vary on space and time. For example, large surface heat flux on lands causes temporal growth of convective mixed layers in which strong turbulent mixing occurs. Therefore, sea breeze is affected by the convective turbulence.

In this study, we examine the self-similar solution of the horizontal convection is deformed in realistic atmosphere in which spatially and temporally varying turbulence is considered. To this end, a large eddy simulation (LES) model that can reasonably reproduce the convective turbulence in the atmospheric boundary layer (Nakanishi 2000; Ito et al. 2010) is employed. The three-dimensional model uses a grid spacing of 100 m for both horizontal and vertical directions. The size of domain is 1229 km in the cross-shore (x-) direction, 5 km in the along-shore (y-) directions and 5 km in the vertical (z-) direction. The land where constant surface heat flux Q is imposed occupies the bottom center of the calculation domain (360 km < x < 840 km), while seas where no surface heat flux is imposed both ends of the bottom (0 < x < 360 km, 840 < x < 1229 km). The cyclic boundary condition is imposed at both lateral boundaries in the x- and y- directions. The calculation is started from a stably stratified atmosphere with a constant potential temperature gradient of 4 K/km.

Cross-circulations are initiated at both shorelines at x=360 km and 840 km, but we focus on a part of them. Its length and velocity scales grow with time. A convective mixed layer develops over the land in the meantime. After a short period from the initial stage, a sea-breeze front, which is characterized by stronger updrafts or noticeable horizontal temperature gradient, is found. As is reported in Antonelli and Rottuno (2007), convection pattern is cellular on the land-side of the front and roll-shaped on the sea-side, respectively. When Q is a constant, the self-similar solution (Mori and Niino, 2002) suggests that horizontal and vertical length scales of the cross-shore circulation grows with the 1.5 and 0.5 power of time in both gravity current and gravity wave regime, respectively, and with 0.5 and 0.5 power of time in diffusion regime, respectively. In the present simulation, the vertical length scale of the convective mixed layer over the land turns out to grow also with 0.5 power of time when Q is a constant. Thus, the self-similar solution might be realized even for a realistic atmosphere in which turbulence varies both in time and space. Horizontal scale of the cross-shore circulation is evaluated every 1 minute by the distance of the sea breeze front from the shoreline is detected by a sharp temperature gap. Simulated dependence of the horizontal scale on time shows that the sea breeze belongs to the diffusion regime until 1 hour from the initiation and thereafter to the gravity current regime. Advancing velocity of the gravity current depends on Q and initial strafication, which determine the temperature gap across the front and the vertical scale of the cross-shore circulation. The simulation results for various combinations of Q and initial strafication confirm that the development of the circulation is consistent with the gravity current regime. It has been argued that convective mixing would retard the advancement of the sea breeze front on land. We have not observed such an effect of turbulence in our LES over time integration of 12 hours. This suggests that the self-similar solution continues to be realized, although turbulence is developed in the convective mixed layer.

The cross-shore circulation is accompanied by little increase of the temperature over the sea, and no front is formed. Temperature profiles over the sea show horizontal scale of cross-shore circulation extends 3 times faster than that over the land. This suggests that a gravity wave regime is realized. Note that the development of the horizontal scale for both the gravity current regime and the gravity wave regime depends on the same power of time when Q is constant, although the proportional constant may be different.