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DNS database of boundary layer transitions at M=0.8 over heated, pseudo-adiabatic, and cooled walls
Originally uploaded on July 6, 2026

Copyright (c) Yuta Iwatani, Hiroyuki Asada, and Soshi Kawai. All Rights Reserved.
Contact: kawai@tohoku.ac.jp
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Original Paper:
  Iwatani, Y., Asada, H., and Kawai, S., 
  "Direct Numerical Simulation of Subharmonic Transition in Pseudo-Adiabatic, Heated and Cooled Boundary Layers at Mach Number 0.8,"
  International Journal of Heat and Fluid Flow, 116, 109896 (2025)
  https://doi.org/10.1016/j.ijheatfluidflow.2025.109896

Nomenclature:
	<>: Reynolds-averaged quantities
	{}: Favre-averaged quantities
	_w : wall quantities
	_inf : freestream quantities
	x,y,z : streamwise, wall-normal, spanwise direction.
	x0 : reference length
	X = (x-xd)/x0 : distrance from the disturbance slot at x=xd (see below for xd of each case)
	u,v,w : streamwise, wall-normal, spanwise compoenents of velocity vector
	r,p,T : density, pressure, temperature
	mu : dynamic viscosity given by Sutherland's law
	tau_w : wall shear stress

Parameters:
	Re_x0=10^5: reference Reynolds number based on the distance from leading edge(x0)
	M_inf = 0.8: free stream Mach number
	U_inf = M_inf*a_inf = 0.8 : freestream speed
	Pr = 0.72 : Prandtl number
	gamma = 1.4 : specific heat ratio

Wall Temperature Cases ${case}:
	- A10: Tw/Tr = 1.0 (pseudo-adiabatic)
	- H11: Tw/Tr = 1.1 (heated)
	- C09: Tw/Tr = 0.9 (cooled)
	where Tw (isothermal wall temperature), Tr:= 1+ 0.5(gamma-1)*sqrt(Pr)*M_inf^2 ~ 1.108 (recovery temperature for laminar boundary layer)

Streamwise location of disturbance slot (xd):
	- A10 : xd = 3.40x0
	- H11 : xd = 2.82x0
	- C09 : xd = 4.18x0

<Note>
	- Helper functions for loading the dataset are provided at the end of this file.

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Contents
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Streamwise evolution of boundary layer parameters
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## Boundary layer integral values
    - filename: BLintegralparams-${case}.dat
	- For Fig. 6
    - contents
    col 1. x/x0
    col 2. X
    col 3. 99% boundary layer thickness based generalized velocity, del99 (Fig.6(a))
    col 4. (compressible) displacement thickness , del^* (Fig.6(b))
    col 5. (compressible) momentum thickness , theta (Fig.6(c))
    col 6. (compressible) shape factor H:= del^*/theta (Fig.6(d))
    col 7. generalized velocity based shape factor	Hg:=del*_g/theta_g (Fig.6(d)) 

## Skin friction coef./ Stanton number (pseudo-adiabatic (A10) case is filled with zero)
    - filename: Cf-Ch-${case}.dat
	- For Fig. 7
    - contents
    col 1. x/x0	
    col 2. X
    col 3. Cf (skin friction coef.)
    col 4. Ch (Stanton number)

## y-maxima of the amplitudes of linear instability modes 
    - filename: modeamp-${case}.dat
	- For Fig.15
    - contents
    col 1. x/x0
    col 2. X
    col 3. y-maxima of the amp. of the Mack's first mode (TS), (h,k)=(1,0), where (h,k) denote the temporal and spanwise wavenumbers (see Eq.(24))
    col 4. y-maxima of the amp. of the oblique subharmonic mode (OS), (h,k)=(1/2,1)
    col 5. y-maxima of the amp. of the vortex streak mode (VS), (h,k)=(0,2)

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# Wall-normal profiles at fixed distance from the initial disturbance X
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- example julia function to read files with this format is provided below

## Wall normal profiles of <u>/Uinf, <T>/Tinf, <r>/rinf at X=1,2,...,11
	- filename: yprof-uTr-${case}.dat
	- For Fig. 3
	- contents
	row 1. label
	row 2. y/x_0
	row 3. <u>/Uinf  : Reynolds averaged streamwise velocity normalized by freestream value
	row 4. <T>/Tinf 
	row 5. <r>/rinf

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# Wall-normal profiles at fixed momentum-thickness-based Reynolds number
=========================================================================================================
- example Julia function to read files with this format is provided below
- contents of every file
	row 1: label (Re_theta)
	row 2: y/x_0
	row 3: y^* (For definition of y^*, see Eq.(20))
	row 4: quantities

## Semi-local scaled streamwise velocity u^* (Fig. 9)
	- filename: ustar-ystar-${case}.dat

## Reynolds shear stress normalized by wall friction -<r>{u''v''}/<tau_w> (Fig. 9)
	- filename: RSS_tauw-${case}.dat

## Reynolds averaged temperature normalized by freestream temperature <T>/Tinf (Fig. 10) 
	- filename: T-${case}.dat

## Turbulent heat flux <r>{v''T''}/(rinf*Uinf*Tinf) (Fig. 10) 
	- filename: RVT-${case}.dat

## Temperature fluctuation sqrt(<T'T'>)/Tinf (Fig. 10)
	- filename: Trms-${case}.dat

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# Binary data of (time- and spanwise-averaged) 2D Flow statics in 2D x-y cross-view plane (PLOT3D format)
	- Example codes PLOT3D format provided at the bottom of this file.
    - Once reading the PLOT3D format file, we may get a 3D array, data(i,j,n).
    - (i,j) directions correspond to (streamwise, wall-normal) directions, respectively. 
    - The 3rd index 'n' corresponds to the variable.
	- All datasets include the domain of X in [0,12] and Y in [0, 0.22].
	- Grid size
		-- A10: (imax,jmax) = (7501,358)
		-- H11: (imax,jmax) = (9513,358)
		-- C09: (imax,jmax) = (11424,434)
=========================================================================================================
## Grid (normalized by x0)
    - filename:  grid-${case}.xy
	- Variables
	xy(i,j,1) :  x/x_0 (streamwise coordinate)
	xy(i,j,2) :  y/x_0 (wall-normal coordinate)

