Introduction

The turbulent Channel Flow is one of the canonical flows used to study turbulence in wall bounded turbulence. DNS of turbulent channel flow were undertaken at $Re_{\tau }=180$ . DNS were undertaken using PyFR (http://www.pyfr.org/) version 1.12.0:

based on the high-order flux reconstruction method of Huynh
compressible solver
a Rusanov Riemann solver was employed to calculate the inter-element fluxes
an explicit RK45[2R+] scheme was used to advance the solution in time
Fifth order polynomials are used for the computations

Review of previous studies

Provide a brief review of related past studies, either experimental or computational. Identify the configuration chosen for the present study and position it with respect to previous studies. If the test case is geared on a certain experiment, explain what simplifications ( e.g. concern- ing geometry, boundary conditions) have been introduced with respect to the experiment in the computational setup to make the computations feasible and avoid uncertainty or ambiguity.

Description of the test case

An idealised channel flow, without side walls, is considered. The details of the case are given in Iyer et al.(2019). The current set of simulations has a higher grid resolution in the wall normal direction.

Geometry and flow parameters

The geometry is a cuboid of dimensions $8\pi$ units in the streamwise direction $(x)$ , 2 units in the transverse direction $(y)$ and $4\pi$ units in the spanwise direction $(z)$ . The dimensions are normalised by the channel half-width, $h$ and centreline velocity.

Boundary conditions

The domain is periodic in the streamwise and spanwise directions which gives a flow developing in time. The transverse boundaries are viscous walls with no-slip boundary conditions. The initial density and pressure fields are uniform. The initial velocity field is $(u,v,w)=\left(1-y^{2}/h^{2},0,0\right)$ . The solution is started at order 2 and progressively increased to order 5.