The Distribution of Short-term Wind Gusts and the Dissipation Regime of Turbulence on Mars with the SuperCam Microphone
Authors: Stott Alexander , Murdoch Naomi , Gillier Martin , Mimoun David , de la Torre Juarez Manuel , Rodriguez-Manfredi Jose Antonio , Maurice Sylvestre , Chide Baptiste , Lorenz Ralph 
Published: July 2024

Introduction:The winds are an important dynamic for Mars, changing the surface of the planet to this day. These wind flows are often turbulent, either convective during the day or more shear flows from topographically induced instabilities. This turbulent variation represents one of the fastest changing dynamics taking place on Mars. As a result, its full characterisation is of interest. Here, we will show the use of the microphone data collected by the Perseverance mission to inform on the highest frequencies of turbulence [1,2]. First, we will present the characteristics of wind speed time series inferred from the SuperCam microphone through a machine learning model developed in [3]. This highlights a range of gust timescales from 1-10s as well as both isolated gusts (perhaps due to intermittent turbulence) and also consistently gusty periods. Next, we demonstrate that the microphone spectra can be used to analyse the dissipative regime of turbulence on Mars. This is at the highest frequencies where the energy is removed through viscous forces. This provides an estimate of the Kolmogorov lengthscale and dissipation rate on Mars, as well as friction velocity, useful for model comparisons.The microphone signal:A dedicated campaign was performed on Mars to record background, ambient, winds with the microphone across different times of sol without the influence of acoustic sources from the rover. These recordings are each 167 s long and recorded at 25k samples per second [1]. This high sampling rate means that the microphone spectra cover the highest frequencies of turbulent fluctuations, at the dissipation regime where the energy is dissipated by viscous forces [2]. On Mars, dissipation is expected to occur at lower frequencies than on Earth. We use the microphone data to quantify the behaviour at the transition between the inertial and dissipative regime.In an outdoor environment, the dominant mechanism for generating wind noise on microphone data is through the stagnation pressure [4,5]. This is the pressure fluctuations induced by the microphone blocking a wind flow. This is in agreement with the observations by the SuperCam microphone on Mars [3]. The resulting sensitivity of the microphone data to the wind was used to extract estimates of wind speed at high frequencies [3]. Moreover, as demonstrated in microphone wind noise models [4,5], the pressure fluctuations recorded by the microphone are a transduction of turbulent wind variations, modified by a transfer function. As a result, the spectra of the microphone data from Mars can be interpreted in terms of the turbulence spectra of the wind in the surface layer of Mars.Winds and intermittent turbulence:In [3] we proposed a machine learning (Gaussian process regression) model to extract a wind speed estimate from the microphone data. These wind speeds were shown to be suitable to examine turbulent intensity, and shown gusting characteristics ranging from 1-10s. This highlights that the wind gust characteristics change. The behaviour of the gusting can be due to the intermittency of the turbulence, whether the wind flow has entered a regime of consistent turbulence or whether it is more sporadic [6]. Subsequently, the Perseverance rover has moved over a wider range of topography driving up to the rim of Jezero crater. The statistical assessment of the microphone data over this time can be used to aid the meteorological data studies from the dedicated MEDA (Mars environmental dynamics analyser) pressure and temperature sensors onboard Perseverance.Figure 1: (Left) Transfer function corrrected spectrum for a microphone recording on Mars. (Right top) Sound pressure level from microphone recording. (Right bottom) wind speed estimate from microphone recording using method in [3].Turbulent spectra: Spectra of wind flows are commonly used to describe turbulent behaviour. Energy is injected at large scales in the source region before cascading to smaller scale eddies in the inertial regime. Classically this inertial regime is characterized by the Kolmogorov power law of -5/3. However, this requires the measurement in an isotropic flow and and so is difficult to identify in measurements, which are a superposition of several effects [7]. Figure 1 shows an example of a spectrum for a microphone recording during a period of consistent gusting, along with the wind speed estimate from [3]. The spectrum in Figure 1 shows a curve between two regions, which we interpret to be the transition between the inertial and dissipative regime on Mars. Calculating the corner frequency of this curve yields an estimate of the Kolmogorov lengthscale, &#951;, which is 0.014 m for this recording. This lengthscale is calculated for recordings over the mission with good SNR, leading to values &#951;= 0.005-0.05 m, which are close to those expected [8].&#160; This estimate can be used to calculate values of the dissipation rate and friction velocity, without applying assumptions based on extrapolations from Earth. As such, this can be a useful tool for model parameterization.ConclusionWe present an analysis of Martian wind flows from microphone recordings by the SuperCam instrument on the Perseverance rover. As the microphone records at a high frequency (for atmospheric instruments so far operating on Mars) we use it to characterise the turbulent properties of the wind flow. This leads to information on the distribution of gusts and their intermittency, as well as the observation of turbulent energy dissipation on Mars. The microphone can also examine turbulence through the propagation of sound, as in [9,10]. Combining these results along with those from the dedicated weather station of MEDA at larger scales can help provide a detailed picture of turbulent behaviour on Mars and its relationship with dust and topography over seasons.&#160;References&#160;[1] Mimoun et al. (2023), SSR[2] Maurice et al. (2022), Nature[3] Stott et al. (2023), JGR:Planets[4] Raspet et al. (2006), JASA[5] Van den Berg et al. (2006), JASA[6] Allouche et al. (2021), Journal of the atmospheric sciences[7] Murdoch et al. (2023), PSJ[8] Petrosyan et al. (2011), Review of Geophysics[9] Chide et al, (2024) JASA[10] Gillier et al. (2024) JGR: Planets