## Primitive variables (related to Figs. 8 and 13)
    - filename:  primitive-${case}.func 
	- Contours of the Reynolds averaged Reynolds stresses are similar to the Favre averaged ones
	- Variables
	data(i,j,1) : <r>/r_inf (Reynolds-averaged density normalized by freestream density)
	data(i,j,2) : <u>/u_inf (Reynolds-averaged streamwise velocity normalized by freestream velocity)
	data(i,j,3) : <v>/u_inf (Reynolds-averaged wall-normal velocity normalized by freestream velocity)
	data(i,j,4) : <w>/u_inf (Reynolds-averaged spanwise velocity normalized by freestream velocity)
	data(i,j,5) : <T>/T_inf (Reynolds-averaged temperature normalized by freestream temperature)
	data(i,j,6) : {u}/u_inf (Favre-averaged streamwise velocity normalized by freestream velocity)
	data(i,j,7) : {v}/u_inf (Favre-averaged wall-normal velocity normalized by freestream velocity)
	data(i,j,8) : {T}/T_inf (Favre-averaged temperature normalized by freestream temperature)

## Semi-local-scaled quantities (related to Figs. 9,10)
    - filename: semilocals-${case}.func
	- Variables
	data(i,j,1) : y^*
	data(i,j,2) : u^* (see Eq.(20)) 
	data(i,j,3) : Semi-local Reynolds number (Reynolds^*_tau=\sqrt(<r>/<r_w>)<mu_w>/<mu>Re_tau, Re_tau := <r_w><u_tau><d99>/<mu_w> ) (see between Eq.(20),(21))

## Reynolds normal stresses and shear stress normalized by tau_w (related to Fig. 9, 16)
	- filename: ReStress_tauw-${case}.func
	- Variables
	data(i,j,1) : sqrt(<r>{u''u''}/tau_w) (sqrt of Reynolds normal stress in the streamwise direction normalized by wall friction)
	data(i,j,2) : sqrt(<r>{v''v''}/tau_w) (sqrt of Reynolds normal stress in the wall-normal direction normalized by wall friction)
	data(i,j,3) : sqrt(<r>{w''w''}/tau_w) (sqrt of Reynolds normal stress in the spanwise direction normalized by wall friction)
	data(i,j,4) : -<r>{u''v''}/tau_w (Reynolds shear stress normalized by wall friction)

## Skewness (related to Figs. 18)
    - filename: skewness-${case}.func
	- Variables
	data(i,j,1) : {u''u''u''}/{u_inf^3} 	( streamwise components (numerator) )
	data(i,j,2) : {v''v''v''}/{u_inf^3} 	( wall-normal components (numerator) )
	data(i,j,3) : {u''u''}^{3/2}/{u_inf^3} 	( streamwise components (denominator) )
	data(i,j,4) :  {v''v''}^{3/2}/{u_inf^3} ( wall-normal components (denominator) )


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Helper functions for loading wall-normal profiles and 2D binary datasets.
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	example Julia script to read text data of wall-normal profiles
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"""
	load_data_as_blocks(filename, N_skip, N_batch, idx,idy)

	# Arguments
	- filename : name of file to read
	- N_skip: number of rows of header
	- N_batch : number of lines of each block (including label line)
	- idx: id of content for x axis (see explanation in the code below)
	- idy: id of content for y axis

	# example
	filename = "RSS_tauw-A10.dat" # Reynolds shear stress of pseudo-adiabatic case
	T =  load_data_as_blocks(filename,Nskips,Nblock,2,3);  # get 2nd and 3rd row quantities
	x = T.x; # 3rd line(row) is y^*
	y = T.y; # 4th line(row) is Reynolds shear stress
"""
function load_data_as_blocks(filename, N_skip, N_batch, idx,idy)
    blocks_data = []
    
    lines = collect(eachline(filename))
    content = lines[N_skip+1:end] # skip header 
    
    for block in Iterators.partition(content, N_batch)
		# if data is written as
		# row 1: label row
		# row 2: content 1
		# row 3: content 2
		# setting idx=1, idy=2 returns row1 and row2 vectors
        try
            x_vals = parse.(Float64, split(block[idx]))
            y_vals = parse.(Float64, split(block[idy]))
            push!(blocks_data, (x=x_vals, y=y_vals))
        catch e
            @warn "fail. Check N_skip and N_batch"
        end
    end
    return blocks_data
end

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Example functions for reading PLOT3D format files (C binary, little-endian, single precision)
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# Fortran example for grid data (.xy)
  read(iu) imax,jmax
  read(iu) (((x(i,j,k),i=1,imax),j=1,jmax))
  read(iu) (((y(i,j,k),i=1,imax),j=1,jmax))

# Fortran example for function data (.func)
  read(iu) imax,kmax,nfunc
  read(iu) (((data(i,j,n),i=1,imax),j=1,jmax),n=1,nfunc)